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21Z",[472,497],{"id":498,"d":499},"MJX-1-TEX-N-36","M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z",[472,501],{"id":502,"d":503},"MJX-1-TEX-N-3F","M226 668Q190 668 162 656T124 632L114 621Q116 621 119 620T130 616T145 607T157 591T162 567Q162 544 147 529T109 514T71 528T55 566Q55 625 100 661T199 704Q201 704 210 704T224 705H228Q281 705 320 692T378 656T407 612T416 567Q416 503 361 462Q267 395 247 303Q242 279 242 241V224Q242 205 239 202T222 198T205 201T202 218V249Q204 320 220 371T255 445T292 491T315 537Q317 546 317 574V587Q317 604 315 615T304 640T277 661T226 668ZM162 61Q162 89 180 105T224 121Q247 119 264 104T281 61Q281 31 264 16T222 1Q197 1 180 16T162 61Z",[505,506,510],"g",{"stroke":507,"fill":507,"stroke-width":508,"transform":509},"currentColor","0","scale(1,-1)",[505,511,513,538,546,563,570,583,588,601,606,611],{"dataMmlNode":512},"math",[505,514,516,524],{"dataMmlNode":515},"msup",[505,517,519],{"dataMmlNode":518},"mn",[520,521],"use",{"dataC":522,"xLinkHref":523},"32","#MJX-1-TEX-N-32",[505,525,529],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},"TeXAtom","translate(533,363) scale(0.707)","ORD",[505,530,531,535],{"dataMmlNode":518},[520,532],{"dataC":533,"xLinkHref":534},"31","#MJX-1-TEX-N-31",[520,536],{"dataC":522,"xLinkHref":523,"transform":537},"translate(500,0)",[505,539,542],{"dataMmlNode":540,"transform":541},"mo","translate(1512.3,0)",[520,543],{"dataC":544,"xLinkHref":545},"2B","#MJX-1-TEX-N-2B",[505,547,549,553],{"dataMmlNode":515,"transform":548},"translate(2512.6,0)",[505,550,551],{"dataMmlNode":518},[520,552],{"dataC":522,"xLinkHref":523},[505,554,555],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,556,557,559],{"dataMmlNode":518},[520,558],{"dataC":533,"xLinkHref":534},[520,560],{"dataC":561,"xLinkHref":562,"transform":537},"30","#MJX-1-TEX-N-30",[505,564,566],{"dataMmlNode":540,"transform":565},"translate(4024.9,0)",[520,567],{"dataC":568,"xLinkHref":569},"2212","#MJX-1-TEX-N-2212",[505,571,573,577],{"dataMmlNode":515,"transform":572},"translate(5025.1,0)",[505,574,575],{"dataMmlNode":518},[520,576],{"dataC":522,"xLinkHref":523},[505,578,579],{"dataMmlNode":518,"transform":527},[520,580],{"dataC":581,"xLinkHref":582},"38","#MJX-1-TEX-N-38",[505,584,586],{"dataMmlNode":540,"transform":585},"translate(6183.9,0)",[520,587],{"dataC":568,"xLinkHref":569},[505,589,591,595],{"dataMmlNode":515,"transform":590},"translate(7184.1,0)",[505,592,593],{"dataMmlNode":518},[520,594],{"dataC":522,"xLinkHref":523},[505,596,597],{"dataMmlNode":518,"transform":527},[520,598],{"dataC":599,"xLinkHref":600},"36","#MJX-1-TEX-N-36",[505,602,604],{"dataMmlNode":540,"transform":603},"translate(8342.9,0)",[520,605],{"dataC":544,"xLinkHref":545},[505,607,609],{"dataMmlNode":518,"transform":608},"translate(9343.1,0)",[520,610],{"dataC":599,"xLinkHref":600},[505,612,614],{"dataMmlNode":540,"transform":613},"translate(9843.1,0)",[520,615],{"dataC":616,"xLinkHref":617},"3F","#MJX-1-TEX-N-3F",[619,620,622],"h5",{"id":621},"решение","Решение:",[624,625,627],"h6",{"id":626},"решение-аналитическое","Решение аналитическое",[402,629,630],{},"Упростим решение, чтобы не выделять в исходном выражении какие-либо пары слагаемых, а оперировать только со значениями их показателей степеней и знаками сложения\u002Fвычитания.",[632,633,634,645],"ol",{},[635,636,637,638,641,642,644],"li",{},"Для степеней двойки операция сложения ",[418,639,640],{},"всегда"," добавляет 1. Будем также считать, что операция вычитания ",[418,643,640],{}," добавляет количество единиц, равное разности значений показателей степени данного вычитаемого и предыдущего слагаемого\u002Fвычитаемого, уменьшенной на 1. Исключение составляет последнее слагаемое, в котором количество единиц может быть просто подсчитано.",[635,646,647],{},"Составим таблицу, в которой будем согласно вышеуказанным правилам подсчитывать, сколько единиц добавляет каждое слагаемое или вычитаемое:",[649,650,651,667],"table",{},[652,653,654],"thead",{},[655,656,657,661,664],"tr",{},[658,659,660],"th",{},"Слагаемые",[658,662,663],{},"Степени и знаки",[658,665,666],{},"Добавляется единиц",[668,669,670,718,775,824,871],"tbody",{},[655,671,672,712,715],{},[673,674,675],"td",{},[452,676,678],{"className":677,"jax":456},[455],[458,679,684,692],{"style":680,"xmlns":461,"width":681,"height":682,"role":464,"focusable":465,"viewBox":683,"xmlnsXLink":467},"vertical-align: 0;","2.919ex","1.887ex","0 -833.9 1290.1 833.9",[469,685,686,689],{},[472,687],{"id":688,"d":475},"MJX-2-TEX-N-32",[472,690],{"id":691,"d":479},"MJX-2-TEX-N-31",[505,693,694],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,695,696],{"dataMmlNode":512},[505,697,698,703],{"dataMmlNode":515},[505,699,700],{"dataMmlNode":518},[520,701],{"dataC":522,"xLinkHref":702},"#MJX-2-TEX-N-32",[505,704,705],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,706,707,710],{"dataMmlNode":518},[520,708],{"dataC":533,"xLinkHref":709},"#MJX-2-TEX-N-31",[520,711],{"dataC":522,"xLinkHref":702,"transform":537},[673,713,714],{},"Степень = 12, знак \"+\"",[673,716,717],{},"1",[655,719,720,770,773],{},[673,721,722],{},[452,723,725],{"className":724,"jax":456},[455],[458,726,729,743],{"style":460,"xmlns":461,"width":727,"height":463,"role":464,"focusable":465,"viewBox":728,"xmlnsXLink":467},"4.679ex","0 -833.9 2068.1 915.9",[469,730,731,734,737,740],{},[472,732],{"id":733,"d":483},"MJX-3-TEX-N-2B",[472,735],{"id":736,"d":475},"MJX-3-TEX-N-32",[472,738],{"id":739,"d":479},"MJX-3-TEX-N-31",[472,741],{"id":742,"d":487},"MJX-3-TEX-N-30",[505,744,745],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,746,747,752],{"dataMmlNode":512},[505,748,749],{"dataMmlNode":540},[520,750],{"dataC":544,"xLinkHref":751},"#MJX-3-TEX-N-2B",[505,753,755,760],{"dataMmlNode":515,"transform":754},"translate(778,0)",[505,756,757],{"dataMmlNode":518},[520,758],{"dataC":522,"xLinkHref":759},"#MJX-3-TEX-N-32",[505,761,762],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,763,764,767],{"dataMmlNode":518},[520,765],{"dataC":533,"xLinkHref":766},"#MJX-3-TEX-N-31",[520,768],{"dataC":561,"xLinkHref":769,"transform":537},"#MJX-3-TEX-N-30",[673,771,772],{},"Степень = 10, знак \"+\"",[673,774,717],{},[655,776,777,818,821],{},[673,778,779],{},[452,780,782],{"className":781,"jax":456},[455],[458,783,786,797],{"style":460,"xmlns":461,"width":784,"height":463,"role":464,"focusable":465,"viewBox":785,"xmlnsXLink":467},"3.879ex","0 -833.9 1714.6 915.9",[469,787,788,791,794],{},[472,789],{"id":790,"d":491},"MJX-4-TEX-N-2212",[472,792],{"id":793,"d":475},"MJX-4-TEX-N-32",[472,795],{"id":796,"d":495},"MJX-4-TEX-N-38",[505,798,799],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,800,801,806],{"dataMmlNode":512},[505,802,803],{"dataMmlNode":540},[520,804],{"dataC":568,"xLinkHref":805},"#MJX-4-TEX-N-2212",[505,807,808,813],{"dataMmlNode":515,"transform":754},[505,809,810],{"dataMmlNode":518},[520,811],{"dataC":522,"xLinkHref":812},"#MJX-4-TEX-N-32",[505,814,815],{"dataMmlNode":518,"transform":527},[520,816],{"dataC":581,"xLinkHref":817},"#MJX-4-TEX-N-38",[673,819,820],{},"Степень = 8, знак \"-\"",[673,822,823],{},"(10-8)-1=1",[655,825,826,865,868],{},[673,827,828],{},[452,829,831],{"className":830,"jax":456},[455],[458,832,833,844],{"style":460,"xmlns":461,"width":784,"height":463,"role":464,"focusable":465,"viewBox":785,"xmlnsXLink":467},[469,834,835,838,841],{},[472,836],{"id":837,"d":491},"MJX-5-TEX-N-2212",[472,839],{"id":840,"d":475},"MJX-5-TEX-N-32",[472,842],{"id":843,"d":499},"MJX-5-TEX-N-36",[505,845,846],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,847,848,853],{"dataMmlNode":512},[505,849,850],{"dataMmlNode":540},[520,851],{"dataC":568,"xLinkHref":852},"#MJX-5-TEX-N-2212",[505,854,855,860],{"dataMmlNode":515,"transform":754},[505,856,857],{"dataMmlNode":518},[520,858],{"dataC":522,"xLinkHref":859},"#MJX-5-TEX-N-32",[505,861,862],{"dataMmlNode":518,"transform":527},[520,863],{"dataC":599,"xLinkHref":864},"#MJX-5-TEX-N-36",[673,866,867],{},"Степень = 6, знак \"-\"",[673,869,870],{},"(8-6)-1=1",[655,872,873,876,879],{},[673,874,875],{},"+ 6",[673,877,878],{},"Знак \"+\"",[673,880,881],{},"2",[632,883,885,888],{"start":884},3,[635,886,887],{},"Суммируем количества добавляемых единиц, указанные в последнем столбце таблицы: 1+1+1+1+2=6.",[635,889,890],{},"Количество значащих нулей подсчитывается точно так же, как в первом столбце, зная, что всё число содержит 13 разрядов: 13 - 6 = 7.",[402,892,893],{},[406,894,895],{},"Ответ: 6 единиц, 7 нулей.",[444,897,899],{"id":898},"задача-2","Задача 2",[402,901,902,903],{},"Сколько единиц и сколько значащих нулей содержится в двоичной записи числа:\n",[452,904,906],{"className":905,"jax":456},[455],[458,907,911,939],{"style":460,"xmlns":461,"width":908,"height":909,"role":464,"focusable":465,"viewBox":910,"xmlnsXLink":467},"27.446ex","2.09ex","0 -841.7 12131 923.7",[469,912,913,916,919,923,927,930,933,936],{},[472,914],{"id":915,"d":495},"MJX-6-TEX-N-38",[472,917],{"id":918,"d":479},"MJX-6-TEX-N-31",[472,920],{"id":921,"d":922},"MJX-6-TEX-N-33","M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z",[472,924],{"id":925,"d":926},"MJX-6-TEX-N-34","M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 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слагаемое переведём в двоичную систему счисления: 1344 = 10101000000 и представим его как сумму степеней двоек: ",[452,1492,1494],{"className":1493,"jax":456},[455],[458,1495,1498,1530],{"style":460,"xmlns":461,"width":1496,"height":463,"role":464,"focusable":465,"viewBox":1497,"xmlnsXLink":467},"20.859ex","0 -833.9 9219.7 915.9",[469,1499,1500,1503,1506,1509,1512,1515,1518,1521,1524,1527],{},[472,1501],{"id":1502,"d":479},"MJX-10-TEX-N-31",[472,1504],{"id":1505,"d":922},"MJX-10-TEX-N-33",[472,1507],{"id":1508,"d":926},"MJX-10-TEX-N-34",[472,1510],{"id":1511,"d":1086},"MJX-10-TEX-N-3D",[472,1513],{"id":1514,"d":475},"MJX-10-TEX-N-32",[472,1516],{"id":1517,"d":487},"MJX-10-TEX-N-30",[472,1519],{"id":1520,"d":483},"MJX-10-TEX-N-2B",[472,1522],{"id":1523,"d":495},"MJX-10-TEX-N-38",[472,1525],{"id":1526,"d":499},"MJX-10-TEX-N-36",[472,1528],{"id":1529,"d":1395},"MJX-10-TEX-N-2E",[505,1531,1532],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,1533,1534,1547,1553,1570,1576,1590,1595,1609],{"dataMmlNode":512},[505,1535,1536,1539,1542,1545],{"dataMmlNode":518},[520,1537],{"dataC":533,"xLinkHref":1538},"#MJX-10-TEX-N-31",[520,1540],{"dataC":959,"xLinkHref":1541,"transform":537},"#MJX-10-TEX-N-33",[520,1543],{"dataC":963,"xLinkHref":1544,"transform":965},"#MJX-10-TEX-N-34",[520,1546],{"dataC":963,"xLinkHref":1544,"transform":968},[505,1548,1550],{"dataMmlNode":540,"transform":1549},"translate(2277.8,0)",[520,1551],{"dataC":1179,"xLinkHref":1552},"#MJX-10-TEX-N-3D",[505,1554,1556,1561],{"dataMmlNode":515,"transform":1555},"translate(3333.6,0)",[505,1557,1558],{"dataMmlNode":518},[520,1559],{"dataC":522,"xLinkHref":1560},"#MJX-10-TEX-N-32",[505,1562,1563],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,1564,1565,1567],{"dataMmlNode":518},[520,1566],{"dataC":533,"xLinkHref":1538},[520,1568],{"dataC":561,"xLinkHref":1569,"transform":537},"#MJX-10-TEX-N-30",[505,1571,1573],{"dataMmlNode":540,"transform":1572},"translate(4845.9,0)",[520,1574],{"dataC":544,"xLinkHref":1575},"#MJX-10-TEX-N-2B",[505,1577,1579,1583],{"dataMmlNode":515,"transform":1578},"translate(5846.1,0)",[505,1580,1581],{"dataMmlNode":518},[520,1582],{"dataC":522,"xLinkHref":1560},[505,1584,1585],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,1586,1587],{"dataMmlNode":518},[520,1588],{"dataC":581,"xLinkHref":1589},"#MJX-10-TEX-N-38",[505,1591,1593],{"dataMmlNode":540,"transform":1592},"translate(7004.9,0)",[520,1594],{"dataC":544,"xLinkHref":1575},[505,1596,1598,1602],{"dataMmlNode":515,"transform":1597},"translate(8005.1,0)",[505,1599,1600],{"dataMmlNode":518},[520,1601],{"dataC":522,"xLinkHref":1560},[505,1603,1604],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,1605,1606],{"dataMmlNode":518},[520,1607],{"dataC":599,"xLinkHref":1608},"#MJX-10-TEX-N-36",[505,1610,1612],{"dataMmlNode":540,"transform":1611},"translate(8941.7,0)",[520,1613],{"dataC":1487,"xLinkHref":1614},"#MJX-10-TEX-N-2E"," Перепишем исходное выражение: ",[452,1617,1619],{"className":1618,"jax":456},[455],[458,1620,1623,1655],{"style":460,"xmlns":461,"width":1621,"height":909,"role":464,"focusable":465,"viewBox":1622,"xmlnsXLink":467},"35.17ex","0 -841.7 15545.1 923.7",[469,1624,1625,1628,1631,1634,1637,1640,1643,1646,1649,1652],{},[472,1626],{"id":1627,"d":475},"MJX-11-TEX-N-32",[472,1629],{"id":1630,"d":926},"MJX-11-TEX-N-34",[472,1632],{"id":1633,"d":487},"MJX-11-TEX-N-30",[472,1635],{"id":1636,"d":922},"MJX-11-TEX-N-33",[472,1638],{"id":1639,"d":491},"MJX-11-TEX-N-2212",[472,1641],{"id":1642,"d":499},"MJX-11-TEX-N-36",[472,1644],{"id":1645,"d":495},"MJX-11-TEX-N-38",[472,1647],{"id":1648,"d":483},"MJX-11-TEX-N-2B",[472,1650],{"id":1651,"d":479},"MJX-11-TEX-N-31",[472,1653],{"id":1654,"d":1395},"MJX-11-TEX-N-2E",[505,1656,1657],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,1658,1659,1681,1686,1706,1711,1730,1734,1748,1753,1764,1769,1780],{"dataMmlNode":512},[505,1660,1661,1666],{"dataMmlNode":515},[505,1662,1663],{"dataMmlNode":518},[520,1664],{"dataC":522,"xLinkHref":1665},"#MJX-11-TEX-N-32",[505,1667,1668],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,1669,1670,1673,1676,1678],{"dataMmlNode":518},[520,1671],{"dataC":963,"xLinkHref":1672},"#MJX-11-TEX-N-34",[520,1674],{"dataC":561,"xLinkHref":1675,"transform":537},"#MJX-11-TEX-N-30",[520,1677],{"dataC":522,"xLinkHref":1665,"transform":965},[520,1679],{"dataC":959,"xLinkHref":1680,"transform":968},"#MJX-11-TEX-N-33",[505,1682,1683],{"dataMmlNode":540,"transform":971},[520,1684],{"dataC":568,"xLinkHref":1685},"#MJX-11-TEX-N-2212",[505,1687,1688,1692],{"dataMmlNode":515,"transform":977},[505,1689,1690],{"dataMmlNode":518},[520,1691],{"dataC":522,"xLinkHref":1665},[505,1693,1694],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,1695,1696,1698,1701,1704],{"dataMmlNode":518},[520,1697],{"dataC":522,"xLinkHref":1665},[520,1699],{"dataC":599,"xLinkHref":1700,"transform":537},"#MJX-11-TEX-N-36",[520,1702],{"dataC":581,"xLinkHref":1703,"transform":965},"#MJX-11-TEX-N-38",[520,1705],{"dataC":963,"xLinkHref":1672,"transform":968},[505,1707,1708],{"dataMmlNode":540,"transform":997},[520,1709],{"dataC":544,"xLinkHref":1710},"#MJX-11-TEX-N-2B",[505,1712,1713,1717],{"dataMmlNode":515,"transform":1003},[505,1714,1715],{"dataMmlNode":518},[520,1716],{"dataC":522,"xLinkHref":1665},[505,1718,1719],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,1720,1721,1724,1726,1728],{"dataMmlNode":518},[520,1722],{"dataC":533,"xLinkHref":1723},"#MJX-11-TEX-N-31",[520,1725],{"dataC":959,"xLinkHref":1680,"transform":537},[520,1727],{"dataC":963,"xLinkHref":1672,"transform":965},[520,1729],{"dataC":522,"xLinkHref":1665,"transform":968},[505,1731,1732],{"dataMmlNode":540,"transform":1022},[520,1733],{"dataC":568,"xLinkHref":1685},[505,1735,1736,1740],{"dataMmlNode":515,"transform":1027},[505,1737,1738],{"dataMmlNode":518},[520,1739],{"dataC":522,"xLinkHref":1665},[505,1741,1742],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,1743,1744,1746],{"dataMmlNode":518},[520,1745],{"dataC":533,"xLinkHref":1723},[520,1747],{"dataC":561,"xLinkHref":1675,"transform":537},[505,1749,1751],{"dataMmlNode":540,"transform":1750},"translate(11171.3,0)",[520,1752],{"dataC":568,"xLinkHref":1685},[505,1754,1756,1760],{"dataMmlNode":515,"transform":1755},"translate(12171.5,0)",[505,1757,1758],{"dataMmlNode":518},[520,1759],{"dataC":522,"xLinkHref":1665},[505,1761,1762],{"dataMmlNode":518,"transform":527},[520,1763],{"dataC":581,"xLinkHref":1703},[505,1765,1767],{"dataMmlNode":540,"transform":1766},"translate(13330.3,0)",[520,1768],{"dataC":568,"xLinkHref":1685},[505,1770,1772,1776],{"dataMmlNode":515,"transform":1771},"translate(14330.5,0)",[505,1773,1774],{"dataMmlNode":518},[520,1775],{"dataC":522,"xLinkHref":1665},[505,1777,1778],{"dataMmlNode":518,"transform":527},[520,1779],{"dataC":599,"xLinkHref":1700},[505,1781,1783],{"dataMmlNode":540,"transform":1782},"translate(15267.1,0)",[520,1784],{"dataC":1487,"xLinkHref":1785},"#MJX-11-TEX-N-2E",[635,1787,1788],{},"Составим таблицу:",[649,1790,1791,1804],{},[652,1792,1793],{},[655,1794,1795,1797,1799,1801],{},[658,1796,660],{},[658,1798,663],{},[658,1800,666],{},[658,1802,1803],{},"Единиц в числе",[668,1805,1806,1865,1933,1998,2056,2104],{},[655,1807,1808,1858,1861,1863],{},[673,1809,1810],{},[452,1811,1813],{"className":1812,"jax":456},[455],[458,1814,1818,1832],{"style":680,"xmlns":461,"width":1815,"height":1816,"role":464,"focusable":465,"viewBox":1817,"xmlnsXLink":467},"4.519ex","1.904ex","0 -841.7 1997.2 841.7",[469,1819,1820,1823,1826,1829],{},[472,1821],{"id":1822,"d":475},"MJX-12-TEX-N-32",[472,1824],{"id":1825,"d":926},"MJX-12-TEX-N-34",[472,1827],{"id":1828,"d":487},"MJX-12-TEX-N-30",[472,1830],{"id":1831,"d":922},"MJX-12-TEX-N-33",[505,1833,1834],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,1835,1836],{"dataMmlNode":512},[505,1837,1838,1843],{"dataMmlNode":515},[505,1839,1840],{"dataMmlNode":518},[520,1841],{"dataC":522,"xLinkHref":1842},"#MJX-12-TEX-N-32",[505,1844,1845],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,1846,1847,1850,1853,1855],{"dataMmlNode":518},[520,1848],{"dataC":963,"xLinkHref":1849},"#MJX-12-TEX-N-34",[520,1851],{"dataC":561,"xLinkHref":1852,"transform":537},"#MJX-12-TEX-N-30",[520,1854],{"dataC":522,"xLinkHref":1842,"transform":965},[520,1856],{"dataC":959,"xLinkHref":1857,"transform":968},"#MJX-12-TEX-N-33",[673,1859,1860],{},"Степень = 4023, знак \"+\"",[673,1862,717],{},[673,1864,717],{},[655,1866,1867,1924,1927,1930],{},[673,1868,1869],{},[452,1870,1872],{"className":1871,"jax":456},[455],[458,1873,1876,1893],{"style":460,"xmlns":461,"width":1874,"height":909,"role":464,"focusable":465,"viewBox":1875,"xmlnsXLink":467},"6.279ex","0 -841.7 2775.2 923.7",[469,1877,1878,1881,1884,1887,1890],{},[472,1879],{"id":1880,"d":491},"MJX-13-TEX-N-2212",[472,1882],{"id":1883,"d":475},"MJX-13-TEX-N-32",[472,1885],{"id":1886,"d":499},"MJX-13-TEX-N-36",[472,1888],{"id":1889,"d":495},"MJX-13-TEX-N-38",[472,1891],{"id":1892,"d":926},"MJX-13-TEX-N-34",[505,1894,1895],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,1896,1897,1902],{"dataMmlNode":512},[505,1898,1899],{"dataMmlNode":540},[520,1900],{"dataC":568,"xLinkHref":1901},"#MJX-13-TEX-N-2212",[505,1903,1904,1909],{"dataMmlNode":515,"transform":754},[505,1905,1906],{"dataMmlNode":518},[520,1907],{"dataC":522,"xLinkHref":1908},"#MJX-13-TEX-N-32",[505,1910,1911],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,1912,1913,1915,1918,1921],{"dataMmlNode":518},[520,1914],{"dataC":522,"xLinkHref":1908},[520,1916],{"dataC":599,"xLinkHref":1917,"transform":537},"#MJX-13-TEX-N-36",[520,1919],{"dataC":581,"xLinkHref":1920,"transform":965},"#MJX-13-TEX-N-38",[520,1922],{"dataC":963,"xLinkHref":1923,"transform":968},"#MJX-13-TEX-N-34",[673,1925,1926],{},"Степень = 2684, знак \"-\"",[673,1928,1929],{},"(4023-2684)-1=1338",[673,1931,1932],{},"1338",[655,1934,1935,1990,1993,1995],{},[673,1936,1937],{},[452,1938,1940],{"className":1939,"jax":456},[455],[458,1941,1942,1959],{"style":460,"xmlns":461,"width":1874,"height":909,"role":464,"focusable":465,"viewBox":1875,"xmlnsXLink":467},[469,1943,1944,1947,1950,1953,1956],{},[472,1945],{"id":1946,"d":483},"MJX-14-TEX-N-2B",[472,1948],{"id":1949,"d":475},"MJX-14-TEX-N-32",[472,1951],{"id":1952,"d":479},"MJX-14-TEX-N-31",[472,1954],{"id":1955,"d":922},"MJX-14-TEX-N-33",[472,1957],{"id":1958,"d":926},"MJX-14-TEX-N-34",[505,1960,1961],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,1962,1963,1968],{"dataMmlNode":512},[505,1964,1965],{"dataMmlNode":540},[520,1966],{"dataC":544,"xLinkHref":1967},"#MJX-14-TEX-N-2B",[505,1969,1970,1975],{"dataMmlNode":515,"transform":754},[505,1971,1972],{"dataMmlNode":518},[520,1973],{"dataC":522,"xLinkHref":1974},"#MJX-14-TEX-N-32",[505,1976,1977],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,1978,1979,1982,1985,1988],{"dataMmlNode":518},[520,1980],{"dataC":533,"xLinkHref":1981},"#MJX-14-TEX-N-31",[520,1983],{"dataC":959,"xLinkHref":1984,"transform":537},"#MJX-14-TEX-N-33",[520,1986],{"dataC":963,"xLinkHref":1987,"transform":965},"#MJX-14-TEX-N-34",[520,1989],{"dataC":959,"xLinkHref":1984,"transform":968},[673,1991,1992],{},"Степень = 1343, знак \"+\"",[673,1994,717],{},[673,1996,1997],{},"1339",[655,1999,2000,2047,2050,2053],{},[673,2001,2002],{},[452,2003,2005],{"className":2004,"jax":456},[455],[458,2006,2007,2021],{"style":460,"xmlns":461,"width":727,"height":463,"role":464,"focusable":465,"viewBox":728,"xmlnsXLink":467},[469,2008,2009,2012,2015,2018],{},[472,2010],{"id":2011,"d":491},"MJX-15-TEX-N-2212",[472,2013],{"id":2014,"d":475},"MJX-15-TEX-N-32",[472,2016],{"id":2017,"d":479},"MJX-15-TEX-N-31",[472,2019],{"id":2020,"d":487},"MJX-15-TEX-N-30",[505,2022,2023],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,2024,2025,2030],{"dataMmlNode":512},[505,2026,2027],{"dataMmlNode":540},[520,2028],{"dataC":568,"xLinkHref":2029},"#MJX-15-TEX-N-2212",[505,2031,2032,2037],{"dataMmlNode":515,"transform":754},[505,2033,2034],{"dataMmlNode":518},[520,2035],{"dataC":522,"xLinkHref":2036},"#MJX-15-TEX-N-32",[505,2038,2039],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,2040,2041,2044],{"dataMmlNode":518},[520,2042],{"dataC":533,"xLinkHref":2043},"#MJX-15-TEX-N-31",[520,2045],{"dataC":561,"xLinkHref":2046,"transform":537},"#MJX-15-TEX-N-30",[673,2048,2049],{},"Степень = 10, знак \"-\"",[673,2051,2052],{},"(1343-10)-1=1332",[673,2054,2055],{},"2671",[655,2057,2058,2097,2099,2101],{},[673,2059,2060],{},[452,2061,2063],{"className":2062,"jax":456},[455],[458,2064,2065,2076],{"style":460,"xmlns":461,"width":784,"height":463,"role":464,"focusable":465,"viewBox":785,"xmlnsXLink":467},[469,2066,2067,2070,2073],{},[472,2068],{"id":2069,"d":491},"MJX-16-TEX-N-2212",[472,2071],{"id":2072,"d":475},"MJX-16-TEX-N-32",[472,2074],{"id":2075,"d":495},"MJX-16-TEX-N-38",[505,2077,2078],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,2079,2080,2085],{"dataMmlNode":512},[505,2081,2082],{"dataMmlNode":540},[520,2083],{"dataC":568,"xLinkHref":2084},"#MJX-16-TEX-N-2212",[505,2086,2087,2092],{"dataMmlNode":515,"transform":754},[505,2088,2089],{"dataMmlNode":518},[520,2090],{"dataC":522,"xLinkHref":2091},"#MJX-16-TEX-N-32",[505,2093,2094],{"dataMmlNode":518,"transform":527},[520,2095],{"dataC":581,"xLinkHref":2096},"#MJX-16-TEX-N-38",[673,2098,820],{},[673,2100,823],{},[673,2102,2103],{},"2672",[655,2105,2106,2145,2147,2149],{},[673,2107,2108],{},[452,2109,2111],{"className":2110,"jax":456},[455],[458,2112,2113,2124],{"style":460,"xmlns":461,"width":784,"height":463,"role":464,"focusable":465,"viewBox":785,"xmlnsXLink":467},[469,2114,2115,2118,2121],{},[472,2116],{"id":2117,"d":491},"MJX-17-TEX-N-2212",[472,2119],{"id":2120,"d":475},"MJX-17-TEX-N-32",[472,2122],{"id":2123,"d":499},"MJX-17-TEX-N-36",[505,2125,2126],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,2127,2128,2133],{"dataMmlNode":512},[505,2129,2130],{"dataMmlNode":540},[520,2131],{"dataC":568,"xLinkHref":2132},"#MJX-17-TEX-N-2212",[505,2134,2135,2140],{"dataMmlNode":515,"transform":754},[505,2136,2137],{"dataMmlNode":518},[520,2138],{"dataC":522,"xLinkHref":2139},"#MJX-17-TEX-N-32",[505,2141,2142],{"dataMmlNode":518,"transform":527},[520,2143],{"dataC":599,"xLinkHref":2144},"#MJX-17-TEX-N-36",[673,2146,867],{},[673,2148,870],{},[673,2150,2151],{},"2673",[402,2153,2154],{},"Получается, что в заданном числе 2673 единицы в двоичном представлении.",[632,2156,2157],{"start":884},[635,2158,2159],{},"Вычисляем количество нулей. Количество разрядов в числе равно значению наибольшего показателя степени (4023), увеличенному на 1 (нулевой разряд). Следовательно, число имеет 4024 разряда.\nТогда, если в нём 2673 единицы, то количество нулей равно: 4024 - 2673 = 1353.",[402,2161,2162],{},[406,2163,2164],{},"Ответ: 2673 единицы, 1353 нуля.",[444,2166,2168],{"id":2167},"задача-3","Задача 3",[402,2170,2171,2172],{},"Сколько единиц в двоичной записи числа: ",[452,2173,2175],{"className":2174,"jax":456},[455],[458,2176,2179,2212],{"style":460,"xmlns":461,"width":2177,"height":463,"role":464,"focusable":465,"viewBox":2178,"xmlnsXLink":467},"22.452ex","0 -833.9 9923.9 915.9",[469,2180,2181,2184,2187,2190,2193,2196,2200,2203,2206,2209],{},[472,2182],{"id":2183,"d":495},"MJX-18-TEX-N-38",[472,2185],{"id":2186,"d":479},"MJX-18-TEX-N-31",[472,2188],{"id":2189,"d":487},"MJX-18-TEX-N-30",[472,2191],{"id":2192,"d":483},"MJX-18-TEX-N-2B",[472,2194],{"id":2195,"d":926},"MJX-18-TEX-N-34",[472,2197],{"id":2198,"d":2199},"MJX-18-TEX-N-35","M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z",[472,2201],{"id":2202,"d":491},"MJX-18-TEX-N-2212",[472,2204],{"id":2205,"d":475},"MJX-18-TEX-N-32",[472,2207],{"id":2208,"d":922},"MJX-18-TEX-N-33",[472,2210],{"id":2211,"d":503},"MJX-18-TEX-N-3F",[505,2213,2214],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,2215,2216,2237,2242,2261,2267,2285,2290,2296],{"dataMmlNode":512},[505,2217,2218,2223],{"dataMmlNode":515},[505,2219,2220],{"dataMmlNode":518},[520,2221],{"dataC":581,"xLinkHref":2222},"#MJX-18-TEX-N-38",[505,2224,2225],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,2226,2227,2230,2233,2235],{"dataMmlNode":518},[520,2228],{"dataC":533,"xLinkHref":2229},"#MJX-18-TEX-N-31",[520,2231],{"dataC":561,"xLinkHref":2232,"transform":537},"#MJX-18-TEX-N-30",[520,2234],{"dataC":561,"xLinkHref":2232,"transform":965},[520,2236],{"dataC":561,"xLinkHref":2232,"transform":968},[505,2238,2239],{"dataMmlNode":540,"transform":971},[520,2240],{"dataC":544,"xLinkHref":2241},"#MJX-18-TEX-N-2B",[505,2243,2244,2249],{"dataMmlNode":515,"transform":977},[505,2245,2246],{"dataMmlNode":518},[520,2247],{"dataC":963,"xLinkHref":2248},"#MJX-18-TEX-N-34",[505,2250,2251],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,2252,2253,2257,2259],{"dataMmlNode":518},[520,2254],{"dataC":2255,"xLinkHref":2256},"35","#MJX-18-TEX-N-35",[520,2258],{"dataC":561,"xLinkHref":2232,"transform":537},[520,2260],{"dataC":561,"xLinkHref":2232,"transform":965},[505,2262,2264],{"dataMmlNode":540,"transform":2263},"translate(5085.5,0)",[520,2265],{"dataC":568,"xLinkHref":2266},"#MJX-18-TEX-N-2212",[505,2268,2270,2275],{"dataMmlNode":515,"transform":2269},"translate(6085.8,0)",[505,2271,2272],{"dataMmlNode":518},[520,2273],{"dataC":522,"xLinkHref":2274},"#MJX-18-TEX-N-32",[505,2276,2277],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,2278,2279,2281,2283],{"dataMmlNode":518},[520,2280],{"dataC":522,"xLinkHref":2274},[520,2282],{"dataC":2255,"xLinkHref":2256,"transform":537},[520,2284],{"dataC":561,"xLinkHref":2232,"transform":965},[505,2286,2288],{"dataMmlNode":540,"transform":2287},"translate(7951.6,0)",[520,2289],{"dataC":544,"xLinkHref":2241},[505,2291,2293],{"dataMmlNode":518,"transform":2292},"translate(8951.9,0)",[520,2294],{"dataC":959,"xLinkHref":2295},"#MJX-18-TEX-N-33",[505,2297,2299],{"dataMmlNode":540,"transform":2298},"translate(9451.9,0)",[520,2300],{"dataC":616,"xLinkHref":2301},"#MJX-18-TEX-N-3F",[619,2303,622],{"id":2304},"решение-2",[624,2306,627],{"id":2307},"решение-аналитическое-2",[632,2309,2310,2430],{},[635,2311,2312,2313],{},"Все числа, кроме последнего, представим как степени двоек (учитывая, что 8 = 2 в кубе, а 4 = 2 в квадрате). Последнее число 3 оставляем без изменений - оно имеет знак \"плюс\" и, как легко определить, содержит две единицы. Получаем запись: ",[452,2314,2316],{"className":2315,"jax":456},[455],[458,2317,2320,2346],{"style":460,"xmlns":461,"width":2318,"height":463,"role":464,"focusable":465,"viewBox":2319,"xmlnsXLink":467},"22.813ex","0 -833.9 10083.4 915.9",[469,2321,2322,2325,2328,2331,2334,2337,2340,2343],{},[472,2323],{"id":2324,"d":475},"MJX-19-TEX-N-32",[472,2326],{"id":2327,"d":922},"MJX-19-TEX-N-33",[472,2329],{"id":2330,"d":487},"MJX-19-TEX-N-30",[472,2332],{"id":2333,"d":483},"MJX-19-TEX-N-2B",[472,2335],{"id":2336,"d":479},"MJX-19-TEX-N-31",[472,2338],{"id":2339,"d":491},"MJX-19-TEX-N-2212",[472,2341],{"id":2342,"d":2199},"MJX-19-TEX-N-35",[472,2344],{"id":2345,"d":1395},"MJX-19-TEX-N-2E",[505,2347,2348],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,2349,2350,2371,2376,2395,2400,2417,2422],{"dataMmlNode":512},[505,2351,2352,2357],{"dataMmlNode":515},[505,2353,2354],{"dataMmlNode":518},[520,2355],{"dataC":522,"xLinkHref":2356},"#MJX-19-TEX-N-32",[505,2358,2359],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,2360,2361,2364,2367,2369],{"dataMmlNode":518},[520,2362],{"dataC":959,"xLinkHref":2363},"#MJX-19-TEX-N-33",[520,2365],{"dataC":561,"xLinkHref":2366,"transform":537},"#MJX-19-TEX-N-30",[520,2368],{"dataC":561,"xLinkHref":2366,"transform":965},[520,2370],{"dataC":561,"xLinkHref":2366,"transform":968},[505,2372,2373],{"dataMmlNode":540,"transform":971},[520,2374],{"dataC":544,"xLinkHref":2375},"#MJX-19-TEX-N-2B",[505,2377,2378,2382],{"dataMmlNode":515,"transform":977},[505,2379,2380],{"dataMmlNode":518},[520,2381],{"dataC":522,"xLinkHref":2356},[505,2383,2384],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,2385,2386,2389,2391,2393],{"dataMmlNode":518},[520,2387],{"dataC":533,"xLinkHref":2388},"#MJX-19-TEX-N-31",[520,2390],{"dataC":561,"xLinkHref":2366,"transform":537},[520,2392],{"dataC":561,"xLinkHref":2366,"transform":965},[520,2394],{"dataC":561,"xLinkHref":2366,"transform":968},[505,2396,2397],{"dataMmlNode":540,"transform":997},[520,2398],{"dataC":568,"xLinkHref":2399},"#MJX-19-TEX-N-2212",[505,2401,2402,2406],{"dataMmlNode":515,"transform":1003},[505,2403,2404],{"dataMmlNode":518},[520,2405],{"dataC":522,"xLinkHref":2356},[505,2407,2408],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,2409,2410,2412,2415],{"dataMmlNode":518},[520,2411],{"dataC":522,"xLinkHref":2356},[520,2413],{"dataC":2255,"xLinkHref":2414,"transform":537},"#MJX-19-TEX-N-35",[520,2416],{"dataC":561,"xLinkHref":2366,"transform":965},[505,2418,2420],{"dataMmlNode":540,"transform":2419},"translate(8305.2,0)",[520,2421],{"dataC":544,"xLinkHref":2375},[505,2423,2425,2427],{"dataMmlNode":518,"transform":2424},"translate(9305.4,0)",[520,2426],{"dataC":959,"xLinkHref":2363},[520,2428],{"dataC":1487,"xLinkHref":2429,"transform":537},"#MJX-19-TEX-N-2E",[635,2431,2432],{},"Составим таблицу для подсчёта количества добавляемых единиц:",[649,2434,2435,2446],{},[652,2436,2437],{},[655,2438,2439,2441,2443],{},[658,2440,660],{},[658,2442,663],{},[658,2444,2445],{},"Добавление единиц",[668,2447,2448,2499,2558,2617],{},[655,2449,2450,2494,2497],{},[673,2451,2452],{},[452,2453,2455],{"className":2454,"jax":456},[455],[458,2456,2458,2469],{"style":680,"xmlns":461,"width":1815,"height":682,"role":464,"focusable":465,"viewBox":2457,"xmlnsXLink":467},"0 -833.9 1997.2 833.9",[469,2459,2460,2463,2466],{},[472,2461],{"id":2462,"d":475},"MJX-20-TEX-N-32",[472,2464],{"id":2465,"d":922},"MJX-20-TEX-N-33",[472,2467],{"id":2468,"d":487},"MJX-20-TEX-N-30",[505,2470,2471],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,2472,2473],{"dataMmlNode":512},[505,2474,2475,2480],{"dataMmlNode":515},[505,2476,2477],{"dataMmlNode":518},[520,2478],{"dataC":522,"xLinkHref":2479},"#MJX-20-TEX-N-32",[505,2481,2482],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,2483,2484,2487,2490,2492],{"dataMmlNode":518},[520,2485],{"dataC":959,"xLinkHref":2486},"#MJX-20-TEX-N-33",[520,2488],{"dataC":561,"xLinkHref":2489,"transform":537},"#MJX-20-TEX-N-30",[520,2491],{"dataC":561,"xLinkHref":2489,"transform":965},[520,2493],{"dataC":561,"xLinkHref":2489,"transform":968},[673,2495,2496],{},"Степень = 3000, знак \"+\"",[673,2498,717],{},[655,2500,2501,2553,2556],{},[673,2502,2503],{},[452,2504,2506],{"className":2505,"jax":456},[455],[458,2507,2509,2523],{"style":460,"xmlns":461,"width":1874,"height":463,"role":464,"focusable":465,"viewBox":2508,"xmlnsXLink":467},"0 -833.9 2775.2 915.9",[469,2510,2511,2514,2517,2520],{},[472,2512],{"id":2513,"d":483},"MJX-21-TEX-N-2B",[472,2515],{"id":2516,"d":475},"MJX-21-TEX-N-32",[472,2518],{"id":2519,"d":479},"MJX-21-TEX-N-31",[472,2521],{"id":2522,"d":487},"MJX-21-TEX-N-30",[505,2524,2525],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,2526,2527,2532],{"dataMmlNode":512},[505,2528,2529],{"dataMmlNode":540},[520,2530],{"dataC":544,"xLinkHref":2531},"#MJX-21-TEX-N-2B",[505,2533,2534,2539],{"dataMmlNode":515,"transform":754},[505,2535,2536],{"dataMmlNode":518},[520,2537],{"dataC":522,"xLinkHref":2538},"#MJX-21-TEX-N-32",[505,2540,2541],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,2542,2543,2546,2549,2551],{"dataMmlNode":518},[520,2544],{"dataC":533,"xLinkHref":2545},"#MJX-21-TEX-N-31",[520,2547],{"dataC":561,"xLinkHref":2548,"transform":537},"#MJX-21-TEX-N-30",[520,2550],{"dataC":561,"xLinkHref":2548,"transform":965},[520,2552],{"dataC":561,"xLinkHref":2548,"transform":968},[673,2554,2555],{},"Степень = 1000, знак \"+\"",[673,2557,717],{},[655,2559,2560,2611,2614],{},[673,2561,2562],{},[452,2563,2565],{"className":2564,"jax":456},[455],[458,2566,2569,2583],{"style":460,"xmlns":461,"width":2567,"height":463,"role":464,"focusable":465,"viewBox":2568,"xmlnsXLink":467},"5.479ex","0 -833.9 2421.7 915.9",[469,2570,2571,2574,2577,2580],{},[472,2572],{"id":2573,"d":491},"MJX-22-TEX-N-2212",[472,2575],{"id":2576,"d":475},"MJX-22-TEX-N-32",[472,2578],{"id":2579,"d":2199},"MJX-22-TEX-N-35",[472,2581],{"id":2582,"d":487},"MJX-22-TEX-N-30",[505,2584,2585],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,2586,2587,2592],{"dataMmlNode":512},[505,2588,2589],{"dataMmlNode":540},[520,2590],{"dataC":568,"xLinkHref":2591},"#MJX-22-TEX-N-2212",[505,2593,2594,2599],{"dataMmlNode":515,"transform":754},[505,2595,2596],{"dataMmlNode":518},[520,2597],{"dataC":522,"xLinkHref":2598},"#MJX-22-TEX-N-32",[505,2600,2601],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,2602,2603,2605,2608],{"dataMmlNode":518},[520,2604],{"dataC":522,"xLinkHref":2598},[520,2606],{"dataC":2255,"xLinkHref":2607,"transform":537},"#MJX-22-TEX-N-35",[520,2609],{"dataC":561,"xLinkHref":2610,"transform":965},"#MJX-22-TEX-N-30",[673,2612,2613],{},"Степень = 250, знак \"-\"",[673,2615,2616],{},"(1000-250)-1=749",[655,2618,2619,2651,2653],{},[673,2620,2621],{},[452,2622,2624],{"className":2623,"jax":456},[455],[458,2625,2629,2637],{"style":460,"xmlns":461,"width":2626,"height":2627,"role":464,"focusable":465,"viewBox":2628,"xmlnsXLink":467},"2.891ex","1.69ex","0 -665 1278 747",[469,2630,2631,2634],{},[472,2632],{"id":2633,"d":483},"MJX-23-TEX-N-2B",[472,2635],{"id":2636,"d":922},"MJX-23-TEX-N-33",[505,2638,2639],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,2640,2641,2646],{"dataMmlNode":512},[505,2642,2643],{"dataMmlNode":540},[520,2644],{"dataC":544,"xLinkHref":2645},"#MJX-23-TEX-N-2B",[505,2647,2648],{"dataMmlNode":518,"transform":754},[520,2649],{"dataC":959,"xLinkHref":2650},"#MJX-23-TEX-N-33",[673,2652,878],{},[673,2654,881],{},[632,2656,2657],{"start":884},[635,2658,2659,2660],{},"Суммируем найденные количества единиц: ",[452,2661,2663],{"className":2662,"jax":456},[455],[458,2664,2668,2702],{"style":460,"xmlns":461,"width":2665,"height":2666,"role":464,"focusable":465,"viewBox":2667,"xmlnsXLink":467},"22.124ex","1.717ex","0 -677 9778.9 759",[469,2669,2670,2673,2676,2680,2683,2687,2690,2693,2696,2699],{},[472,2671],{"id":2672,"d":479},"MJX-24-TEX-N-31",[472,2674],{"id":2675,"d":483},"MJX-24-TEX-N-2B",[472,2677],{"id":2678,"d":2679},"MJX-24-TEX-N-37","M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z",[472,2681],{"id":2682,"d":926},"MJX-24-TEX-N-34",[472,2684],{"id":2685,"d":2686},"MJX-24-TEX-N-39","M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z",[472,2688],{"id":2689,"d":475},"MJX-24-TEX-N-32",[472,2691],{"id":2692,"d":1086},"MJX-24-TEX-N-3D",[472,2694],{"id":2695,"d":2199},"MJX-24-TEX-N-35",[472,2697],{"id":2698,"d":922},"MJX-24-TEX-N-33",[472,2700],{"id":2701,"d":1395},"MJX-24-TEX-N-2E",[505,2703,2704],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,2705,2706,2711,2717,2722,2727,2741,2746,2752,2758],{"dataMmlNode":512},[505,2707,2708],{"dataMmlNode":518},[520,2709],{"dataC":533,"xLinkHref":2710},"#MJX-24-TEX-N-31",[505,2712,2714],{"dataMmlNode":540,"transform":2713},"translate(722.2,0)",[520,2715],{"dataC":544,"xLinkHref":2716},"#MJX-24-TEX-N-2B",[505,2718,2720],{"dataMmlNode":518,"transform":2719},"translate(1722.4,0)",[520,2721],{"dataC":533,"xLinkHref":2710},[505,2723,2725],{"dataMmlNode":540,"transform":2724},"translate(2444.7,0)",[520,2726],{"dataC":544,"xLinkHref":2716},[505,2728,2730,2734,2737],{"dataMmlNode":518,"transform":2729},"translate(3444.9,0)",[520,2731],{"dataC":2732,"xLinkHref":2733},"37","#MJX-24-TEX-N-37",[520,2735],{"dataC":963,"xLinkHref":2736,"transform":537},"#MJX-24-TEX-N-34",[520,2738],{"dataC":2739,"xLinkHref":2740,"transform":965},"39","#MJX-24-TEX-N-39",[505,2742,2744],{"dataMmlNode":540,"transform":2743},"translate(5167.1,0)",[520,2745],{"dataC":544,"xLinkHref":2716},[505,2747,2749],{"dataMmlNode":518,"transform":2748},"translate(6167.3,0)",[520,2750],{"dataC":522,"xLinkHref":2751},"#MJX-24-TEX-N-32",[505,2753,2755],{"dataMmlNode":540,"transform":2754},"translate(6945.1,0)",[520,2756],{"dataC":1179,"xLinkHref":2757},"#MJX-24-TEX-N-3D",[505,2759,2761,2763,2766,2769],{"dataMmlNode":518,"transform":2760},"translate(8000.9,0)",[520,2762],{"dataC":2732,"xLinkHref":2733},[520,2764],{"dataC":2255,"xLinkHref":2765,"transform":537},"#MJX-24-TEX-N-35",[520,2767],{"dataC":959,"xLinkHref":2768,"transform":965},"#MJX-24-TEX-N-33",[520,2770],{"dataC":1487,"xLinkHref":2771,"transform":968},"#MJX-24-TEX-N-2E",[402,2773,2774],{},[406,2775,2776],{},"Ответ: 753.",[444,2778,2780],{"id":2779},"задача-4","Задача 4",[402,2782,2783,2784],{},"Сколько значащих нулей в двоичной записи числа: ",[452,2785,2787],{"className":2786,"jax":456},[455],[458,2788,2792,2821],{"style":460,"xmlns":461,"width":2789,"height":2790,"role":464,"focusable":465,"viewBox":2791,"xmlnsXLink":467},"25.046ex","2.14ex","0 -864 11070.3 946",[469,2793,2794,2797,2800,2803,2806,2809,2812,2815,2818],{},[472,2795],{"id":2796,"d":495},"MJX-25-TEX-N-38",[472,2798],{"id":2799,"d":475},"MJX-25-TEX-N-32",[472,2801],{"id":2802,"d":2199},"MJX-25-TEX-N-35",[472,2804],{"id":2805,"d":499},"MJX-25-TEX-N-36",[472,2807],{"id":2808,"d":483},"MJX-25-TEX-N-2B",[472,2810],{"id":2811,"d":479},"MJX-25-TEX-N-31",[472,2813],{"id":2814,"d":491},"MJX-25-TEX-N-2212",[472,2816],{"id":2817,"d":926},"MJX-25-TEX-N-34",[472,2819],{"id":2820,"d":503},"MJX-25-TEX-N-3F",[505,2822,2823],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,2824,2825,2845,2851,2872,2878,2895,2900,2910],{"dataMmlNode":512},[505,2826,2827,2832],{"dataMmlNode":515},[505,2828,2829],{"dataMmlNode":518},[520,2830],{"dataC":581,"xLinkHref":2831},"#MJX-25-TEX-N-38",[505,2833,2834],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,2835,2836,2839,2842],{"dataMmlNode":518},[520,2837],{"dataC":522,"xLinkHref":2838},"#MJX-25-TEX-N-32",[520,2840],{"dataC":2255,"xLinkHref":2841,"transform":537},"#MJX-25-TEX-N-35",[520,2843],{"dataC":599,"xLinkHref":2844,"transform":965},"#MJX-25-TEX-N-36",[505,2846,2848],{"dataMmlNode":540,"transform":2847},"translate(1865.9,0)",[520,2849],{"dataC":544,"xLinkHref":2850},"#MJX-25-TEX-N-2B",[505,2852,2854,2861],{"dataMmlNode":515,"transform":2853},"translate(2866.1,0)",[505,2855,2856,2859],{"dataMmlNode":518},[520,2857],{"dataC":533,"xLinkHref":2858},"#MJX-25-TEX-N-31",[520,2860],{"dataC":599,"xLinkHref":2844,"transform":537},[505,2862,2864],{"dataMmlNode":526,"transform":2863,"dataMjxTexclass":528},"translate(1033,393.1) scale(0.707)",[505,2865,2866,2868,2870],{"dataMmlNode":518},[520,2867],{"dataC":522,"xLinkHref":2838},[520,2869],{"dataC":2255,"xLinkHref":2841,"transform":537},[520,2871],{"dataC":599,"xLinkHref":2844,"transform":965},[505,2873,2875],{"dataMmlNode":540,"transform":2874},"translate(5232,0)",[520,2876],{"dataC":568,"xLinkHref":2877},"#MJX-25-TEX-N-2212",[505,2879,2881,2885],{"dataMmlNode":515,"transform":2880},"translate(6232.2,0)",[505,2882,2883],{"dataMmlNode":518},[520,2884],{"dataC":522,"xLinkHref":2838},[505,2886,2887],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,2888,2889,2891,2893],{"dataMmlNode":518},[520,2890],{"dataC":533,"xLinkHref":2858},[520,2892],{"dataC":522,"xLinkHref":2838,"transform":537},[520,2894],{"dataC":581,"xLinkHref":2831,"transform":965},[505,2896,2898],{"dataMmlNode":540,"transform":2897},"translate(8098.1,0)",[520,2899],{"dataC":568,"xLinkHref":2877},[505,2901,2903,2905,2908],{"dataMmlNode":518,"transform":2902},"translate(9098.3,0)",[520,2904],{"dataC":522,"xLinkHref":2838},[520,2906],{"dataC":963,"xLinkHref":2907,"transform":537},"#MJX-25-TEX-N-34",[520,2909],{"dataC":2255,"xLinkHref":2841,"transform":965},[505,2911,2913],{"dataMmlNode":540,"transform":2912},"translate(10598.3,0)",[520,2914],{"dataC":616,"xLinkHref":2915},"#MJX-25-TEX-N-3F",[619,2917,622],{"id":2918},"решение-3",[624,2920,627],{"id":2921},"решение-аналитическое-3",[2923,2924,2925],"blockquote",{},[402,2926,2927],{},"В двоичной системе количество значащих нулей легко найти как разность общего количества разрядов в числе и количества единиц в нём, поэтому данная задача сводится к подсчёту количества единиц в числе.",[632,2929,2930,3458,3826],{},[635,2931,2932,2933,3057,3268],{},"Аналогично предыдущей задаче, сначала представим все числа как степени двоек. В данном случае число 245 имеет знак \"минус\", и напрямую подсчитывать в нём количество единиц, чтобы добавить к ранее полученному числу, неудобно. Поэтому представим число 245 тоже как набор степеней двоек, например: 245 = 256 - 8 - 2 - 1.\nТогда получаем следующую запись: ",[452,2934,2936],{"className":2935,"jax":456},[455],[458,2937,2940,2969],{"style":460,"xmlns":461,"width":2938,"height":2790,"role":464,"focusable":465,"viewBox":2939,"xmlnsXLink":467},"26.367ex","0 -864 11654.1 946",[469,2941,2942,2945,2948,2951,2954,2957,2960,2963,2966],{},[472,2943],{"id":2944,"d":495},"MJX-26-TEX-N-38",[472,2946],{"id":2947,"d":475},"MJX-26-TEX-N-32",[472,2949],{"id":2950,"d":2199},"MJX-26-TEX-N-35",[472,2952],{"id":2953,"d":499},"MJX-26-TEX-N-36",[472,2955],{"id":2956,"d":483},"MJX-26-TEX-N-2B",[472,2958],{"id":2959,"d":479},"MJX-26-TEX-N-31",[472,2961],{"id":2962,"d":491},"MJX-26-TEX-N-2212",[472,2964],{"id":2965,"d":926},"MJX-26-TEX-N-34",[472,2967],{"id":2968,"d":1086},"MJX-26-TEX-N-3D",[505,2970,2971],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,2972,2973,2993,2998,3017,3022,3038,3042,3051],{"dataMmlNode":512},[505,2974,2975,2980],{"dataMmlNode":515},[505,2976,2977],{"dataMmlNode":518},[520,2978],{"dataC":581,"xLinkHref":2979},"#MJX-26-TEX-N-38",[505,2981,2982],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,2983,2984,2987,2990],{"dataMmlNode":518},[520,2985],{"dataC":522,"xLinkHref":2986},"#MJX-26-TEX-N-32",[520,2988],{"dataC":2255,"xLinkHref":2989,"transform":537},"#MJX-26-TEX-N-35",[520,2991],{"dataC":599,"xLinkHref":2992,"transform":965},"#MJX-26-TEX-N-36",[505,2994,2995],{"dataMmlNode":540,"transform":2847},[520,2996],{"dataC":544,"xLinkHref":2997},"#MJX-26-TEX-N-2B",[505,2999,3000,3007],{"dataMmlNode":515,"transform":2853},[505,3001,3002,3005],{"dataMmlNode":518},[520,3003],{"dataC":533,"xLinkHref":3004},"#MJX-26-TEX-N-31",[520,3006],{"dataC":599,"xLinkHref":2992,"transform":537},[505,3008,3009],{"dataMmlNode":526,"transform":2863,"dataMjxTexclass":528},[505,3010,3011,3013,3015],{"dataMmlNode":518},[520,3012],{"dataC":522,"xLinkHref":2986},[520,3014],{"dataC":2255,"xLinkHref":2989,"transform":537},[520,3016],{"dataC":599,"xLinkHref":2992,"transform":965},[505,3018,3019],{"dataMmlNode":540,"transform":2874},[520,3020],{"dataC":568,"xLinkHref":3021},"#MJX-26-TEX-N-2212",[505,3023,3024,3028],{"dataMmlNode":515,"transform":2880},[505,3025,3026],{"dataMmlNode":518},[520,3027],{"dataC":522,"xLinkHref":2986},[505,3029,3030],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,3031,3032,3034,3036],{"dataMmlNode":518},[520,3033],{"dataC":533,"xLinkHref":3004},[520,3035],{"dataC":522,"xLinkHref":2986,"transform":537},[520,3037],{"dataC":581,"xLinkHref":2979,"transform":965},[505,3039,3040],{"dataMmlNode":540,"transform":2897},[520,3041],{"dataC":568,"xLinkHref":3021},[505,3043,3044,3046,3049],{"dataMmlNode":518,"transform":2902},[520,3045],{"dataC":522,"xLinkHref":2986},[520,3047],{"dataC":963,"xLinkHref":3048,"transform":537},"#MJX-26-TEX-N-34",[520,3050],{"dataC":2255,"xLinkHref":2989,"transform":965},[505,3052,3054],{"dataMmlNode":540,"transform":3053},"translate(10876.1,0)",[520,3055],{"dataC":1179,"xLinkHref":3056},"#MJX-26-TEX-N-3D",[452,3058,3060],{"className":3059,"jax":456},[455],[458,3061,3064,3105],{"style":1186,"xmlns":461,"width":3062,"height":1188,"role":464,"focusable":465,"viewBox":3063,"xmlnsXLink":467},"43.563ex","0 -841.7 19255 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таблицу:",[649,3830,3831,3841],{},[652,3832,3833],{},[655,3834,3835,3837,3839],{},[658,3836,660],{},[658,3838,663],{},[658,3840,2445],{},[668,3842,3843,3897,3959,4016,4064,4114,4162],{},[655,3844,3845,3892,3895],{},[673,3846,3847],{},[452,3848,3850],{"className":3849,"jax":456},[455],[458,3851,3852,3866],{"style":680,"xmlns":461,"width":1815,"height":1816,"role":464,"focusable":465,"viewBox":1817,"xmlnsXLink":467},[469,3853,3854,3857,3860,3863],{},[472,3855],{"id":3856,"d":475},"MJX-31-TEX-N-32",[472,3858],{"id":3859,"d":479},"MJX-31-TEX-N-31",[472,3861],{"id":3862,"d":487},"MJX-31-TEX-N-30",[472,3864],{"id":3865,"d":926},"MJX-31-TEX-N-34",[505,3867,3868],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,3869,3870],{"dataMmlNode":512},[505,3871,3872,3877],{"dataMmlNode":515},[505,3873,3874],{"dataMmlNode":518},[520,3875],{"dataC":522,"xLinkHref":3876},"#MJX-31-TEX-N-32",[505,3878,3879],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,3880,3881,3884,3887,3889],{"dataMmlNode":518},[520,3882],{"dataC":533,"xLinkHref":3883},"#MJX-31-TEX-N-31",[520,3885],{"dataC":561,"xLinkHref":3886,"transform":537},"#MJX-31-TEX-N-30",[520,3888],{"dataC":522,"xLinkHref":3876,"transform":965},[520,3890],{"dataC":963,"xLinkHref":3891,"transform":968},"#MJX-31-TEX-N-34",[673,3893,3894],{},"Степень 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\"+\"",[673,4113,717],{},[655,4115,4116,4157,4160],{},[673,4117,4118],{},[452,4119,4121],{"className":4120,"jax":456},[455],[458,4122,4123,4134],{"style":460,"xmlns":461,"width":784,"height":463,"role":464,"focusable":465,"viewBox":785,"xmlnsXLink":467},[469,4124,4125,4128,4131],{},[472,4126],{"id":4127,"d":483},"MJX-36-TEX-N-2B",[472,4129],{"id":4130,"d":475},"MJX-36-TEX-N-32",[472,4132],{"id":4133,"d":479},"MJX-36-TEX-N-31",[505,4135,4136],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,4137,4138,4143],{"dataMmlNode":512},[505,4139,4140],{"dataMmlNode":540},[520,4141],{"dataC":544,"xLinkHref":4142},"#MJX-36-TEX-N-2B",[505,4144,4145,4150],{"dataMmlNode":515,"transform":754},[505,4146,4147],{"dataMmlNode":518},[520,4148],{"dataC":522,"xLinkHref":4149},"#MJX-36-TEX-N-32",[505,4151,4152],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,4153,4154],{"dataMmlNode":518},[520,4155],{"dataC":533,"xLinkHref":4156},"#MJX-36-TEX-N-31",[673,4158,4159],{},"Степень = 1, знак \"+\"",[673,4161,717],{},[655,4163,4164,4205,4208],{},[673,4165,4166],{},[452,4167,4169],{"className":4168,"jax":456},[455],[458,4170,4171,4182],{"style":460,"xmlns":461,"width":784,"height":463,"role":464,"focusable":465,"viewBox":785,"xmlnsXLink":467},[469,4172,4173,4176,4179],{},[472,4174],{"id":4175,"d":483},"MJX-37-TEX-N-2B",[472,4177],{"id":4178,"d":475},"MJX-37-TEX-N-32",[472,4180],{"id":4181,"d":487},"MJX-37-TEX-N-30",[505,4183,4184],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,4185,4186,4191],{"dataMmlNode":512},[505,4187,4188],{"dataMmlNode":540},[520,4189],{"dataC":544,"xLinkHref":4190},"#MJX-37-TEX-N-2B",[505,4192,4193,4198],{"dataMmlNode":515,"transform":754},[505,4194,4195],{"dataMmlNode":518},[520,4196],{"dataC":522,"xLinkHref":4197},"#MJX-37-TEX-N-32",[505,4199,4200],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,4201,4202],{"dataMmlNode":518},[520,4203],{"dataC":561,"xLinkHref":4204},"#MJX-37-TEX-N-30",[673,4206,4207],{},"Степень = 0, знак \"+\"",[673,4209,717],{},[632,4211,4213,4216],{"start":4212},4,[635,4214,4215],{},"Суммируем вычисленные в таблице количества единиц: 1 + 1 + 639 + 119 + 1 + 1 + 1 = 763.",[635,4217,4218],{},"Общее количество значащих разрядов определяется самой старшей степенью двойки, в нашем случае — числом 2 в 1024 степени. Такое число содержит единицу в старшем разряде и 1024 нуля после неё, т.е. общая длина числа равна 1025 знаков. Тогда количество значащих нулей в результирующем двоичном числе равно 1025 - 763 = 262.",[402,4220,4221],{},[406,4222,4223],{},"Ответ: 262",[2923,4225,4226],{},[402,4227,4228],{},"Решение подобных задач для других систем счисления в целом аналогично. При этом обычно в условии фигурируют цифры, получаемые вычитанием \"из нуля\", так что рассмотренные выше принципы решения вполне применимы и в этих случаях.",[444,4230,4232],{"id":4231},"задача-5","Задача 5",[402,4234,4235,4236,4321],{},"Значение арифметического выражения ",[452,4237,4239],{"className":4238,"jax":456},[455],[458,4240,4243,4269],{"style":460,"xmlns":461,"width":4241,"height":909,"role":464,"focusable":465,"viewBox":4242,"xmlnsXLink":467},"12.5ex","0 -841.7 5525.1 923.7",[469,4244,4245,4248,4251,4254,4257,4260,4263,4266],{},[472,4246],{"id":4247,"d":2686},"MJX-38-TEX-N-39",[472,4249],{"id":4250,"d":479},"MJX-38-TEX-N-31",[472,4252],{"id":4253,"d":495},"MJX-38-TEX-N-38",[472,4255],{"id":4256,"d":483},"MJX-38-TEX-N-2B",[472,4258],{"id":4259,"d":922},"MJX-38-TEX-N-33",[472,4261],{"id":4262,"d":2199},"MJX-38-TEX-N-35",[472,4264],{"id":4265,"d":926},"MJX-38-TEX-N-34",[472,4267],{"id":4268,"d":491},"MJX-38-TEX-N-2212",[505,4270,4271],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,4272,4273,4290,4295,4312,4317],{"dataMmlNode":512},[505,4274,4275,4280],{"dataMmlNode":515},[505,4276,4277],{"dataMmlNode":518},[520,4278],{"dataC":2739,"xLinkHref":4279},"#MJX-38-TEX-N-39",[505,4281,4282],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,4283,4284,4287],{"dataMmlNode":518},[520,4285],{"dataC":533,"xLinkHref":4286},"#MJX-38-TEX-N-31",[520,4288],{"dataC":581,"xLinkHref":4289,"transform":537},"#MJX-38-TEX-N-38",[505,4291,4292],{"dataMmlNode":540,"transform":541},[520,4293],{"dataC":544,"xLinkHref":4294},"#MJX-38-TEX-N-2B",[505,4296,4297,4302],{"dataMmlNode":515,"transform":548},[505,4298,4299],{"dataMmlNode":518},[520,4300],{"dataC":959,"xLinkHref":4301},"#MJX-38-TEX-N-33",[505,4303,4304],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,4305,4306,4309],{"dataMmlNode":518},[520,4307],{"dataC":2255,"xLinkHref":4308},"#MJX-38-TEX-N-35",[520,4310],{"dataC":963,"xLinkHref":4311,"transform":537},"#MJX-38-TEX-N-34",[505,4313,4314],{"dataMmlNode":540,"transform":565},[520,4315],{"dataC":568,"xLinkHref":4316},"#MJX-38-TEX-N-2212",[505,4318,4319],{"dataMmlNode":518,"transform":572},[520,4320],{"dataC":2739,"xLinkHref":4279}," записано в системе счисления с основанием 3. Сколько цифр 2 содержится в этой записи?",[619,4323,622],{"id":4324},"решение-4",[624,4326,627],{"id":4327},"решение-аналитическое-4",[632,4329,4330,4495,4594],{},[635,4331,4332,4333],{},"Представим все числа как степени троек(т.е. как степени заданного основания системы счисления): ",[452,4334,4336],{"className":4335,"jax":456},[455],[458,4337,4340,4378],{"style":460,"xmlns":461,"width":4338,"height":909,"role":464,"focusable":465,"viewBox":4339,"xmlnsXLink":467},"29.634ex","0 -841.7 13098.3 923.7",[469,4341,4342,4345,4348,4351,4354,4357,4360,4363,4366,4369,4372,4375],{},[472,4343],{"id":4344,"d":2686},"MJX-39-TEX-N-39",[472,4346],{"id":4347,"d":479},"MJX-39-TEX-N-31",[472,4349],{"id":4350,"d":495},"MJX-39-TEX-N-38",[472,4352],{"id":4353,"d":483},"MJX-39-TEX-N-2B",[472,4355],{"id":4356,"d":922},"MJX-39-TEX-N-33",[472,4358],{"id":4359,"d":2199},"MJX-39-TEX-N-35",[472,4361],{"id":4362,"d":926},"MJX-39-TEX-N-34",[472,4364],{"id":4365,"d":491},"MJX-39-TEX-N-2212",[472,4367],{"id":4368,"d":1086},"MJX-39-TEX-N-3D",[472,4370],{"id":4371,"d":499},"MJX-39-TEX-N-36",[472,4373],{"id":4374,"d":475},"MJX-39-TEX-N-32",[472,4376],{"id":4377,"d":1395},"MJX-39-TEX-N-2E",[505,4379,4380],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,4381,4382,4399,4404,4421,4426,4430,4436,4452,4457,4472,4477,4489],{"dataMmlNode":512},[505,4383,4384,4389],{"dataMmlNode":515},[505,4385,4386],{"dataMmlNode":518},[520,4387],{"dataC":2739,"xLinkHref":4388},"#MJX-39-TEX-N-39",[505,4390,4391],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,4392,4393,4396],{"dataMmlNode":518},[520,4394],{"dataC":533,"xLinkHref":4395},"#MJX-39-TEX-N-31",[520,4397],{"dataC":581,"xLinkHref":4398,"transform":537},"#MJX-39-TEX-N-38",[505,4400,4401],{"dataMmlNode":540,"transform":541},[520,4402],{"dataC":544,"xLinkHref":4403},"#MJX-39-TEX-N-2B",[505,4405,4406,4411],{"dataMmlNode":515,"transform":548},[505,4407,4408],{"dataMmlNode":518},[520,4409],{"dataC":959,"xLinkHref":4410},"#MJX-39-TEX-N-33",[505,4412,4413],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,4414,4415,4418],{"dataMmlNode":518},[520,4416],{"dataC":2255,"xLinkHref":4417},"#MJX-39-TEX-N-35",[520,4419],{"dataC":963,"xLinkHref":4420,"transform":537},"#MJX-39-TEX-N-34",[505,4422,4423],{"dataMmlNode":540,"transform":565},[520,4424],{"dataC":568,"xLinkHref":4425},"#MJX-39-TEX-N-2212",[505,4427,4428],{"dataMmlNode":518,"transform":572},[520,4429],{"dataC":2739,"xLinkHref":4388},[505,4431,4433],{"dataMmlNode":540,"transform":4432},"translate(5802.9,0)",[520,4434],{"dataC":1179,"xLinkHref":4435},"#MJX-39-TEX-N-3D",[505,4437,4439,4443],{"dataMmlNode":515,"transform":4438},"translate(6858.7,0)",[505,4440,4441],{"dataMmlNode":518},[520,4442],{"dataC":959,"xLinkHref":4410},[505,4444,4445],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,4446,4447,4449],{"dataMmlNode":518},[520,4448],{"dataC":959,"xLinkHref":4410},[520,4450],{"dataC":599,"xLinkHref":4451,"transform":537},"#MJX-39-TEX-N-36",[505,4453,4455],{"dataMmlNode":540,"transform":4454},"translate(8371,0)",[520,4456],{"dataC":544,"xLinkHref":4403},[505,4458,4460,4464],{"dataMmlNode":515,"transform":4459},"translate(9371.2,0)",[505,4461,4462],{"dataMmlNode":518},[520,4463],{"dataC":959,"xLinkHref":4410},[505,4465,4466],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,4467,4468,4470],{"dataMmlNode":518},[520,4469],{"dataC":2255,"xLinkHref":4417},[520,4471],{"dataC":963,"xLinkHref":4420,"transform":537},[505,4473,4475],{"dataMmlNode":540,"transform":4474},"translate(10883.5,0)",[520,4476],{"dataC":568,"xLinkHref":4425},[505,4478,4480,4484],{"dataMmlNode":515,"transform":4479},"translate(11883.8,0)",[505,4481,4482],{"dataMmlNode":518},[520,4483],{"dataC":959,"xLinkHref":4410},[505,4485,4486],{"dataMmlNode":518,"transform":527},[520,4487],{"dataC":522,"xLinkHref":4488},"#MJX-39-TEX-N-32",[505,4490,4492],{"dataMmlNode":540,"transform":4491},"translate(12820.3,0)",[520,4493],{"dataC":1487,"xLinkHref":4494},"#MJX-39-TEX-N-2E",[635,4496,4497,4498],{},"Перепишем полученные значения по убыванию степеней: ",[452,4499,4501],{"className":4500,"jax":456},[455],[458,4502,4505,4531],{"style":460,"xmlns":461,"width":4503,"height":909,"role":464,"focusable":465,"viewBox":4504,"xmlnsXLink":467},"14.117ex","0 -841.7 6239.7 923.7",[469,4506,4507,4510,4513,4516,4519,4522,4525,4528],{},[472,4508],{"id":4509,"d":922},"MJX-40-TEX-N-33",[472,4511],{"id":4512,"d":2199},"MJX-40-TEX-N-35",[472,4514],{"id":4515,"d":926},"MJX-40-TEX-N-34",[472,4517],{"id":4518,"d":483},"MJX-40-TEX-N-2B",[472,4520],{"id":4521,"d":499},"MJX-40-TEX-N-36",[472,4523],{"id":4524,"d":491},"MJX-40-TEX-N-2212",[472,4526],{"id":4527,"d":475},"MJX-40-TEX-N-32",[472,4529],{"id":4530,"d":1395},"MJX-40-TEX-N-2E",[505,4532,4533],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,4534,4535,4552,4557,4572,4577,4588],{"dataMmlNode":512},[505,4536,4537,4542],{"dataMmlNode":515},[505,4538,4539],{"dataMmlNode":518},[520,4540],{"dataC":959,"xLinkHref":4541},"#MJX-40-TEX-N-33",[505,4543,4544],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,4545,4546,4549],{"dataMmlNode":518},[520,4547],{"dataC":2255,"xLinkHref":4548},"#MJX-40-TEX-N-35",[520,4550],{"dataC":963,"xLinkHref":4551,"transform":537},"#MJX-40-TEX-N-34",[505,4553,4554],{"dataMmlNode":540,"transform":541},[520,4555],{"dataC":544,"xLinkHref":4556},"#MJX-40-TEX-N-2B",[505,4558,4559,4563],{"dataMmlNode":515,"transform":548},[505,4560,4561],{"dataMmlNode":518},[520,4562],{"dataC":959,"xLinkHref":4541},[505,4564,4565],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,4566,4567,4569],{"dataMmlNode":518},[520,4568],{"dataC":959,"xLinkHref":4541},[520,4570],{"dataC":599,"xLinkHref":4571,"transform":537},"#MJX-40-TEX-N-36",[505,4573,4574],{"dataMmlNode":540,"transform":565},[520,4575],{"dataC":568,"xLinkHref":4576},"#MJX-40-TEX-N-2212",[505,4578,4579,4583],{"dataMmlNode":515,"transform":572},[505,4580,4581],{"dataMmlNode":518},[520,4582],{"dataC":959,"xLinkHref":4541},[505,4584,4585],{"dataMmlNode":518,"transform":527},[520,4586],{"dataC":522,"xLinkHref":4587},"#MJX-40-TEX-N-32",[505,4589,4591],{"dataMmlNode":540,"transform":4590},"translate(5961.7,0)",[520,4592],{"dataC":1487,"xLinkHref":4593},"#MJX-40-TEX-N-2E",[635,4595,4596],{},"Составляем таблицу подсчёта, аналогичную ранее рассмотренным при решении задач на двоичную систему, но теперь учитываем отдельно возникающие в троичной системе единицы (при знаке \"плюс\") и двойки (при знаке \"минус\"; в троичной системе цифра 2 является аналогом появления в числе \"девяти\" в десятичной). При этом обратим внимание: во время заёмов из более старших разрядов двойки распространяются слева направо до тех пор, пока в очередном более старшем разряде не будет встречена единица; именно эта единица будет потрачена, а количество двоек будет равно просто разности степеней предыдущего и данного слагаемых.",[649,4598,4599,4609],{},[652,4600,4601],{},[655,4602,4603,4605,4607],{},[658,4604,660],{},[658,4606,663],{},[658,4608,2445],{},[668,4610,4611,4661,4712],{},[655,4612,4613,4655,4658],{},[673,4614,4615],{},[452,4616,4618],{"className":4617,"jax":456},[455],[458,4619,4623,4634],{"style":4620,"xmlns":461,"width":681,"height":4621,"role":464,"focusable":465,"viewBox":4622,"xmlnsXLink":467},"vertical-align: -0.05ex;","1.954ex","0 -841.7 1290.1 863.7",[469,4624,4625,4628,4631],{},[472,4626],{"id":4627,"d":922},"MJX-41-TEX-N-33",[472,4629],{"id":4630,"d":2199},"MJX-41-TEX-N-35",[472,4632],{"id":4633,"d":926},"MJX-41-TEX-N-34",[505,4635,4636],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,4637,4638],{"dataMmlNode":512},[505,4639,4640,4645],{"dataMmlNode":515},[505,4641,4642],{"dataMmlNode":518},[520,4643],{"dataC":959,"xLinkHref":4644},"#MJX-41-TEX-N-33",[505,4646,4647],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,4648,4649,4652],{"dataMmlNode":518},[520,4650],{"dataC":2255,"xLinkHref":4651},"#MJX-41-TEX-N-35",[520,4653],{"dataC":963,"xLinkHref":4654,"transform":537},"#MJX-41-TEX-N-34",[673,4656,4657],{},"Степень = 54, знак \"+\"",[673,4659,4660],{},"1 единица",[655,4662,4663,4706,4709],{},[673,4664,4665],{},[452,4666,4668],{"className":4667,"jax":456},[455],[458,4669,4670,4681],{"style":460,"xmlns":461,"width":727,"height":463,"role":464,"focusable":465,"viewBox":728,"xmlnsXLink":467},[469,4671,4672,4675,4678],{},[472,4673],{"id":4674,"d":483},"MJX-42-TEX-N-2B",[472,4676],{"id":4677,"d":922},"MJX-42-TEX-N-33",[472,4679],{"id":4680,"d":499},"MJX-42-TEX-N-36",[505,4682,4683],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,4684,4685,4690],{"dataMmlNode":512},[505,4686,4687],{"dataMmlNode":540},[520,4688],{"dataC":544,"xLinkHref":4689},"#MJX-42-TEX-N-2B",[505,4691,4692,4697],{"dataMmlNode":515,"transform":754},[505,4693,4694],{"dataMmlNode":518},[520,4695],{"dataC":959,"xLinkHref":4696},"#MJX-42-TEX-N-33",[505,4698,4699],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,4700,4701,4703],{"dataMmlNode":518},[520,4702],{"dataC":959,"xLinkHref":4696},[520,4704],{"dataC":599,"xLinkHref":4705,"transform":537},"#MJX-42-TEX-N-36",[673,4707,4708],{},"Степень = 36, знак \"+\"",[673,4710,4711],{},"1 единица(уходит в заём)",[655,4713,4714,4755,4758],{},[673,4715,4716],{},[452,4717,4719],{"className":4718,"jax":456},[455],[458,4720,4721,4732],{"style":460,"xmlns":461,"width":784,"height":463,"role":464,"focusable":465,"viewBox":785,"xmlnsXLink":467},[469,4722,4723,4726,4729],{},[472,4724],{"id":4725,"d":491},"MJX-43-TEX-N-2212",[472,4727],{"id":4728,"d":922},"MJX-43-TEX-N-33",[472,4730],{"id":4731,"d":475},"MJX-43-TEX-N-32",[505,4733,4734],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,4735,4736,4741],{"dataMmlNode":512},[505,4737,4738],{"dataMmlNode":540},[520,4739],{"dataC":568,"xLinkHref":4740},"#MJX-43-TEX-N-2212",[505,4742,4743,4748],{"dataMmlNode":515,"transform":754},[505,4744,4745],{"dataMmlNode":518},[520,4746],{"dataC":959,"xLinkHref":4747},"#MJX-43-TEX-N-33",[505,4749,4750],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,4751,4752],{"dataMmlNode":518},[520,4753],{"dataC":522,"xLinkHref":4754},"#MJX-43-TEX-N-32",[673,4756,4757],{},"Степень = 2, знак \"-\"",[673,4759,4760],{},"36-2=34(двойки)",[402,4762,4763],{},"В задаче нас интересуют только двойки, поэтому количества единиц мы не учитываем, а количество двоек равно 34.",[402,4765,4766],{},[406,4767,4768],{},"Ответ: 34",[444,4770,4772],{"id":4771},"задача-6","Задача 6",[402,4774,4235,4775,4909],{},[452,4776,4778],{"className":4777,"jax":456},[455],[458,4779,4783,4815],{"style":460,"xmlns":461,"width":4780,"height":4781,"role":464,"focusable":465,"viewBox":4782,"xmlnsXLink":467},"24.778ex","2.181ex","0 -882.1 10951.9 964.1",[469,4784,4785,4788,4791,4794,4797,4800,4803,4806,4809,4812],{},[472,4786],{"id":4787,"d":922},"MJX-44-TEX-N-33",[472,4789],{"id":4790,"d":926},"MJX-44-TEX-N-34",[472,4792],{"id":4793,"d":475},"MJX-44-TEX-N-32",[472,4795],{"id":4796,"d":487},"MJX-44-TEX-N-30",[472,4798],{"id":4799,"d":479},"MJX-44-TEX-N-31",[472,4801],{"id":4802,"d":2679},"MJX-44-TEX-N-37",[472,4804],{"id":4805,"d":483},"MJX-44-TEX-N-2B",[472,4807],{"id":4808,"d":2686},"MJX-44-TEX-N-39",[472,4810],{"id":4811,"d":2199},"MJX-44-TEX-N-35",[472,4813],{"id":4814,"d":491},"MJX-44-TEX-N-2212",[505,4816,4817],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,4818,4819,4848,4854,4876,4882,4899,4904],{"dataMmlNode":512},[505,4820,4821,4831],{"dataMmlNode":515},[505,4822,4823,4826,4829],{"dataMmlNode":518},[520,4824],{"dataC":959,"xLinkHref":4825},"#MJX-44-TEX-N-33",[520,4827],{"dataC":963,"xLinkHref":4828,"transform":537},"#MJX-44-TEX-N-34",[520,4830],{"dataC":959,"xLinkHref":4825,"transform":965},[505,4832,4834],{"dataMmlNode":526,"transform":4833,"dataMjxTexclass":528},"translate(1533,404.1) scale(0.707)",[505,4835,4836,4839,4842,4845],{"dataMmlNode":518},[520,4837],{"dataC":522,"xLinkHref":4838},"#MJX-44-TEX-N-32",[520,4840],{"dataC":561,"xLinkHref":4841,"transform":537},"#MJX-44-TEX-N-30",[520,4843],{"dataC":533,"xLinkHref":4844,"transform":965},"#MJX-44-TEX-N-31",[520,4846],{"dataC":2732,"xLinkHref":4847,"transform":968},"#MJX-44-TEX-N-37",[505,4849,4851],{"dataMmlNode":540,"transform":4850},"translate(3219.4,0)",[520,4852],{"dataC":544,"xLinkHref":4853},"#MJX-44-TEX-N-2B",[505,4855,4857,4864],{"dataMmlNode":515,"transform":4856},"translate(4219.7,0)",[505,4858,4859,4861],{"dataMmlNode":518},[520,4860],{"dataC":963,"xLinkHref":4828},[520,4862],{"dataC":2739,"xLinkHref":4863,"transform":537},"#MJX-44-TEX-N-39",[505,4865,4867],{"dataMmlNode":526,"transform":4866,"dataMjxTexclass":528},"translate(1033,404.1) scale(0.707)",[505,4868,4869,4872,4874],{"dataMmlNode":518},[520,4870],{"dataC":2255,"xLinkHref":4871},"#MJX-44-TEX-N-35",[520,4873],{"dataC":561,"xLinkHref":4841,"transform":537},[520,4875],{"dataC":561,"xLinkHref":4841,"transform":965},[505,4877,4879],{"dataMmlNode":540,"transform":4878},"translate(6585.5,0)",[520,4880],{"dataC":568,"xLinkHref":4881},"#MJX-44-TEX-N-2212",[505,4883,4885,4889],{"dataMmlNode":515,"transform":4884},"translate(7585.8,0)",[505,4886,4887],{"dataMmlNode":518},[520,4888],{"dataC":2732,"xLinkHref":4847},[505,4890,4891],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,4892,4893,4895,4897],{"dataMmlNode":518},[520,4894],{"dataC":2732,"xLinkHref":4847},[520,4896],{"dataC":2732,"xLinkHref":4847,"transform":537},[520,4898],{"dataC":2732,"xLinkHref":4847,"transform":965},[505,4900,4902],{"dataMmlNode":540,"transform":4901},"translate(9451.6,0)",[520,4903],{"dataC":544,"xLinkHref":4853},[505,4905,4907],{"dataMmlNode":518,"transform":4906},"translate(10451.9,0)",[520,4908],{"dataC":959,"xLinkHref":4825}," записано в системе счисления с основанием 7. Сколько шестёрок и сколько значащих нулей содержится в этой записи?",[619,4911,622],{"id":4912},"решение-5",[624,4914,627],{"id":4915},"решение-аналитическое-5",[632,4917,4918,5141],{},[635,4919,4920,4921,5140],{},"Представим все числа как степени семёрок: ",[452,4922,4924],{"className":4923,"jax":456},[455],[458,4925,4928,4969],{"style":460,"xmlns":461,"width":4926,"height":4781,"role":464,"focusable":465,"viewBox":4927,"xmlnsXLink":467},"50.608ex","0 -882.1 22368.8 964.1",[469,4929,4930,4933,4936,4939,4942,4945,4948,4951,4954,4957,4960,4963,4966],{},[472,4931],{"id":4932,"d":922},"MJX-45-TEX-N-33",[472,4934],{"id":4935,"d":926},"MJX-45-TEX-N-34",[472,4937],{"id":4938,"d":475},"MJX-45-TEX-N-32",[472,4940],{"id":4941,"d":487},"MJX-45-TEX-N-30",[472,4943],{"id":4944,"d":479},"MJX-45-TEX-N-31",[472,4946],{"id":4947,"d":2679},"MJX-45-TEX-N-37",[472,4949],{"id":4950,"d":483},"MJX-45-TEX-N-2B",[472,4952],{"id":4953,"d":2686},"MJX-45-TEX-N-39",[472,4955],{"id":4956,"d":2199},"MJX-45-TEX-N-35",[472,4958],{"id":4959,"d":491},"MJX-45-TEX-N-2212",[472,4961],{"id":4962,"d":1086},"MJX-45-TEX-N-3D",[472,4964],{"id":4965,"d":499},"MJX-45-TEX-N-36",[472,4967],{"id":4968,"d":1395},"MJX-45-TEX-N-2E",[505,4970,4971],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,4972,4973,5001,5006,5026,5031,5047,5051,5055,5061,5081,5086,5105,5110,5127,5132],{"dataMmlNode":512},[505,4974,4975,4985],{"dataMmlNode":515},[505,4976,4977,4980,4983],{"dataMmlNode":518},[520,4978],{"dataC":959,"xLinkHref":4979},"#MJX-45-TEX-N-33",[520,4981],{"dataC":963,"xLinkHref":4982,"transform":537},"#MJX-45-TEX-N-34",[520,4984],{"dataC":959,"xLinkHref":4979,"transform":965},[505,4986,4987],{"dataMmlNode":526,"transform":4833,"dataMjxTexclass":528},[505,4988,4989,4992,4995,4998],{"dataMmlNode":518},[520,4990],{"dataC":522,"xLinkHref":4991},"#MJX-45-TEX-N-32",[520,4993],{"dataC":561,"xLinkHref":4994,"transform":537},"#MJX-45-TEX-N-30",[520,4996],{"dataC":533,"xLinkHref":4997,"transform":965},"#MJX-45-TEX-N-31",[520,4999],{"dataC":2732,"xLinkHref":5000,"transform":968},"#MJX-45-TEX-N-37",[505,5002,5003],{"dataMmlNode":540,"transform":4850},[520,5004],{"dataC":544,"xLinkHref":5005},"#MJX-45-TEX-N-2B",[505,5007,5008,5015],{"dataMmlNode":515,"transform":4856},[505,5009,5010,5012],{"dataMmlNode":518},[520,5011],{"dataC":963,"xLinkHref":4982},[520,5013],{"dataC":2739,"xLinkHref":5014,"transform":537},"#MJX-45-TEX-N-39",[505,5016,5017],{"dataMmlNode":526,"transform":4866,"dataMjxTexclass":528},[505,5018,5019,5022,5024],{"dataMmlNode":518},[520,5020],{"dataC":2255,"xLinkHref":5021},"#MJX-45-TEX-N-35",[520,5023],{"dataC":561,"xLinkHref":4994,"transform":537},[520,5025],{"dataC":561,"xLinkHref":4994,"transform":965},[505,5027,5028],{"dataMmlNode":540,"transform":4878},[520,5029],{"dataC":568,"xLinkHref":5030},"#MJX-45-TEX-N-2212",[505,5032,5033,5037],{"dataMmlNode":515,"transform":4884},[505,5034,5035],{"dataMmlNode":518},[520,5036],{"dataC":2732,"xLinkHref":5000},[505,5038,5039],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,5040,5041,5043,5045],{"dataMmlNode":518},[520,5042],{"dataC":2732,"xLinkHref":5000},[520,5044],{"dataC":2732,"xLinkHref":5000,"transform":537},[520,5046],{"dataC":2732,"xLinkHref":5000,"transform":965},[505,5048,5049],{"dataMmlNode":540,"transform":4901},[520,5050],{"dataC":544,"xLinkHref":5005},[505,5052,5053],{"dataMmlNode":518,"transform":4906},[520,5054],{"dataC":959,"xLinkHref":4979},[505,5056,5058],{"dataMmlNode":540,"transform":5057},"translate(11229.6,0)",[520,5059],{"dataC":1179,"xLinkHref":5060},"#MJX-45-TEX-N-3D",[505,5062,5064,5068],{"dataMmlNode":515,"transform":5063},"translate(12285.4,0)",[505,5065,5066],{"dataMmlNode":518},[520,5067],{"dataC":2732,"xLinkHref":5000},[505,5069,5070],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,5071,5072,5075,5077,5079],{"dataMmlNode":518},[520,5073],{"dataC":599,"xLinkHref":5074},"#MJX-45-TEX-N-36",[520,5076],{"dataC":561,"xLinkHref":4994,"transform":537},[520,5078],{"dataC":2255,"xLinkHref":5021,"transform":965},[520,5080],{"dataC":533,"xLinkHref":4997,"transform":968},[505,5082,5084],{"dataMmlNode":540,"transform":5083},"translate(14504.9,0)",[520,5085],{"dataC":544,"xLinkHref":5005},[505,5087,5089,5093],{"dataMmlNode":515,"transform":5088},"translate(15505.1,0)",[505,5090,5091],{"dataMmlNode":518},[520,5092],{"dataC":2732,"xLinkHref":5000},[505,5094,5095],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,5096,5097,5099,5101,5103],{"dataMmlNode":518},[520,5098],{"dataC":533,"xLinkHref":4997},[520,5100],{"dataC":561,"xLinkHref":4994,"transform":537},[520,5102],{"dataC":561,"xLinkHref":4994,"transform":965},[520,5104],{"dataC":561,"xLinkHref":4994,"transform":968},[505,5106,5108],{"dataMmlNode":540,"transform":5107},"translate(17724.5,0)",[520,5109],{"dataC":568,"xLinkHref":5030},[505,5111,5113,5117],{"dataMmlNode":515,"transform":5112},"translate(18724.7,0)",[505,5114,5115],{"dataMmlNode":518},[520,5116],{"dataC":2732,"xLinkHref":5000},[505,5118,5119],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,5120,5121,5123,5125],{"dataMmlNode":518},[520,5122],{"dataC":2732,"xLinkHref":5000},[520,5124],{"dataC":2732,"xLinkHref":5000,"transform":537},[520,5126],{"dataC":2732,"xLinkHref":5000,"transform":965},[505,5128,5130],{"dataMmlNode":540,"transform":5129},"translate(20590.6,0)",[520,5131],{"dataC":544,"xLinkHref":5005},[505,5133,5135,5137],{"dataMmlNode":518,"transform":5134},"translate(21590.8,0)",[520,5136],{"dataC":959,"xLinkHref":4979},[520,5138],{"dataC":1487,"xLinkHref":5139,"transform":537},"#MJX-45-TEX-N-2E"," Проверим, что степени записаны в порядке убывания.",[635,5142,5143],{},"Составляем таблицу подсчёта, помня, что знак \"плюс\" добавляет единицы, а знак \"минус\" добавляет шестёрки(\"старшие\" цифры семеричной системы, аналогичные \"девяткам\" в десятичной).",[649,5145,5146,5156],{},[652,5147,5148],{},[655,5149,5150,5152,5154],{},[658,5151,660],{},[658,5153,663],{},[658,5155,2445],{},[668,5157,5158,5218,5275,5324],{},[655,5159,5160,5213,5216],{},[673,5161,5162],{},[452,5163,5165],{"className":5164,"jax":456},[455],[458,5166,5169,5186],{"style":4620,"xmlns":461,"width":1815,"height":5167,"role":464,"focusable":465,"viewBox":5168,"xmlnsXLink":467},"1.937ex","0 -833.9 1997.2 855.9",[469,5170,5171,5174,5177,5180,5183],{},[472,5172],{"id":5173,"d":2679},"MJX-46-TEX-N-37",[472,5175],{"id":5176,"d":499},"MJX-46-TEX-N-36",[472,5178],{"id":5179,"d":487},"MJX-46-TEX-N-30",[472,5181],{"id":5182,"d":2199},"MJX-46-TEX-N-35",[472,5184],{"id":5185,"d":479},"MJX-46-TEX-N-31",[505,5187,5188],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,5189,5190],{"dataMmlNode":512},[505,5191,5192,5197],{"dataMmlNode":515},[505,5193,5194],{"dataMmlNode":518},[520,5195],{"dataC":2732,"xLinkHref":5196},"#MJX-46-TEX-N-37",[505,5198,5199],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,5200,5201,5204,5207,5210],{"dataMmlNode":518},[520,5202],{"dataC":599,"xLinkHref":5203},"#MJX-46-TEX-N-36",[520,5205],{"dataC":561,"xLinkHref":5206,"transform":537},"#MJX-46-TEX-N-30",[520,5208],{"dataC":2255,"xLinkHref":5209,"transform":965},"#MJX-46-TEX-N-35",[520,5211],{"dataC":533,"xLinkHref":5212,"transform":968},"#MJX-46-TEX-N-31",[673,5214,5215],{},"Степень = 6051, знак \"+\"",[673,5217,4660],{},[655,5219,5220,5271,5273],{},[673,5221,5222],{},[452,5223,5225],{"className":5224,"jax":456},[455],[458,5226,5227,5241],{"style":460,"xmlns":461,"width":1874,"height":463,"role":464,"focusable":465,"viewBox":2508,"xmlnsXLink":467},[469,5228,5229,5232,5235,5238],{},[472,5230],{"id":5231,"d":483},"MJX-47-TEX-N-2B",[472,5233],{"id":5234,"d":2679},"MJX-47-TEX-N-37",[472,5236],{"id":5237,"d":479},"MJX-47-TEX-N-31",[472,5239],{"id":5240,"d":487},"MJX-47-TEX-N-30",[505,5242,5243],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,5244,5245,5250],{"dataMmlNode":512},[505,5246,5247],{"dataMmlNode":540},[520,5248],{"dataC":544,"xLinkHref":5249},"#MJX-47-TEX-N-2B",[505,5251,5252,5257],{"dataMmlNode":515,"transform":754},[505,5253,5254],{"dataMmlNode":518},[520,5255],{"dataC":2732,"xLinkHref":5256},"#MJX-47-TEX-N-37",[505,5258,5259],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,5260,5261,5264,5267,5269],{"dataMmlNode":518},[520,5262],{"dataC":533,"xLinkHref":5263},"#MJX-47-TEX-N-31",[520,5265],{"dataC":561,"xLinkHref":5266,"transform":537},"#MJX-47-TEX-N-30",[520,5268],{"dataC":561,"xLinkHref":5266,"transform":965},[520,5270],{"dataC":561,"xLinkHref":5266,"transform":968},[673,5272,2555],{},[673,5274,4711],{},[655,5276,5277,5318,5321],{},[673,5278,5279],{},[452,5280,5282],{"className":5281,"jax":456},[455],[458,5283,5284,5292],{"style":460,"xmlns":461,"width":2567,"height":3906,"role":464,"focusable":465,"viewBox":3907,"xmlnsXLink":467},[469,5285,5286,5289],{},[472,5287],{"id":5288,"d":491},"MJX-48-TEX-N-2212",[472,5290],{"id":5291,"d":2679},"MJX-48-TEX-N-37",[505,5293,5294],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,5295,5296,5301],{"dataMmlNode":512},[505,5297,5298],{"dataMmlNode":540},[520,5299],{"dataC":568,"xLinkHref":5300},"#MJX-48-TEX-N-2212",[505,5302,5303,5308],{"dataMmlNode":515,"transform":754},[505,5304,5305],{"dataMmlNode":518},[520,5306],{"dataC":2732,"xLinkHref":5307},"#MJX-48-TEX-N-37",[505,5309,5310],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,5311,5312,5314,5316],{"dataMmlNode":518},[520,5313],{"dataC":2732,"xLinkHref":5307},[520,5315],{"dataC":2732,"xLinkHref":5307,"transform":537},[520,5317],{"dataC":2732,"xLinkHref":5307,"transform":965},[673,5319,5320],{},"Степень = 777, знак \"-\"",[673,5322,5323],{},"1000-777=223(шестёрки)",[655,5325,5326,5355,5357],{},[673,5327,5328],{},[452,5329,5331],{"className":5330,"jax":456},[455],[458,5332,5333,5341],{"style":460,"xmlns":461,"width":2626,"height":2627,"role":464,"focusable":465,"viewBox":2628,"xmlnsXLink":467},[469,5334,5335,5338],{},[472,5336],{"id":5337,"d":483},"MJX-49-TEX-N-2B",[472,5339],{"id":5340,"d":922},"MJX-49-TEX-N-33",[505,5342,5343],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,5344,5345,5350],{"dataMmlNode":512},[505,5346,5347],{"dataMmlNode":540},[520,5348],{"dataC":544,"xLinkHref":5349},"#MJX-49-TEX-N-2B",[505,5351,5352],{"dataMmlNode":518,"transform":754},[520,5353],{"dataC":959,"xLinkHref":5354},"#MJX-49-TEX-N-33",[673,5356,878],{},[673,5358,5359],{},"1 тройка",[632,5361,5362,5365],{"start":884},[635,5363,5364],{},"Подсчитываем количество шестёрок: их 223.",[635,5366,5367],{},"Подсчитываем количество значащих нулей. Общее число разрядов числа определяется наибольшим значением показателя степени(на 1 больше этого значения), тогда в числе содержится 6051 + 1 = 6052 разряда. Подсчитаем количество всех ненулевых цифр, определяемое как сумма всех цифр, добавляемых каждым слагаемым или вычитаемым, рассмотренным в наибольшей таблице (помня, что одна из добавившихся было единиц была потрачена на заём и, следовательно, превращена в нуль): 1 + 223 + 1 = 225. Тогда количество нулей в числе вычисляется как разность: 6052 - 225 = 5827.",[402,5369,5370],{},[406,5371,5372],{},"Ответ: 223 шестёрки и 5827 нулей.",[444,5374,5376],{"id":5375},"задача-7","Задача 7",[402,5378,5379,5380,5472],{},"Значение выражения ",[452,5381,5383],{"className":5382,"jax":456},[455],[458,5384,5388,5414],{"style":460,"xmlns":461,"width":5385,"height":5386,"role":464,"focusable":465,"viewBox":5387,"xmlnsXLink":467},"15.094ex","2.165ex","0 -875 6671.5 957",[469,5389,5390,5393,5396,5399,5402,5405,5408,5411],{},[472,5391],{"id":5392,"d":922},"MJX-50-TEX-N-33",[472,5394],{"id":5395,"d":926},"MJX-50-TEX-N-34",[472,5397],{"id":5398,"d":499},"MJX-50-TEX-N-36",[472,5400],{"id":5401,"d":491},"MJX-50-TEX-N-2212",[472,5403],{"id":5404,"d":2679},"MJX-50-TEX-N-37",[472,5406],{"id":5407,"d":479},"MJX-50-TEX-N-31",[472,5409],{"id":5410,"d":487},"MJX-50-TEX-N-30",[472,5412],{"id":5413,"d":483},"MJX-50-TEX-N-2B",[505,5415,5416],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,5417,5418,5435,5441,5459,5465],{"dataMmlNode":512},[505,5419,5420,5430],{"dataMmlNode":515},[505,5421,5422,5425,5428],{"dataMmlNode":518},[520,5423],{"dataC":959,"xLinkHref":5424},"#MJX-50-TEX-N-33",[520,5426],{"dataC":963,"xLinkHref":5427,"transform":537},"#MJX-50-TEX-N-34",[520,5429],{"dataC":959,"xLinkHref":5424,"transform":965},[505,5431,5432],{"dataMmlNode":518,"transform":4833},[520,5433],{"dataC":599,"xLinkHref":5434},"#MJX-50-TEX-N-36",[505,5436,5438],{"dataMmlNode":540,"transform":5437},"translate(2158.8,0)",[520,5439],{"dataC":568,"xLinkHref":5440},"#MJX-50-TEX-N-2212",[505,5442,5444,5449],{"dataMmlNode":515,"transform":5443},"translate(3159,0)",[505,5445,5446],{"dataMmlNode":518},[520,5447],{"dataC":2732,"xLinkHref":5448},"#MJX-50-TEX-N-37",[505,5450,5451],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,5452,5453,5456],{"dataMmlNode":518},[520,5454],{"dataC":533,"xLinkHref":5455},"#MJX-50-TEX-N-31",[520,5457],{"dataC":561,"xLinkHref":5458,"transform":537},"#MJX-50-TEX-N-30",[505,5460,5462],{"dataMmlNode":540,"transform":5461},"translate(4671.3,0)",[520,5463],{"dataC":544,"xLinkHref":5464},"#MJX-50-TEX-N-2B",[505,5466,5468,5470],{"dataMmlNode":518,"transform":5467},"translate(5671.5,0)",[520,5469],{"dataC":963,"xLinkHref":5427},[520,5471],{"dataC":2732,"xLinkHref":5448,"transform":537}," записали в системе счисления с основанием 7. Сколько цифр 6 содержится в этой записи?",[619,5474,622],{"id":5475},"решение-6",[624,5477,627],{"id":5478},"решение-аналитическое-6",[632,5480,5481,5741],{},[635,5482,5483,5484],{},"Переписываем два первых числа как указанное в условии основание системы счисления(7) в соответствующей степени. Последнее число (47) в данном случае удобнее представить как (49-2), где число 49 представляем как 7 в квадрате. ",[452,5485,5487],{"className":5486,"jax":456},[455],[458,5488,5492,5536],{"style":1186,"xmlns":461,"width":5489,"height":5490,"role":464,"focusable":465,"viewBox":5491,"xmlnsXLink":467},"58.475ex","2.545ex","0 -875 25845.9 1125",[469,5493,5494,5497,5500,5503,5506,5509,5512,5515,5518,5521,5524,5527,5530,5533],{},[472,5495],{"id":5496,"d":922},"MJX-51-TEX-N-33",[472,5498],{"id":5499,"d":926},"MJX-51-TEX-N-34",[472,5501],{"id":5502,"d":499},"MJX-51-TEX-N-36",[472,5504],{"id":5505,"d":491},"MJX-51-TEX-N-2212",[472,5507],{"id":5508,"d":2679},"MJX-51-TEX-N-37",[472,5510],{"id":5511,"d":479},"MJX-51-TEX-N-31",[472,5513],{"id":5514,"d":487},"MJX-51-TEX-N-30",[472,5516],{"id":5517,"d":483},"MJX-51-TEX-N-2B",[472,5519],{"id":5520,"d":1086},"MJX-51-TEX-N-3D",[472,5522],{"id":5523,"d":1195},"MJX-51-TEX-N-28",[472,5525],{"id":5526,"d":1205},"MJX-51-TEX-N-29",[472,5528],{"id":5529,"d":475},"MJX-51-TEX-N-32",[472,5531],{"id":5532,"d":495},"MJX-51-TEX-N-38",[472,5534],{"id":5535,"d":1395},"MJX-51-TEX-N-2E",[505,5537,5538],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,5539,5540,5557,5562,5579,5584,5590,5596,5601,5612,5624,5629,5644,5649,5661,5666,5671,5676,5692,5697,5712,5717,5728,5733],{"dataMmlNode":512},[505,5541,5542,5552],{"dataMmlNode":515},[505,5543,5544,5547,5550],{"dataMmlNode":518},[520,5545],{"dataC":959,"xLinkHref":5546},"#MJX-51-TEX-N-33",[520,5548],{"dataC":963,"xLinkHref":5549,"transform":537},"#MJX-51-TEX-N-34",[520,5551],{"dataC":959,"xLinkHref":5546,"transform":965},[505,5553,5554],{"dataMmlNode":518,"transform":4833},[520,5555],{"dataC":599,"xLinkHref":5556},"#MJX-51-TEX-N-36",[505,5558,5559],{"dataMmlNode":540,"transform":5437},[520,5560],{"dataC":568,"xLinkHref":5561},"#MJX-51-TEX-N-2212",[505,5563,5564,5569],{"dataMmlNode":515,"transform":5443},[505,5565,5566],{"dataMmlNode":518},[520,5567],{"dataC":2732,"xLinkHref":5568},"#MJX-51-TEX-N-37",[505,5570,5571],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,5572,5573,5576],{"dataMmlNode":518},[520,5574],{"dataC":533,"xLinkHref":5575},"#MJX-51-TEX-N-31",[520,5577],{"dataC":561,"xLinkHref":5578,"transform":537},"#MJX-51-TEX-N-30",[505,5580,5581],{"dataMmlNode":540,"transform":5461},[520,5582],{"dataC":544,"xLinkHref":5583},"#MJX-51-TEX-N-2B",[505,5585,5586,5588],{"dataMmlNode":518,"transform":5467},[520,5587],{"dataC":963,"xLinkHref":5549},[520,5589],{"dataC":2732,"xLinkHref":5568,"transform":537},[505,5591,5593],{"dataMmlNode":540,"transform":5592},"translate(6949.3,0)",[520,5594],{"dataC":1179,"xLinkHref":5595},"#MJX-51-TEX-N-3D",[505,5597,5598],{"dataMmlNode":540,"transform":1597},[520,5599],{"dataC":1229,"xLinkHref":5600},"#MJX-51-TEX-N-28",[505,5602,5604,5608],{"dataMmlNode":515,"transform":5603},"translate(8394.1,0)",[505,5605,5606],{"dataMmlNode":518},[520,5607],{"dataC":2732,"xLinkHref":5568},[505,5609,5610],{"dataMmlNode":518,"transform":527},[520,5611],{"dataC":959,"xLinkHref":5546},[505,5613,5615,5620],{"dataMmlNode":515,"transform":5614},"translate(9330.7,0)",[505,5616,5617],{"dataMmlNode":540},[520,5618],{"dataC":1251,"xLinkHref":5619},"#MJX-51-TEX-N-29",[505,5621,5622],{"dataMmlNode":518,"transform":1255},[520,5623],{"dataC":599,"xLinkHref":5556},[505,5625,5627],{"dataMmlNode":540,"transform":5626},"translate(10378.4,0)",[520,5628],{"dataC":568,"xLinkHref":5561},[505,5630,5632,5636],{"dataMmlNode":515,"transform":5631},"translate(11378.7,0)",[505,5633,5634],{"dataMmlNode":518},[520,5635],{"dataC":2732,"xLinkHref":5568},[505,5637,5638],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,5639,5640,5642],{"dataMmlNode":518},[520,5641],{"dataC":533,"xLinkHref":5575},[520,5643],{"dataC":561,"xLinkHref":5578,"transform":537},[505,5645,5647],{"dataMmlNode":540,"transform":5646},"translate(12891,0)",[520,5648],{"dataC":544,"xLinkHref":5583},[505,5650,5652,5656],{"dataMmlNode":515,"transform":5651},"translate(13891.2,0)",[505,5653,5654],{"dataMmlNode":518},[520,5655],{"dataC":2732,"xLinkHref":5568},[505,5657,5658],{"dataMmlNode":518,"transform":527},[520,5659],{"dataC":522,"xLinkHref":5660},"#MJX-51-TEX-N-32",[505,5662,5664],{"dataMmlNode":540,"transform":5663},"translate(15050,0)",[520,5665],{"dataC":568,"xLinkHref":5561},[505,5667,5669],{"dataMmlNode":518,"transform":5668},"translate(16050.2,0)",[520,5670],{"dataC":522,"xLinkHref":5660},[505,5672,5674],{"dataMmlNode":540,"transform":5673},"translate(16828,0)",[520,5675],{"dataC":1179,"xLinkHref":5595},[505,5677,5679,5683],{"dataMmlNode":515,"transform":5678},"translate(17883.8,0)",[505,5680,5681],{"dataMmlNode":518},[520,5682],{"dataC":2732,"xLinkHref":5568},[505,5684,5685],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,5686,5687,5689],{"dataMmlNode":518},[520,5688],{"dataC":533,"xLinkHref":5575},[520,5690],{"dataC":581,"xLinkHref":5691,"transform":537},"#MJX-51-TEX-N-38",[505,5693,5695],{"dataMmlNode":540,"transform":5694},"translate(19396.1,0)",[520,5696],{"dataC":568,"xLinkHref":5561},[505,5698,5700,5704],{"dataMmlNode":515,"transform":5699},"translate(20396.3,0)",[505,5701,5702],{"dataMmlNode":518},[520,5703],{"dataC":2732,"xLinkHref":5568},[505,5705,5706],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,5707,5708,5710],{"dataMmlNode":518},[520,5709],{"dataC":533,"xLinkHref":5575},[520,5711],{"dataC":561,"xLinkHref":5578,"transform":537},[505,5713,5715],{"dataMmlNode":540,"transform":5714},"translate(21908.6,0)",[520,5716],{"dataC":544,"xLinkHref":5583},[505,5718,5720,5724],{"dataMmlNode":515,"transform":5719},"translate(22908.9,0)",[505,5721,5722],{"dataMmlNode":518},[520,5723],{"dataC":2732,"xLinkHref":5568},[505,5725,5726],{"dataMmlNode":518,"transform":527},[520,5727],{"dataC":522,"xLinkHref":5660},[505,5729,5731],{"dataMmlNode":540,"transform":5730},"translate(24067.6,0)",[520,5732],{"dataC":568,"xLinkHref":5561},[505,5734,5736,5738],{"dataMmlNode":518,"transform":5735},"translate(25067.9,0)",[520,5737],{"dataC":522,"xLinkHref":5660},[520,5739],{"dataC":1487,"xLinkHref":5740,"transform":537},"#MJX-51-TEX-N-2E",[635,5742,3828],{},[649,5744,5745,5755],{},[652,5746,5747],{},[655,5748,5749,5751,5753],{},[658,5750,660],{},[658,5752,663],{},[658,5754,2445],{},[668,5756,5757,5804,5858,5905],{},[655,5758,5759,5799,5802],{},[673,5760,5761],{},[452,5762,5764],{"className":5763,"jax":456},[455],[458,5765,5767,5778],{"style":4620,"xmlns":461,"width":681,"height":5167,"role":464,"focusable":465,"viewBox":5766,"xmlnsXLink":467},"0 -833.9 1290.1 855.9",[469,5768,5769,5772,5775],{},[472,5770],{"id":5771,"d":2679},"MJX-52-TEX-N-37",[472,5773],{"id":5774,"d":479},"MJX-52-TEX-N-31",[472,5776],{"id":5777,"d":495},"MJX-52-TEX-N-38",[505,5779,5780],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,5781,5782],{"dataMmlNode":512},[505,5783,5784,5789],{"dataMmlNode":515},[505,5785,5786],{"dataMmlNode":518},[520,5787],{"dataC":2732,"xLinkHref":5788},"#MJX-52-TEX-N-37",[505,5790,5791],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,5792,5793,5796],{"dataMmlNode":518},[520,5794],{"dataC":533,"xLinkHref":5795},"#MJX-52-TEX-N-31",[520,5797],{"dataC":581,"xLinkHref":5798,"transform":537},"#MJX-52-TEX-N-38",[673,5800,5801],{},"Степень = 18, знак \"+\"",[673,5803,4711],{},[655,5805,5806,5853,5855],{},[673,5807,5808],{},[452,5809,5811],{"className":5810,"jax":456},[455],[458,5812,5813,5827],{"style":460,"xmlns":461,"width":727,"height":463,"role":464,"focusable":465,"viewBox":728,"xmlnsXLink":467},[469,5814,5815,5818,5821,5824],{},[472,5816],{"id":5817,"d":491},"MJX-53-TEX-N-2212",[472,5819],{"id":5820,"d":2679},"MJX-53-TEX-N-37",[472,5822],{"id":5823,"d":479},"MJX-53-TEX-N-31",[472,5825],{"id":5826,"d":487},"MJX-53-TEX-N-30",[505,5828,5829],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,5830,5831,5836],{"dataMmlNode":512},[505,5832,5833],{"dataMmlNode":540},[520,5834],{"dataC":568,"xLinkHref":5835},"#MJX-53-TEX-N-2212",[505,5837,5838,5843],{"dataMmlNode":515,"transform":754},[505,5839,5840],{"dataMmlNode":518},[520,5841],{"dataC":2732,"xLinkHref":5842},"#MJX-53-TEX-N-37",[505,5844,5845],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,5846,5847,5850],{"dataMmlNode":518},[520,5848],{"dataC":533,"xLinkHref":5849},"#MJX-53-TEX-N-31",[520,5851],{"dataC":561,"xLinkHref":5852,"transform":537},"#MJX-53-TEX-N-30",[673,5854,2049],{},[673,5856,5857],{},"18-10=8 шестёрок",[655,5859,5860,5901,5903],{},[673,5861,5862],{},[452,5863,5865],{"className":5864,"jax":456},[455],[458,5866,5867,5878],{"style":460,"xmlns":461,"width":784,"height":463,"role":464,"focusable":465,"viewBox":785,"xmlnsXLink":467},[469,5868,5869,5872,5875],{},[472,5870],{"id":5871,"d":483},"MJX-54-TEX-N-2B",[472,5873],{"id":5874,"d":2679},"MJX-54-TEX-N-37",[472,5876],{"id":5877,"d":475},"MJX-54-TEX-N-32",[505,5879,5880],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,5881,5882,5887],{"dataMmlNode":512},[505,5883,5884],{"dataMmlNode":540},[520,5885],{"dataC":544,"xLinkHref":5886},"#MJX-54-TEX-N-2B",[505,5888,5889,5894],{"dataMmlNode":515,"transform":754},[505,5890,5891],{"dataMmlNode":518},[520,5892],{"dataC":2732,"xLinkHref":5893},"#MJX-54-TEX-N-37",[505,5895,5896],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,5897,5898],{"dataMmlNode":518},[520,5899],{"dataC":522,"xLinkHref":5900},"#MJX-54-TEX-N-32",[673,5902,5320],{},[673,5904,4711],{},[655,5906,5907,5938,5941],{},[673,5908,5909],{},[452,5910,5912],{"className":5911,"jax":456},[455],[458,5913,5916,5924],{"style":460,"xmlns":461,"width":2626,"height":5914,"role":464,"focusable":465,"viewBox":5915,"xmlnsXLink":467},"1.692ex","0 -666 1278 748",[469,5917,5918,5921],{},[472,5919],{"id":5920,"d":491},"MJX-55-TEX-N-2212",[472,5922],{"id":5923,"d":475},"MJX-55-TEX-N-32",[505,5925,5926],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,5927,5928,5933],{"dataMmlNode":512},[505,5929,5930],{"dataMmlNode":540},[520,5931],{"dataC":568,"xLinkHref":5932},"#MJX-55-TEX-N-2212",[505,5934,5935],{"dataMmlNode":518,"transform":754},[520,5936],{"dataC":522,"xLinkHref":5937},"#MJX-55-TEX-N-32",[673,5939,5940],{},"Знак \"-\"",[673,5942,5943],{},"В разряде 0 - \"5\" В разряде 1 - \"6\"",[402,5945,5946],{},"Особое внимание уделяем вычитанию семеричной двойки в последнем, нулевом разряде: здесь при вычитании(7-2) появляется шестёрка, а из разряда 1 производится заём единицы. Поэтому в разряде 1 имеем 7-1=6 и заём из разряда 2, где бывшая там единица заменяется на нуль, и цепочка заёмов на этом прекращается.",[632,5948,5949],{"start":884},[635,5950,5951],{},"Итого получили: 8 + 1 = 9 шестёрок.",[402,5953,5954],{},[406,5955,5956],{},"Ответ: 9",[444,5958,5960],{"id":5959},"задача-8","Задача 8",[402,5962,5379,5963,6054],{},[452,5964,5966],{"className":5965,"jax":456},[455],[458,5967,5970,5999],{"style":460,"xmlns":461,"width":5968,"height":463,"role":464,"focusable":465,"viewBox":5969,"xmlnsXLink":467},"12.832ex","0 -833.9 5671.5 915.9",[469,5971,5972,5975,5978,5981,5984,5987,5990,5993,5996],{},[472,5973],{"id":5974,"d":2686},"MJX-56-TEX-N-39",[472,5976],{"id":5977,"d":495},"MJX-56-TEX-N-38",[472,5979],{"id":5980,"d":483},"MJX-56-TEX-N-2B",[472,5982],{"id":5983,"d":922},"MJX-56-TEX-N-33",[472,5985],{"id":5986,"d":475},"MJX-56-TEX-N-32",[472,5988],{"id":5989,"d":2199},"MJX-56-TEX-N-35",[472,5991],{"id":5992,"d":491},"MJX-56-TEX-N-2212",[472,5994],{"id":5995,"d":479},"MJX-56-TEX-N-31",[472,5997],{"id":5998,"d":926},"MJX-56-TEX-N-34",[505,6000,6001],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,6002,6003,6015,6021,6039,6045],{"dataMmlNode":512},[505,6004,6005,6010],{"dataMmlNode":515},[505,6006,6007],{"dataMmlNode":518},[520,6008],{"dataC":2739,"xLinkHref":6009},"#MJX-56-TEX-N-39",[505,6011,6012],{"dataMmlNode":518,"transform":527},[520,6013],{"dataC":581,"xLinkHref":6014},"#MJX-56-TEX-N-38",[505,6016,6018],{"dataMmlNode":540,"transform":6017},"translate(1158.8,0)",[520,6019],{"dataC":544,"xLinkHref":6020},"#MJX-56-TEX-N-2B",[505,6022,6024,6029],{"dataMmlNode":515,"transform":6023},"translate(2159,0)",[505,6025,6026],{"dataMmlNode":518},[520,6027],{"dataC":959,"xLinkHref":6028},"#MJX-56-TEX-N-33",[505,6030,6031],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,6032,6033,6036],{"dataMmlNode":518},[520,6034],{"dataC":522,"xLinkHref":6035},"#MJX-56-TEX-N-32",[520,6037],{"dataC":2255,"xLinkHref":6038,"transform":537},"#MJX-56-TEX-N-35",[505,6040,6042],{"dataMmlNode":540,"transform":6041},"translate(3671.3,0)",[520,6043],{"dataC":568,"xLinkHref":6044},"#MJX-56-TEX-N-2212",[505,6046,6048,6051],{"dataMmlNode":518,"transform":6047},"translate(4671.5,0)",[520,6049],{"dataC":533,"xLinkHref":6050},"#MJX-56-TEX-N-31",[520,6052],{"dataC":963,"xLinkHref":6053,"transform":537},"#MJX-56-TEX-N-34"," записали в системе счисления с основанием 3. Найдите сумму цифр в этой записи. Ответ запишите в десятичной системе.",[619,6056,622],{"id":6057},"решение-7",[624,6059,627],{"id":6060},"решение-аналитическое-7",[632,6062,6063,6398],{},[635,6064,6065,6266,6267],{},[452,6066,6068],{"className":6067,"jax":456},[455],[458,6069,6073,6114],{"style":1186,"xmlns":461,"width":6070,"height":6071,"role":464,"focusable":465,"viewBox":6072,"xmlnsXLink":467},"42.267ex","2.452ex","0 -833.9 18682 1083.9",[469,6074,6075,6078,6081,6084,6087,6090,6093,6096,6099,6102,6105,6108,6111],{},[472,6076],{"id":6077,"d":2686},"MJX-57-TEX-N-39",[472,6079],{"id":6080,"d":495},"MJX-57-TEX-N-38",[472,6082],{"id":6083,"d":483},"MJX-57-TEX-N-2B",[472,6085],{"id":6086,"d":922},"MJX-57-TEX-N-33",[472,6088],{"id":6089,"d":475},"MJX-57-TEX-N-32",[472,6091],{"id":6092,"d":2199},"MJX-57-TEX-N-35",[472,6094],{"id":6095,"d":491},"MJX-57-TEX-N-2212",[472,6097],{"id":6098,"d":479},"MJX-57-TEX-N-31",[472,6100],{"id":6101,"d":926},"MJX-57-TEX-N-34",[472,6103],{"id":6104,"d":1086},"MJX-57-TEX-N-3D",[472,6106],{"id":6107,"d":499},"MJX-57-TEX-N-36",[472,6109],{"id":6110,"d":1195},"MJX-57-TEX-N-28",[472,6112],{"id":6113,"d":1205},"MJX-57-TEX-N-29",[505,6115,6116],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,6117,6118,6130,6135,6152,6157,6165,6171,6187,6192,6207,6212,6218,6229,6234,6245,6250,6255,6261],{"dataMmlNode":512},[505,6119,6120,6125],{"dataMmlNode":515},[505,6121,6122],{"dataMmlNode":518},[520,6123],{"dataC":2739,"xLinkHref":6124},"#MJX-57-TEX-N-39",[505,6126,6127],{"dataMmlNode":518,"transform":527},[520,6128],{"dataC":581,"xLinkHref":6129},"#MJX-57-TEX-N-38",[505,6131,6132],{"dataMmlNode":540,"transform":6017},[520,6133],{"dataC":544,"xLinkHref":6134},"#MJX-57-TEX-N-2B",[505,6136,6137,6142],{"dataMmlNode":515,"transform":6023},[505,6138,6139],{"dataMmlNode":518},[520,6140],{"dataC":959,"xLinkHref":6141},"#MJX-57-TEX-N-33",[505,6143,6144],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,6145,6146,6149],{"dataMmlNode":518},[520,6147],{"dataC":522,"xLinkHref":6148},"#MJX-57-TEX-N-32",[520,6150],{"dataC":2255,"xLinkHref":6151,"transform":537},"#MJX-57-TEX-N-35",[505,6153,6154],{"dataMmlNode":540,"transform":6041},[520,6155],{"dataC":568,"xLinkHref":6156},"#MJX-57-TEX-N-2212",[505,6158,6159,6162],{"dataMmlNode":518,"transform":6047},[520,6160],{"dataC":533,"xLinkHref":6161},"#MJX-57-TEX-N-31",[520,6163],{"dataC":963,"xLinkHref":6164,"transform":537},"#MJX-57-TEX-N-34",[505,6166,6168],{"dataMmlNode":540,"transform":6167},"translate(5949.3,0)",[520,6169],{"dataC":1179,"xLinkHref":6170},"#MJX-57-TEX-N-3D",[505,6172,6174,6178],{"dataMmlNode":515,"transform":6173},"translate(7005.1,0)",[505,6175,6176],{"dataMmlNode":518},[520,6177],{"dataC":959,"xLinkHref":6141},[505,6179,6180],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,6181,6182,6184],{"dataMmlNode":518},[520,6183],{"dataC":533,"xLinkHref":6161},[520,6185],{"dataC":599,"xLinkHref":6186,"transform":537},"#MJX-57-TEX-N-36",[505,6188,6190],{"dataMmlNode":540,"transform":6189},"translate(8517.4,0)",[520,6191],{"dataC":544,"xLinkHref":6134},[505,6193,6195,6199],{"dataMmlNode":515,"transform":6194},"translate(9517.7,0)",[505,6196,6197],{"dataMmlNode":518},[520,6198],{"dataC":959,"xLinkHref":6141},[505,6200,6201],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,6202,6203,6205],{"dataMmlNode":518},[520,6204],{"dataC":522,"xLinkHref":6148},[520,6206],{"dataC":2255,"xLinkHref":6151,"transform":537},[505,6208,6210],{"dataMmlNode":540,"transform":6209},"translate(11030,0)",[520,6211],{"dataC":568,"xLinkHref":6156},[505,6213,6215],{"dataMmlNode":540,"transform":6214},"translate(12030.2,0)",[520,6216],{"dataC":1229,"xLinkHref":6217},"#MJX-57-TEX-N-28",[505,6219,6221,6225],{"dataMmlNode":515,"transform":6220},"translate(12419.2,0)",[505,6222,6223],{"dataMmlNode":518},[520,6224],{"dataC":959,"xLinkHref":6141},[505,6226,6227],{"dataMmlNode":518,"transform":527},[520,6228],{"dataC":522,"xLinkHref":6148},[505,6230,6232],{"dataMmlNode":540,"transform":6231},"translate(13578,0)",[520,6233],{"dataC":544,"xLinkHref":6134},[505,6235,6237,6241],{"dataMmlNode":515,"transform":6236},"translate(14578.2,0)",[505,6238,6239],{"dataMmlNode":518},[520,6240],{"dataC":959,"xLinkHref":6141},[505,6242,6243],{"dataMmlNode":518,"transform":527},[520,6244],{"dataC":533,"xLinkHref":6161},[505,6246,6248],{"dataMmlNode":540,"transform":6247},"translate(15737,0)",[520,6249],{"dataC":544,"xLinkHref":6134},[505,6251,6253],{"dataMmlNode":518,"transform":6252},"translate(16737.2,0)",[520,6254],{"dataC":522,"xLinkHref":6148},[505,6256,6258],{"dataMmlNode":540,"transform":6257},"translate(17237.2,0)",[520,6259],{"dataC":1251,"xLinkHref":6260},"#MJX-57-TEX-N-29",[505,6262,6264],{"dataMmlNode":540,"transform":6263},"translate(17904,0)",[520,6265],{"dataC":1179,"xLinkHref":6170}," ",[452,6268,6270],{"className":6269,"jax":456},[455],[458,6271,6274,6303],{"style":460,"xmlns":461,"width":6272,"height":463,"role":464,"focusable":465,"viewBox":6273,"xmlnsXLink":467},"25.287ex","0 -833.9 11176.9 915.9",[469,6275,6276,6279,6282,6285,6288,6291,6294,6297,6300],{},[472,6277],{"id":6278,"d":1086},"MJX-58-TEX-N-3D",[472,6280],{"id":6281,"d":922},"MJX-58-TEX-N-33",[472,6283],{"id":6284,"d":475},"MJX-58-TEX-N-32",[472,6286],{"id":6287,"d":2199},"MJX-58-TEX-N-35",[472,6289],{"id":6290,"d":483},"MJX-58-TEX-N-2B",[472,6292],{"id":6293,"d":479},"MJX-58-TEX-N-31",[472,6295],{"id":6296,"d":499},"MJX-58-TEX-N-36",[472,6298],{"id":6299,"d":491},"MJX-58-TEX-N-2212",[472,6301],{"id":6302,"d":1395},"MJX-58-TEX-N-2E",[505,6304,6305],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,6306,6307,6312,6329,6335,6352,6358,6369,6374,6385,6390],{"dataMmlNode":512},[505,6308,6309],{"dataMmlNode":540},[520,6310],{"dataC":1179,"xLinkHref":6311},"#MJX-58-TEX-N-3D",[505,6313,6314,6319],{"dataMmlNode":515,"transform":3116},[505,6315,6316],{"dataMmlNode":518},[520,6317],{"dataC":959,"xLinkHref":6318},"#MJX-58-TEX-N-33",[505,6320,6321],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,6322,6323,6326],{"dataMmlNode":518},[520,6324],{"dataC":522,"xLinkHref":6325},"#MJX-58-TEX-N-32",[520,6327],{"dataC":2255,"xLinkHref":6328,"transform":537},"#MJX-58-TEX-N-35",[505,6330,6332],{"dataMmlNode":540,"transform":6331},"translate(2568.1,0)",[520,6333],{"dataC":544,"xLinkHref":6334},"#MJX-58-TEX-N-2B",[505,6336,6338,6342],{"dataMmlNode":515,"transform":6337},"translate(3568.3,0)",[505,6339,6340],{"dataMmlNode":518},[520,6341],{"dataC":959,"xLinkHref":6318},[505,6343,6344],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,6345,6346,6349],{"dataMmlNode":518},[520,6347],{"dataC":533,"xLinkHref":6348},"#MJX-58-TEX-N-31",[520,6350],{"dataC":599,"xLinkHref":6351,"transform":537},"#MJX-58-TEX-N-36",[505,6353,6355],{"dataMmlNode":540,"transform":6354},"translate(5080.7,0)",[520,6356],{"dataC":568,"xLinkHref":6357},"#MJX-58-TEX-N-2212",[505,6359,6361,6365],{"dataMmlNode":515,"transform":6360},"translate(6080.9,0)",[505,6362,6363],{"dataMmlNode":518},[520,6364],{"dataC":959,"xLinkHref":6318},[505,6366,6367],{"dataMmlNode":518,"transform":527},[520,6368],{"dataC":522,"xLinkHref":6325},[505,6370,6372],{"dataMmlNode":540,"transform":6371},"translate(7239.7,0)",[520,6373],{"dataC":568,"xLinkHref":6357},[505,6375,6377,6381],{"dataMmlNode":515,"transform":6376},"translate(8239.9,0)",[505,6378,6379],{"dataMmlNode":518},[520,6380],{"dataC":959,"xLinkHref":6318},[505,6382,6383],{"dataMmlNode":518,"transform":527},[520,6384],{"dataC":533,"xLinkHref":6348},[505,6386,6388],{"dataMmlNode":540,"transform":6387},"translate(9398.7,0)",[520,6389],{"dataC":568,"xLinkHref":6357},[505,6391,6393,6395],{"dataMmlNode":518,"transform":6392},"translate(10398.9,0)",[520,6394],{"dataC":522,"xLinkHref":6325},[520,6396],{"dataC":1487,"xLinkHref":6397,"transform":537},"#MJX-58-TEX-N-2E",[635,6399,3828],{},[649,6401,6402,6412],{},[652,6403,6404],{},[655,6405,6406,6408,6410],{},[658,6407,660],{},[658,6409,663],{},[658,6411,2445],{},[668,6413,6414,6460,6514,6562,6611],{},[655,6415,6416,6455,6458],{},[673,6417,6418],{},[452,6419,6421],{"className":6420,"jax":456},[455],[458,6422,6423,6434],{"style":4620,"xmlns":461,"width":681,"height":5167,"role":464,"focusable":465,"viewBox":5766,"xmlnsXLink":467},[469,6424,6425,6428,6431],{},[472,6426],{"id":6427,"d":922},"MJX-59-TEX-N-33",[472,6429],{"id":6430,"d":475},"MJX-59-TEX-N-32",[472,6432],{"id":6433,"d":2199},"MJX-59-TEX-N-35",[505,6435,6436],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,6437,6438],{"dataMmlNode":512},[505,6439,6440,6445],{"dataMmlNode":515},[505,6441,6442],{"dataMmlNode":518},[520,6443],{"dataC":959,"xLinkHref":6444},"#MJX-59-TEX-N-33",[505,6446,6447],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,6448,6449,6452],{"dataMmlNode":518},[520,6450],{"dataC":522,"xLinkHref":6451},"#MJX-59-TEX-N-32",[520,6453],{"dataC":2255,"xLinkHref":6454,"transform":537},"#MJX-59-TEX-N-35",[673,6456,6457],{},"Степень = 25, знак \"+\"",[673,6459,4660],{},[655,6461,6462,6509,6512],{},[673,6463,6464],{},[452,6465,6467],{"className":6466,"jax":456},[455],[458,6468,6469,6483],{"style":460,"xmlns":461,"width":727,"height":463,"role":464,"focusable":465,"viewBox":728,"xmlnsXLink":467},[469,6470,6471,6474,6477,6480],{},[472,6472],{"id":6473,"d":483},"MJX-60-TEX-N-2B",[472,6475],{"id":6476,"d":922},"MJX-60-TEX-N-33",[472,6478],{"id":6479,"d":479},"MJX-60-TEX-N-31",[472,6481],{"id":6482,"d":499},"MJX-60-TEX-N-36",[505,6484,6485],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,6486,6487,6492],{"dataMmlNode":512},[505,6488,6489],{"dataMmlNode":540},[520,6490],{"dataC":544,"xLinkHref":6491},"#MJX-60-TEX-N-2B",[505,6493,6494,6499],{"dataMmlNode":515,"transform":754},[505,6495,6496],{"dataMmlNode":518},[520,6497],{"dataC":959,"xLinkHref":6498},"#MJX-60-TEX-N-33",[505,6500,6501],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,6502,6503,6506],{"dataMmlNode":518},[520,6504],{"dataC":533,"xLinkHref":6505},"#MJX-60-TEX-N-31",[520,6507],{"dataC":599,"xLinkHref":6508,"transform":537},"#MJX-60-TEX-N-36",[673,6510,6511],{},"Степень = 16, знак \"+\"",[673,6513,4711],{},[655,6515,6516,6557,6559],{},[673,6517,6518],{},[452,6519,6521],{"className":6520,"jax":456},[455],[458,6522,6523,6534],{"style":460,"xmlns":461,"width":784,"height":463,"role":464,"focusable":465,"viewBox":785,"xmlnsXLink":467},[469,6524,6525,6528,6531],{},[472,6526],{"id":6527,"d":491},"MJX-61-TEX-N-2212",[472,6529],{"id":6530,"d":922},"MJX-61-TEX-N-33",[472,6532],{"id":6533,"d":475},"MJX-61-TEX-N-32",[505,6535,6536],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,6537,6538,6543],{"dataMmlNode":512},[505,6539,6540],{"dataMmlNode":540},[520,6541],{"dataC":568,"xLinkHref":6542},"#MJX-61-TEX-N-2212",[505,6544,6545,6550],{"dataMmlNode":515,"transform":754},[505,6546,6547],{"dataMmlNode":518},[520,6548],{"dataC":959,"xLinkHref":6549},"#MJX-61-TEX-N-33",[505,6551,6552],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,6553,6554],{"dataMmlNode":518},[520,6555],{"dataC":522,"xLinkHref":6556},"#MJX-61-TEX-N-32",[673,6558,4757],{},[673,6560,6561],{},"16-2=14 двоек, одна истрачена на заём — 13 двоек и 1 единица",[655,6563,6564,6605,6608],{},[673,6565,6566],{},[452,6567,6569],{"className":6568,"jax":456},[455],[458,6570,6571,6582],{"style":460,"xmlns":461,"width":784,"height":463,"role":464,"focusable":465,"viewBox":785,"xmlnsXLink":467},[469,6572,6573,6576,6579],{},[472,6574],{"id":6575,"d":491},"MJX-62-TEX-N-2212",[472,6577],{"id":6578,"d":922},"MJX-62-TEX-N-33",[472,6580],{"id":6581,"d":479},"MJX-62-TEX-N-31",[505,6583,6584],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,6585,6586,6591],{"dataMmlNode":512},[505,6587,6588],{"dataMmlNode":540},[520,6589],{"dataC":568,"xLinkHref":6590},"#MJX-62-TEX-N-2212",[505,6592,6593,6598],{"dataMmlNode":515,"transform":754},[505,6594,6595],{"dataMmlNode":518},[520,6596],{"dataC":959,"xLinkHref":6597},"#MJX-62-TEX-N-33",[505,6599,6600],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,6601,6602],{"dataMmlNode":518},[520,6603],{"dataC":533,"xLinkHref":6604},"#MJX-62-TEX-N-31",[673,6606,6607],{},"Степень = 1, знак \"-\"",[673,6609,6610],{},"1 двойка, истрачена на заём — получена 1 единица",[655,6612,6613,6642,6644],{},[673,6614,6615],{},[452,6616,6618],{"className":6617,"jax":456},[455],[458,6619,6620,6628],{"style":460,"xmlns":461,"width":2626,"height":5914,"role":464,"focusable":465,"viewBox":5915,"xmlnsXLink":467},[469,6621,6622,6625],{},[472,6623],{"id":6624,"d":491},"MJX-63-TEX-N-2212",[472,6626],{"id":6627,"d":475},"MJX-63-TEX-N-32",[505,6629,6630],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,6631,6632,6637],{"dataMmlNode":512},[505,6633,6634],{"dataMmlNode":540},[520,6635],{"dataC":568,"xLinkHref":6636},"#MJX-63-TEX-N-2212",[505,6638,6639],{"dataMmlNode":518,"transform":754},[520,6640],{"dataC":522,"xLinkHref":6641},"#MJX-63-TEX-N-32",[673,6643,5940],{},[673,6645,4660],{},[632,6647,6648],{"start":884},[635,6649,6650],{},"Сумма цифр записи: 1 + 0 + 13 ⋅ 2 + 1 + 1 + 1 = 30.",[402,6652,6653],{},[406,6654,6655],{},"Ответ: 30",[402,6657,6658],{},[418,6659,6660],{},"Далее используем язык программирования Python для решения подобных и более сложных задач.",[444,6662,6664],{"id":6663},"задача-9-классическая","Задача 9 (Классическая)",[402,6666,6667,6668,6823],{},"Значение выражения: ",[452,6669,6671],{"className":6670,"jax":456},[455],[458,6672,6676,6715],{"style":460,"xmlns":461,"width":6673,"height":6674,"role":464,"focusable":465,"viewBox":6675,"xmlnsXLink":467},"29.847ex","2.163ex","0 -874 13192.4 956",[469,6677,6678,6681,6685,6688,6691,6694,6697,6700,6703,6706,6709,6712],{},[472,6679],{"id":6680,"d":2679},"MJX-64-TEX-N-37",[472,6682],{"id":6683,"d":6684},"MJX-64-TEX-N-22C5","M78 250Q78 274 95 292T138 310Q162 310 180 294T199 251Q199 226 182 208T139 190T96 207T78 250Z",[472,6686],{"id":6687,"d":499},"MJX-64-TEX-N-36",[472,6689],{"id":6690,"d":2199},"MJX-64-TEX-N-35",[472,6692],{"id":6693,"d":479},"MJX-64-TEX-N-31",[472,6695],{"id":6696,"d":926},"MJX-64-TEX-N-34",[472,6698],{"id":6699,"d":483},"MJX-64-TEX-N-2B",[472,6701],{"id":6702,"d":495},"MJX-64-TEX-N-38",[472,6704],{"id":6705,"d":475},"MJX-64-TEX-N-32",[472,6707],{"id":6708,"d":2686},"MJX-64-TEX-N-39",[472,6710],{"id":6711,"d":491},"MJX-64-TEX-N-2212",[472,6713],{"id":6714,"d":922},"MJX-64-TEX-N-33",[505,6716,6717],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,6718,6719,6724,6730,6756,6762,6768,6773,6795,6801,6806,6811],{"dataMmlNode":512},[505,6720,6721],{"dataMmlNode":518},[520,6722],{"dataC":2732,"xLinkHref":6723},"#MJX-64-TEX-N-37",[505,6725,6726],{"dataMmlNode":540,"transform":2713},[520,6727],{"dataC":6728,"xLinkHref":6729},"22C5","#MJX-64-TEX-N-22C5",[505,6731,6733,6746],{"dataMmlNode":515,"transform":6732},"translate(1222.4,0)",[505,6734,6735,6738,6741,6743],{"dataMmlNode":518},[520,6736],{"dataC":599,"xLinkHref":6737},"#MJX-64-TEX-N-36",[520,6739],{"dataC":2255,"xLinkHref":6740,"transform":537},"#MJX-64-TEX-N-35",[520,6742],{"dataC":599,"xLinkHref":6737,"transform":965},[520,6744],{"dataC":533,"xLinkHref":6745,"transform":968},"#MJX-64-TEX-N-31",[505,6747,6749],{"dataMmlNode":526,"transform":6748,"dataMjxTexclass":528},"translate(2033,393.1) scale(0.707)",[505,6750,6751,6754],{"dataMmlNode":518},[520,6752],{"dataC":963,"xLinkHref":6753},"#MJX-64-TEX-N-34",[520,6755],{"dataC":599,"xLinkHref":6737,"transform":537},[505,6757,6759],{"dataMmlNode":540,"transform":6758},"translate(4234.8,0)",[520,6760],{"dataC":544,"xLinkHref":6761},"#MJX-64-TEX-N-2B",[505,6763,6765],{"dataMmlNode":518,"transform":6764},"translate(5235,0)",[520,6766],{"dataC":581,"xLinkHref":6767},"#MJX-64-TEX-N-38",[505,6769,6771],{"dataMmlNode":540,"transform":6770},"translate(5957.2,0)",[520,6772],{"dataC":6728,"xLinkHref":6729},[505,6774,6776,6786],{"dataMmlNode":515,"transform":6775},"translate(6457.4,0)",[505,6777,6778,6780,6783],{"dataMmlNode":518},[520,6779],{"dataC":2732,"xLinkHref":6723},[520,6781],{"dataC":522,"xLinkHref":6782,"transform":537},"#MJX-64-TEX-N-32",[520,6784],{"dataC":2739,"xLinkHref":6785,"transform":965},"#MJX-64-TEX-N-39",[505,6787,6789],{"dataMmlNode":526,"transform":6788,"dataMjxTexclass":528},"translate(1533,403.1) scale(0.707)",[505,6790,6791,6793],{"dataMmlNode":518},[520,6792],{"dataC":533,"xLinkHref":6745},[520,6794],{"dataC":2255,"xLinkHref":6740,"transform":537},[505,6796,6798],{"dataMmlNode":540,"transform":6797},"translate(8969.8,0)",[520,6799],{"dataC":568,"xLinkHref":6800},"#MJX-64-TEX-N-2212",[505,6802,6804],{"dataMmlNode":518,"transform":6803},"translate(9970,0)",[520,6805],{"dataC":599,"xLinkHref":6737},[505,6807,6809],{"dataMmlNode":540,"transform":6808},"translate(10692.2,0)",[520,6810],{"dataC":6728,"xLinkHref":6729},[505,6812,6814,6816,6818,6821],{"dataMmlNode":518,"transform":6813},"translate(11192.4,0)",[520,6815],{"dataC":2255,"xLinkHref":6740},[520,6817],{"dataC":581,"xLinkHref":6767,"transform":537},[520,6819],{"dataC":959,"xLinkHref":6820,"transform":965},"#MJX-64-TEX-N-33",[520,6822],{"dataC":522,"xLinkHref":6782,"transform":968}," записано в системе счисления с основанием 9. Сколько цифр 7 имеется в этой записи?",[619,6825,622],{"id":6826},"решение-8",[624,6828,6830],{"id":6829},"решение-на-python","Решение на Python",[6832,6833,6838],"pre",{"className":6834,"code":6835,"language":6836,"meta":6837,"style":6837},"language-python shiki shiki-themes github-light","f = 7 * 6561**46 + 8 * 729**15 - 6 * 5832\nc = 0\nwhile f > 0:\n    if f % 9 == 7:\n        c += 1\n    f \u002F\u002F= 9\nprint(c)\n","python","",[6839,6840,6841,6897,6908,6925,6945,6957,6969],"code",{"__ignoreMap":6837},[6842,6843,6846,6850,6854,6858,6861,6864,6867,6870,6873,6876,6878,6881,6883,6886,6889,6892,6894],"span",{"class":6844,"line":6845},"line",1,[6842,6847,6849],{"class":6848},"sgsFI","f ",[6842,6851,6853],{"class":6852},"sD7c4","=",[6842,6855,6857],{"class":6856},"sYu0t"," 7",[6842,6859,6860],{"class":6852}," *",[6842,6862,6863],{"class":6856}," 6561",[6842,6865,6866],{"class":6852},"**",[6842,6868,6869],{"class":6856},"46",[6842,6871,6872],{"class":6852}," +",[6842,6874,6875],{"class":6856}," 8",[6842,6877,6860],{"class":6852},[6842,6879,6880],{"class":6856}," 729",[6842,6882,6866],{"class":6852},[6842,6884,6885],{"class":6856},"15",[6842,6887,6888],{"class":6852}," -",[6842,6890,6891],{"class":6856}," 6",[6842,6893,6860],{"class":6852},[6842,6895,6896],{"class":6856}," 5832\n",[6842,6898,6900,6903,6905],{"class":6844,"line":6899},2,[6842,6901,6902],{"class":6848},"c ",[6842,6904,6853],{"class":6852},[6842,6906,6907],{"class":6856}," 0\n",[6842,6909,6910,6913,6916,6919,6922],{"class":6844,"line":884},[6842,6911,6912],{"class":6852},"while",[6842,6914,6915],{"class":6848}," f ",[6842,6917,6918],{"class":6852},">",[6842,6920,6921],{"class":6856}," 0",[6842,6923,6924],{"class":6848},":\n",[6842,6926,6927,6930,6932,6935,6938,6941,6943],{"class":6844,"line":4212},[6842,6928,6929],{"class":6852},"    if",[6842,6931,6915],{"class":6848},[6842,6933,6934],{"class":6852},"%",[6842,6936,6937],{"class":6856}," 9",[6842,6939,6940],{"class":6852}," ==",[6842,6942,6857],{"class":6856},[6842,6944,6924],{"class":6848},[6842,6946,6948,6951,6954],{"class":6844,"line":6947},5,[6842,6949,6950],{"class":6848},"        c ",[6842,6952,6953],{"class":6852},"+=",[6842,6955,6956],{"class":6856}," 1\n",[6842,6958,6960,6963,6966],{"class":6844,"line":6959},6,[6842,6961,6962],{"class":6848},"    f ",[6842,6964,6965],{"class":6852},"\u002F\u002F=",[6842,6967,6968],{"class":6856}," 9\n",[6842,6970,6972,6975],{"class":6844,"line":6971},7,[6842,6973,6974],{"class":6856},"print",[6842,6976,6977],{"class":6848},"(c)\n",[402,6979,6980],{},"В переменную f записываем арифметическое выражение. Две звёздочки подряд обозначают возведение в степень. Заводим переменную c, которая будет отвечать за ответ. Сам перевод числа f в девятеричную систему происходит в цикле WHILE.",[402,6982,6983],{},"Вычисляем остатки от деления на 9. Очередная цифра в 9-ричной системе, это и есть остаток при делении f на 9. Если очередной остаток равен нужной цифре \"7\", то мы прибавляем счётчик с. Так же производим целочисленное деление на 9, чтобы остатки менялись. Алгоритм точно такой же, как если бы переводили на листке бумаги делением уголком.",[402,6985,6986],{},"Продолжая данный алгоритм, в переменной f будет рано или поздно ноль.",[402,6988,6989],{},"Важно понимать, что в начале у нас идёт последняя цифра в девятеричной системе, при следующем проходе цикла - предпоследняя и т.д.",[402,6991,6992],{},[406,6993,6994],{},"Ответ: 2",[444,6996,6998],{"id":6997},"задача-10-количество-цифр-превышающих-9","Задача 10 (Количество цифр, превышающих 9)",[402,7000,7001,7002],{},"Определите количество цифр с числовым значением, превышающим 9, в 27-ричной записи числа, заданного выражением: ",[452,7003,7005],{"className":7004,"jax":456},[455],[458,7006,7010,7052],{"style":460,"xmlns":461,"width":7007,"height":7008,"role":464,"focusable":465,"viewBox":7009,"xmlnsXLink":467},"64.703ex","2.18ex","0 -881.8 28598.5 963.8",[469,7011,7012,7015,7019,7022,7025,7028,7031,7034,7037,7040,7043,7046,7049],{},[472,7013],{"id":7014,"d":475},"MJX-65-TEX-N-32",[472,7016],{"id":7017,"d":7018},"MJX-65-TEX-N-2219","M55 251Q55 328 112 386T249 444T386 388T444 249Q444 171 388 113T250 55Q170 55 113 112T55 251Z",[472,7020],{"id":7021,"d":2679},"MJX-65-TEX-N-37",[472,7023],{"id":7024,"d":2686},"MJX-65-TEX-N-39",[472,7026],{"id":7027,"d":487},"MJX-65-TEX-N-30",[472,7029],{"id":7030,"d":479},"MJX-65-TEX-N-31",[472,7032],{"id":7033,"d":926},"MJX-65-TEX-N-34",[472,7035],{"id":7036,"d":483},"MJX-65-TEX-N-2B",[472,7038],{"id":7039,"d":922},"MJX-65-TEX-N-33",[472,7041],{"id":7042,"d":499},"MJX-65-TEX-N-36",[472,7044],{"id":7045,"d":491},"MJX-65-TEX-N-2212",[472,7047],{"id":7048,"d":495},"MJX-65-TEX-N-38",[472,7050],{"id":7051,"d":1395},"MJX-65-TEX-N-2E",[505,7053,7054],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,7055,7056,7061,7067,7095,7101,7106,7111,7136,7142,7147,7152,7174,7179,7184,7189,7211,7216,7221,7226,7245,7250],{"dataMmlNode":512},[505,7057,7058],{"dataMmlNode":518},[520,7059],{"dataC":522,"xLinkHref":7060},"#MJX-65-TEX-N-32",[505,7062,7063],{"dataMmlNode":540,"transform":2713},[520,7064],{"dataC":7065,"xLinkHref":7066},"2219","#MJX-65-TEX-N-2219",[505,7068,7070,7080],{"dataMmlNode":515,"transform":7069},"translate(1444.4,0)",[505,7071,7072,7075,7077],{"dataMmlNode":518},[520,7073],{"dataC":2732,"xLinkHref":7074},"#MJX-65-TEX-N-37",[520,7076],{"dataC":522,"xLinkHref":7060,"transform":537},[520,7078],{"dataC":2739,"xLinkHref":7079,"transform":965},"#MJX-65-TEX-N-39",[505,7081,7082],{"dataMmlNode":526,"transform":6788,"dataMjxTexclass":528},[505,7083,7084,7086,7089,7092],{"dataMmlNode":518},[520,7085],{"dataC":522,"xLinkHref":7060},[520,7087],{"dataC":561,"xLinkHref":7088,"transform":537},"#MJX-65-TEX-N-30",[520,7090],{"dataC":533,"xLinkHref":7091,"transform":965},"#MJX-65-TEX-N-31",[520,7093],{"dataC":963,"xLinkHref":7094,"transform":968},"#MJX-65-TEX-N-34",[505,7096,7098],{"dataMmlNode":540,"transform":7097},"translate(4663.9,0)",[520,7099],{"dataC":544,"xLinkHref":7100},"#MJX-65-TEX-N-2B",[505,7102,7104],{"dataMmlNode":518,"transform":7103},"translate(5664.1,0)",[520,7105],{"dataC":522,"xLinkHref":7060},[505,7107,7109],{"dataMmlNode":540,"transform":7108},"translate(6386.3,0)",[520,7110],{"dataC":7065,"xLinkHref":7066},[505,7112,7114,7123],{"dataMmlNode":515,"transform":7113},"translate(7108.5,0)",[505,7115,7116,7118,7120],{"dataMmlNode":518},[520,7117],{"dataC":522,"xLinkHref":7060},[520,7119],{"dataC":963,"xLinkHref":7094,"transform":537},[520,7121],{"dataC":959,"xLinkHref":7122,"transform":965},"#MJX-65-TEX-N-33",[505,7124,7125],{"dataMmlNode":526,"transform":4833,"dataMjxTexclass":528},[505,7126,7127,7129,7131,7133],{"dataMmlNode":518},[520,7128],{"dataC":522,"xLinkHref":7060},[520,7130],{"dataC":561,"xLinkHref":7088,"transform":537},[520,7132],{"dataC":533,"xLinkHref":7091,"transform":965},[520,7134],{"dataC":599,"xLinkHref":7135,"transform":968},"#MJX-65-TEX-N-36",[505,7137,7139],{"dataMmlNode":540,"transform":7138},"translate(10328,0)",[520,7140],{"dataC":568,"xLinkHref":7141},"#MJX-65-TEX-N-2212",[505,7143,7145],{"dataMmlNode":518,"transform":7144},"translate(11328.2,0)",[520,7146],{"dataC":522,"xLinkHref":7060},[505,7148,7150],{"dataMmlNode":540,"transform":7149},"translate(12050.4,0)",[520,7151],{"dataC":7065,"xLinkHref":7066},[505,7153,7155,7162],{"dataMmlNode":515,"transform":7154},"translate(12772.6,0)",[505,7156,7157,7160],{"dataMmlNode":518},[520,7158],{"dataC":581,"xLinkHref":7159},"#MJX-65-TEX-N-38",[520,7161],{"dataC":533,"xLinkHref":7091,"transform":537},[505,7163,7164],{"dataMmlNode":526,"transform":2863,"dataMjxTexclass":528},[505,7165,7166,7168,7170,7172],{"dataMmlNode":518},[520,7167],{"dataC":522,"xLinkHref":7060},[520,7169],{"dataC":561,"xLinkHref":7088,"transform":537},[520,7171],{"dataC":533,"xLinkHref":7091,"transform":965},[520,7173],{"dataC":581,"xLinkHref":7159,"transform":968},[505,7175,7177],{"dataMmlNode":540,"transform":7176},"translate(15492.1,0)",[520,7178],{"dataC":544,"xLinkHref":7100},[505,7180,7182],{"dataMmlNode":518,"transform":7181},"translate(16492.3,0)",[520,7183],{"dataC":522,"xLinkHref":7060},[505,7185,7187],{"dataMmlNode":540,"transform":7186},"translate(17214.5,0)",[520,7188],{"dataC":7065,"xLinkHref":7066},[505,7190,7192,7198],{"dataMmlNode":515,"transform":7191},"translate(17936.8,0)",[505,7193,7194,7196],{"dataMmlNode":518},[520,7195],{"dataC":522,"xLinkHref":7060},[520,7197],{"dataC":2732,"xLinkHref":7074,"transform":537},[505,7199,7201],{"dataMmlNode":526,"transform":7200,"dataMjxTexclass":528},"translate(1033,403.1) scale(0.707)",[505,7202,7203,7205,7207,7209],{"dataMmlNode":518},[520,7204],{"dataC":522,"xLinkHref":7060},[520,7206],{"dataC":561,"xLinkHref":7088,"transform":537},[520,7208],{"dataC":522,"xLinkHref":7060,"transform":965},[520,7210],{"dataC":561,"xLinkHref":7088,"transform":968},[505,7212,7214],{"dataMmlNode":540,"transform":7213},"translate(20656.2,0)",[520,7215],{"dataC":568,"xLinkHref":7141},[505,7217,7219],{"dataMmlNode":518,"transform":7218},"translate(21656.4,0)",[520,7220],{"dataC":522,"xLinkHref":7060},[505,7222,7224],{"dataMmlNode":540,"transform":7223},"translate(22378.6,0)",[520,7225],{"dataC":7065,"xLinkHref":7066},[505,7227,7229,7233],{"dataMmlNode":515,"transform":7228},"translate(23100.9,0)",[505,7230,7231],{"dataMmlNode":518},[520,7232],{"dataC":2739,"xLinkHref":7079},[505,7234,7235],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,7236,7237,7239,7241,7243],{"dataMmlNode":518},[520,7238],{"dataC":522,"xLinkHref":7060},[520,7240],{"dataC":561,"xLinkHref":7088,"transform":537},[520,7242],{"dataC":522,"xLinkHref":7060,"transform":965},[520,7244],{"dataC":522,"xLinkHref":7060,"transform":968},[505,7246,7248],{"dataMmlNode":540,"transform":7247},"translate(25320.3,0)",[520,7249],{"dataC":568,"xLinkHref":7141},[505,7251,7253,7255,7257,7259,7261],{"dataMmlNode":518,"transform":7252},"translate(26320.5,0)",[520,7254],{"dataC":522,"xLinkHref":7060},[520,7256],{"dataC":561,"xLinkHref":7088,"transform":537},[520,7258],{"dataC":522,"xLinkHref":7060,"transform":965},[520,7260],{"dataC":963,"xLinkHref":7094,"transform":968},[520,7262],{"dataC":1487,"xLinkHref":7263,"transform":1489},"#MJX-65-TEX-N-2E",[619,7265,622],{"id":7266},"решение-9",[624,7268,6830],{"id":7269},"решение-на-python-1",[6832,7271,7273],{"className":6834,"code":7272,"language":6836,"meta":6837,"style":6837},"f = 2 * 729**2014 + 2 * 243**2016 - 2 * 81**2018 + 2 * 27**2020 - 2 * 9**2022 - 2024\nc = 0\nwhile f > 0:\n    if f % 27 > 9:\n        c += 1\n    f \u002F\u002F= 27\nprint(c)\n",[6839,7274,7275,7353,7361,7373,7390,7398,7407],{"__ignoreMap":6837},[6842,7276,7277,7279,7281,7284,7286,7288,7290,7293,7295,7297,7299,7302,7304,7307,7309,7311,7313,7316,7318,7321,7323,7325,7327,7330,7332,7335,7337,7339,7341,7343,7345,7348,7350],{"class":6844,"line":6845},[6842,7278,6849],{"class":6848},[6842,7280,6853],{"class":6852},[6842,7282,7283],{"class":6856}," 2",[6842,7285,6860],{"class":6852},[6842,7287,6880],{"class":6856},[6842,7289,6866],{"class":6852},[6842,7291,7292],{"class":6856},"2014",[6842,7294,6872],{"class":6852},[6842,7296,7283],{"class":6856},[6842,7298,6860],{"class":6852},[6842,7300,7301],{"class":6856}," 243",[6842,7303,6866],{"class":6852},[6842,7305,7306],{"class":6856},"2016",[6842,7308,6888],{"class":6852},[6842,7310,7283],{"class":6856},[6842,7312,6860],{"class":6852},[6842,7314,7315],{"class":6856}," 81",[6842,7317,6866],{"class":6852},[6842,7319,7320],{"class":6856},"2018",[6842,7322,6872],{"class":6852},[6842,7324,7283],{"class":6856},[6842,7326,6860],{"class":6852},[6842,7328,7329],{"class":6856}," 27",[6842,7331,6866],{"class":6852},[6842,7333,7334],{"class":6856},"2020",[6842,7336,6888],{"class":6852},[6842,7338,7283],{"class":6856},[6842,7340,6860],{"class":6852},[6842,7342,6937],{"class":6856},[6842,7344,6866],{"class":6852},[6842,7346,7347],{"class":6856},"2022",[6842,7349,6888],{"class":6852},[6842,7351,7352],{"class":6856}," 2024\n",[6842,7354,7355,7357,7359],{"class":6844,"line":6899},[6842,7356,6902],{"class":6848},[6842,7358,6853],{"class":6852},[6842,7360,6907],{"class":6856},[6842,7362,7363,7365,7367,7369,7371],{"class":6844,"line":884},[6842,7364,6912],{"class":6852},[6842,7366,6915],{"class":6848},[6842,7368,6918],{"class":6852},[6842,7370,6921],{"class":6856},[6842,7372,6924],{"class":6848},[6842,7374,7375,7377,7379,7381,7383,7386,7388],{"class":6844,"line":4212},[6842,7376,6929],{"class":6852},[6842,7378,6915],{"class":6848},[6842,7380,6934],{"class":6852},[6842,7382,7329],{"class":6856},[6842,7384,7385],{"class":6852}," >",[6842,7387,6937],{"class":6856},[6842,7389,6924],{"class":6848},[6842,7391,7392,7394,7396],{"class":6844,"line":6947},[6842,7393,6950],{"class":6848},[6842,7395,6953],{"class":6852},[6842,7397,6956],{"class":6856},[6842,7399,7400,7402,7404],{"class":6844,"line":6959},[6842,7401,6962],{"class":6848},[6842,7403,6965],{"class":6852},[6842,7405,7406],{"class":6856}," 27\n",[6842,7408,7409,7411],{"class":6844,"line":6971},[6842,7410,6974],{"class":6856},[6842,7412,6977],{"class":6848},[402,7414,7415],{},"Решение почти такое же, как в прошлой задаче, но теперь мы подсчитываем только те цифры, которые больше 9.",[402,7417,7418],{},[406,7419,7420],{},"Ответ: 2687",[444,7422,7424],{"id":7423},"задача-11-cумма-цифр","Задача 11 (Cумма цифр)",[402,7426,4235,7427,7522],{},[452,7428,7430],{"className":7429,"jax":456},[455],[458,7431,7434,7457],{"style":460,"xmlns":461,"width":7432,"height":463,"role":464,"focusable":465,"viewBox":7433,"xmlnsXLink":467},"17.231ex","0 -833.9 7616 915.9",[469,7435,7436,7439,7442,7445,7448,7451,7454],{},[472,7437],{"id":7438,"d":2199},"MJX-66-TEX-N-35",[472,7440],{"id":7441,"d":479},"MJX-66-TEX-N-31",[472,7443],{"id":7444,"d":7018},"MJX-66-TEX-N-2219",[472,7446],{"id":7447,"d":2679},"MJX-66-TEX-N-37",[472,7449],{"id":7450,"d":475},"MJX-66-TEX-N-32",[472,7452],{"id":7453,"d":491},"MJX-66-TEX-N-2212",[472,7455],{"id":7456,"d":922},"MJX-66-TEX-N-33",[505,7458,7459],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,7460,7461,7469,7475,7492,7498,7510,7515],{"dataMmlNode":512},[505,7462,7463,7466],{"dataMmlNode":518},[520,7464],{"dataC":2255,"xLinkHref":7465},"#MJX-66-TEX-N-35",[520,7467],{"dataC":533,"xLinkHref":7468,"transform":537},"#MJX-66-TEX-N-31",[505,7470,7472],{"dataMmlNode":540,"transform":7471},"translate(1222.2,0)",[520,7473],{"dataC":7065,"xLinkHref":7474},"#MJX-66-TEX-N-2219",[505,7476,7478,7483],{"dataMmlNode":515,"transform":7477},"translate(1944.4,0)",[505,7479,7480],{"dataMmlNode":518},[520,7481],{"dataC":2732,"xLinkHref":7482},"#MJX-66-TEX-N-37",[505,7484,7485],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,7486,7487,7489],{"dataMmlNode":518},[520,7488],{"dataC":533,"xLinkHref":7468},[520,7490],{"dataC":522,"xLinkHref":7491,"transform":537},"#MJX-66-TEX-N-32",[505,7493,7495],{"dataMmlNode":540,"transform":7494},"translate(3456.8,0)",[520,7496],{"dataC":568,"xLinkHref":7497},"#MJX-66-TEX-N-2212",[505,7499,7501,7505],{"dataMmlNode":515,"transform":7500},"translate(4457,0)",[505,7502,7503],{"dataMmlNode":518},[520,7504],{"dataC":2732,"xLinkHref":7482},[505,7506,7507],{"dataMmlNode":518,"transform":527},[520,7508],{"dataC":959,"xLinkHref":7509},"#MJX-66-TEX-N-33",[505,7511,7513],{"dataMmlNode":540,"transform":7512},"translate(5615.8,0)",[520,7514],{"dataC":568,"xLinkHref":7497},[505,7516,7518,7520],{"dataMmlNode":518,"transform":7517},"translate(6616,0)",[520,7519],{"dataC":522,"xLinkHref":7491},[520,7521],{"dataC":522,"xLinkHref":7491,"transform":537}," записали в системе счисления с основанием 7. В этой записи найдите сумму цифр с числовым значением, превышающим 3.",[619,7524,622],{"id":7525},"решение-10",[624,7527,6830],{"id":7528},"решение-на-python-2",[6832,7530,7532],{"className":6834,"code":7531,"language":6836,"meta":6837,"style":6837},"f = 51 * 7**12 - 7**3 - 22\nsumm = 0\nwhile f > 0:\n    if f % 7 > 3:\n        summ += f % 7\n    f \u002F\u002F= 7\nprint(summ)\n",[6839,7533,7534,7566,7575,7587,7604,7618,7626],{"__ignoreMap":6837},[6842,7535,7536,7538,7540,7543,7545,7547,7549,7552,7554,7556,7558,7561,7563],{"class":6844,"line":6845},[6842,7537,6849],{"class":6848},[6842,7539,6853],{"class":6852},[6842,7541,7542],{"class":6856}," 51",[6842,7544,6860],{"class":6852},[6842,7546,6857],{"class":6856},[6842,7548,6866],{"class":6852},[6842,7550,7551],{"class":6856},"12",[6842,7553,6888],{"class":6852},[6842,7555,6857],{"class":6856},[6842,7557,6866],{"class":6852},[6842,7559,7560],{"class":6856},"3",[6842,7562,6888],{"class":6852},[6842,7564,7565],{"class":6856}," 22\n",[6842,7567,7568,7571,7573],{"class":6844,"line":6899},[6842,7569,7570],{"class":6848},"summ ",[6842,7572,6853],{"class":6852},[6842,7574,6907],{"class":6856},[6842,7576,7577,7579,7581,7583,7585],{"class":6844,"line":884},[6842,7578,6912],{"class":6852},[6842,7580,6915],{"class":6848},[6842,7582,6918],{"class":6852},[6842,7584,6921],{"class":6856},[6842,7586,6924],{"class":6848},[6842,7588,7589,7591,7593,7595,7597,7599,7602],{"class":6844,"line":4212},[6842,7590,6929],{"class":6852},[6842,7592,6915],{"class":6848},[6842,7594,6934],{"class":6852},[6842,7596,6857],{"class":6856},[6842,7598,7385],{"class":6852},[6842,7600,7601],{"class":6856}," 3",[6842,7603,6924],{"class":6848},[6842,7605,7606,7609,7611,7613,7615],{"class":6844,"line":6947},[6842,7607,7608],{"class":6848},"        summ ",[6842,7610,6953],{"class":6852},[6842,7612,6915],{"class":6848},[6842,7614,6934],{"class":6852},[6842,7616,7617],{"class":6856}," 7\n",[6842,7619,7620,7622,7624],{"class":6844,"line":6959},[6842,7621,6962],{"class":6848},[6842,7623,6965],{"class":6852},[6842,7625,7617],{"class":6856},[6842,7627,7628,7630],{"class":6844,"line":6971},[6842,7629,6974],{"class":6856},[6842,7631,7632],{"class":6848},"(summ)\n",[402,7634,7635],{},"Здесь решение похоже на предыдущую задачу. Создаём переменную summ для ответа. Суммируем только те цифры в семеричной системе, которые больше трёх.",[402,7637,7638],{},[406,7639,7640],{},"Ответ: 65",[444,7642,7644],{"id":7643},"задача-12-классическая-второго-типа","Задача 12 (Классическая второго типа)",[402,7646,7647,7648,7800],{},"В выражении ",[406,7649,7650],{},[452,7651,7653],{"className":7652,"jax":456},[455],[458,7654,7659,7701],{"style":7655,"xmlns":461,"width":7656,"height":7657,"role":464,"focusable":465,"viewBox":7658,"xmlnsXLink":467},"vertical-align: -0.375ex;","21.563ex","1.994ex","0 -716 9530.7 881.6",[469,7660,7661,7664,7668,7672,7676,7680,7683,7686,7689,7693,7697],{},[472,7662],{"id":7663,"d":479},"MJX-67-TEX-N-31",[472,7665],{"id":7666,"d":7667},"MJX-67-TEX-I-1D465","M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z",[472,7669],{"id":7670,"d":7671},"MJX-67-TEX-I-1D435","M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z",[472,7673],{"id":7674,"d":7675},"MJX-67-TEX-I-1D434","M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z",[472,7677],{"id":7678,"d":7679},"MJX-67-TEX-I-1D437","M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z",[472,7681],{"id":7682,"d":499},"MJX-67-TEX-N-36",[472,7684],{"id":7685,"d":483},"MJX-67-TEX-N-2B",[472,7687],{"id":7688,"d":475},"MJX-67-TEX-N-32",[472,7690],{"id":7691,"d":7692},"MJX-67-TEX-I-1D436","M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z",[472,7694],{"id":7695,"d":7696},"MJX-67-TEX-I-1D439","M48 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H742Q749 676 749 669Q749 664 736 557T722 447Q720 440 702 440H690Q683 445 683 453Q683 454 686 477T689 530Q689 560 682 579T663 610T626 626T575 633T503 634H480Q398 633 393 631Q388 629 386 623Q385 622 352 492L320 363H375Q378 363 398 363T426 364T448 367T472 374T489 386Q502 398 511 419T524 457T529 475Q532 480 548 480H560Q567 475 567 470Q567 467 536 339T502 207Q500 200 482 200H470Q463 206 463 212Q463 215 468 234T473 274Q473 303 453 310T364 317H309L277 190Q245 66 245 60Q245 46 334 46H359Q365 40 365 39T363 19Q359 6 353 0H336Q295 2 185 2Q120 2 86 2T48 1Z",[472,7698],{"id":7699,"d":7700},"MJX-67-TEX-I-1D438","M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z",[505,7702,7703],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,7704,7705,7710,7717,7724,7731,7751,7757,7763,7770,7775,7782],{"dataMmlNode":512},[505,7706,7707],{"dataMmlNode":518},[520,7708],{"dataC":533,"xLinkHref":7709},"#MJX-67-TEX-N-31",[505,7711,7713],{"dataMmlNode":7712,"transform":537},"mi",[520,7714],{"dataC":7715,"xLinkHref":7716},"1D465","#MJX-67-TEX-I-1D465",[505,7718,7720],{"dataMmlNode":7712,"transform":7719},"translate(1072,0)",[520,7721],{"dataC":7722,"xLinkHref":7723},"1D435","#MJX-67-TEX-I-1D435",[505,7725,7727],{"dataMmlNode":7712,"transform":7726},"translate(1831,0)",[520,7728],{"dataC":7729,"xLinkHref":7730},"1D434","#MJX-67-TEX-I-1D434",[505,7732,7735,7741],{"dataMmlNode":7733,"transform":7734},"msub","translate(2581,0)",[505,7736,7737],{"dataMmlNode":7712},[520,7738],{"dataC":7739,"xLinkHref":7740},"1D437","#MJX-67-TEX-I-1D437",[505,7742,7744],{"dataMmlNode":526,"transform":7743,"dataMjxTexclass":528},"translate(861,-150) scale(0.707)",[505,7745,7746,7748],{"dataMmlNode":518},[520,7747],{"dataC":533,"xLinkHref":7709},[520,7749],{"dataC":599,"xLinkHref":7750,"transform":537},"#MJX-67-TEX-N-36",[505,7752,7754],{"dataMmlNode":540,"transform":7753},"translate(4421.3,0)",[520,7755],{"dataC":544,"xLinkHref":7756},"#MJX-67-TEX-N-2B",[505,7758,7760],{"dataMmlNode":518,"transform":7759},"translate(5421.6,0)",[520,7761],{"dataC":522,"xLinkHref":7762},"#MJX-67-TEX-N-32",[505,7764,7766],{"dataMmlNode":7712,"transform":7765},"translate(5921.6,0)",[520,7767],{"dataC":7768,"xLinkHref":7769},"1D436","#MJX-67-TEX-I-1D436",[505,7771,7773],{"dataMmlNode":7712,"transform":7772},"translate(6681.6,0)",[520,7774],{"dataC":7715,"xLinkHref":7716},[505,7776,7778],{"dataMmlNode":7712,"transform":7777},"translate(7253.6,0)",[520,7779],{"dataC":7780,"xLinkHref":7781},"1D439","#MJX-67-TEX-I-1D439",[505,7783,7785,7791],{"dataMmlNode":7733,"transform":7784},"translate(8002.6,0)",[505,7786,7787],{"dataMmlNode":7712},[520,7788],{"dataC":7789,"xLinkHref":7790},"1D438","#MJX-67-TEX-I-1D438",[505,7792,7794],{"dataMmlNode":526,"transform":7793,"dataMjxTexclass":528},"translate(771,-150) scale(0.707)",[505,7795,7796,7798],{"dataMmlNode":518},[520,7797],{"dataC":533,"xLinkHref":7709},[520,7799],{"dataC":599,"xLinkHref":7750,"transform":537}," x обозначает некоторую цифру из алфавита шестнадцатеричной системы счисления. Определите наименьшее значение x, при котором значение данного выражения кратно 15. Для найденного x вычислите частное от деления данного выражения на 15 и запишите его в ответе в десятичной системе счисления.",[619,7802,622],{"id":7803},"решение-11",[624,7805,6830],{"id":7806},"решение-на-python-3",[402,7808,7809],{},"Необходимо перебирать каждую цифру из шестнадцатеричной системы (0-15) с помощью цикла. Нас будут интересовать те значения x, при котором сумма этих чисел делится на 15.",[6832,7811,7813],{"className":6834,"code":7812,"language":6836,"meta":6837,"style":6837},"for x in range(0, 16):\n    a = 13 * 16 ** 0 + 10 * 16 ** 1 + 11 * 16 ** 2 + x * 16 ** 3 + 1 * 16 ** 4\n    b = 14 * 16 ** 0 + 15 * 16 ** 1 + x * 16 ** 2 + 12 * 16 ** 3 + 2 * 16 ** 4\n    if (a + b) % 15 == 0:\n        print(x, (a + b) \u002F\u002F 15)\n",[6839,7814,7815,7843,7916,7984,8007],{"__ignoreMap":6837},[6842,7816,7817,7820,7823,7826,7829,7832,7834,7837,7840],{"class":6844,"line":6845},[6842,7818,7819],{"class":6852},"for",[6842,7821,7822],{"class":6848}," x ",[6842,7824,7825],{"class":6852},"in",[6842,7827,7828],{"class":6856}," range",[6842,7830,7831],{"class":6848},"(",[6842,7833,508],{"class":6856},[6842,7835,7836],{"class":6848},", ",[6842,7838,7839],{"class":6856},"16",[6842,7841,7842],{"class":6848},"):\n",[6842,7844,7845,7848,7850,7853,7855,7858,7861,7863,7865,7868,7870,7872,7874,7877,7879,7882,7884,7886,7888,7890,7892,7894,7897,7899,7901,7903,7905,7907,7909,7911,7913],{"class":6844,"line":6899},[6842,7846,7847],{"class":6848},"    a ",[6842,7849,6853],{"class":6852},[6842,7851,7852],{"class":6856}," 13",[6842,7854,6860],{"class":6852},[6842,7856,7857],{"class":6856}," 16",[6842,7859,7860],{"class":6852}," **",[6842,7862,6921],{"class":6856},[6842,7864,6872],{"class":6852},[6842,7866,7867],{"class":6856}," 10",[6842,7869,6860],{"class":6852},[6842,7871,7857],{"class":6856},[6842,7873,7860],{"class":6852},[6842,7875,7876],{"class":6856}," 1",[6842,7878,6872],{"class":6852},[6842,7880,7881],{"class":6856}," 11",[6842,7883,6860],{"class":6852},[6842,7885,7857],{"class":6856},[6842,7887,7860],{"class":6852},[6842,7889,7283],{"class":6856},[6842,7891,6872],{"class":6852},[6842,7893,7822],{"class":6848},[6842,7895,7896],{"class":6852},"*",[6842,7898,7857],{"class":6856},[6842,7900,7860],{"class":6852},[6842,7902,7601],{"class":6856},[6842,7904,6872],{"class":6852},[6842,7906,7876],{"class":6856},[6842,7908,6860],{"class":6852},[6842,7910,7857],{"class":6856},[6842,7912,7860],{"class":6852},[6842,7914,7915],{"class":6856}," 4\n",[6842,7917,7918,7921,7923,7926,7928,7930,7932,7934,7936,7939,7941,7943,7945,7947,7949,7951,7953,7955,7957,7959,7961,7964,7966,7968,7970,7972,7974,7976,7978,7980,7982],{"class":6844,"line":884},[6842,7919,7920],{"class":6848},"    b ",[6842,7922,6853],{"class":6852},[6842,7924,7925],{"class":6856}," 14",[6842,7927,6860],{"class":6852},[6842,7929,7857],{"class":6856},[6842,7931,7860],{"class":6852},[6842,7933,6921],{"class":6856},[6842,7935,6872],{"class":6852},[6842,7937,7938],{"class":6856}," 15",[6842,7940,6860],{"class":6852},[6842,7942,7857],{"class":6856},[6842,7944,7860],{"class":6852},[6842,7946,7876],{"class":6856},[6842,7948,6872],{"class":6852},[6842,7950,7822],{"class":6848},[6842,7952,7896],{"class":6852},[6842,7954,7857],{"class":6856},[6842,7956,7860],{"class":6852},[6842,7958,7283],{"class":6856},[6842,7960,6872],{"class":6852},[6842,7962,7963],{"class":6856}," 12",[6842,7965,6860],{"class":6852},[6842,7967,7857],{"class":6856},[6842,7969,7860],{"class":6852},[6842,7971,7601],{"class":6856},[6842,7973,6872],{"class":6852},[6842,7975,7283],{"class":6856},[6842,7977,6860],{"class":6852},[6842,7979,7857],{"class":6856},[6842,7981,7860],{"class":6852},[6842,7983,7915],{"class":6856},[6842,7985,7986,7988,7991,7994,7997,7999,8001,8003,8005],{"class":6844,"line":4212},[6842,7987,6929],{"class":6852},[6842,7989,7990],{"class":6848}," (a ",[6842,7992,7993],{"class":6852},"+",[6842,7995,7996],{"class":6848}," b) ",[6842,7998,6934],{"class":6852},[6842,8000,7938],{"class":6856},[6842,8002,6940],{"class":6852},[6842,8004,6921],{"class":6856},[6842,8006,6924],{"class":6848},[6842,8008,8009,8012,8015,8017,8019,8022,8024],{"class":6844,"line":6947},[6842,8010,8011],{"class":6856},"        print",[6842,8013,8014],{"class":6848},"(x, (a ",[6842,8016,7993],{"class":6852},[6842,8018,7996],{"class":6848},[6842,8020,8021],{"class":6852},"\u002F\u002F",[6842,8023,7938],{"class":6856},[6842,8025,8026],{"class":6848},")\n",[402,8028,8029],{},"Чтобы проверить, делится ли данное выражение на 15, переводим оба слагаемых в нашу родную десятичную систему. В задаче нужно написать для наименьшего найденного значения x результат от деления данной суммы на 15.",[402,8031,8032],{},[406,8033,8034],{},"Ответ: 18341",[444,8036,8038],{"id":8037},"задача-12-две-переменные","Задача 12 (Две переменные)",[402,8040,8041,8042,8212],{},"Числа M и N записаны в системах счисления с основаниями 15 и 13 соответственно.\n",[452,8043,8045],{"className":8044,"jax":456},[455],[458,8046,8051,8096],{"style":8047,"xmlns":461,"width":8048,"height":8049,"role":464,"focusable":465,"viewBox":8050,"xmlnsXLink":467},"vertical-align: -0.464ex;","27.726ex","2.009ex","0 -683 12255 888",[469,8052,8053,8057,8060,8063,8067,8070,8073,8076,8079,8083,8087,8090,8093],{},[472,8054],{"id":8055,"d":8056},"MJX-68-TEX-I-1D440","M289 629Q289 635 232 637Q208 637 201 638T194 648Q194 649 196 659Q197 662 198 666T199 671T201 676T203 679T207 681T212 683T220 683T232 684Q238 684 262 684T307 683Q386 683 398 683T414 678Q415 674 451 396L487 117L510 154Q534 190 574 254T662 394Q837 673 839 675Q840 676 842 678T846 681L852 683H948Q965 683 988 683T1017 684Q1051 684 1051 673Q1051 668 1048 656T1045 643Q1041 637 1008 637Q968 636 957 634T939 623Q936 618 867 340T797 59Q797 55 798 54T805 50T822 48T855 46H886Q892 37 892 35Q892 19 885 5Q880 0 869 0Q864 0 828 1T736 2Q675 2 644 2T609 1Q592 1 592 11Q592 13 594 25Q598 41 602 43T625 46Q652 46 685 49Q699 52 704 61Q706 65 742 207T813 490T848 631L654 322Q458 10 453 5Q451 4 449 3Q444 0 433 0Q418 0 415 7Q413 11 374 317L335 624L267 354Q200 88 200 79Q206 46 272 46H282Q288 41 289 37T286 19Q282 3 278 1Q274 0 267 0Q265 0 255 0T221 1T157 2Q127 2 95 1T58 0Q43 0 39 2T35 11Q35 13 38 25T43 40Q45 46 65 46Q135 46 154 86Q158 92 223 354T289 629Z",[472,8058],{"id":8059,"d":1086},"MJX-68-TEX-N-3D",[472,8061],{"id":8062,"d":475},"MJX-68-TEX-N-32",[472,8064],{"id":8065,"d":8066},"MJX-68-TEX-I-1D466","M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z",[472,8068],{"id":8069,"d":922},"MJX-68-TEX-N-33",[472,8071],{"id":8072,"d":7667},"MJX-68-TEX-I-1D465",[472,8074],{"id":8075,"d":2199},"MJX-68-TEX-N-35",[472,8077],{"id":8078,"d":479},"MJX-68-TEX-N-31",[472,8080],{"id":8081,"d":8082},"MJX-68-TEX-N-2C","M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z",[472,8084],{"id":8085,"d":8086},"MJX-68-TEX-I-1D441","M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z",[472,8088],{"id":8089,"d":499},"MJX-68-TEX-N-36",[472,8091],{"id":8092,"d":2679},"MJX-68-TEX-N-37",[472,8094],{"id":8095,"d":2686},"MJX-68-TEX-N-39",[505,8097,8098],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,8099,8100,8106,8112,8118,8125,8133,8139,8157,8164,8171,8176,8185,8190,8196],{"dataMmlNode":512},[505,8101,8102],{"dataMmlNode":7712},[520,8103],{"dataC":8104,"xLinkHref":8105},"1D440","#MJX-68-TEX-I-1D440",[505,8107,8109],{"dataMmlNode":540,"transform":8108},"translate(1328.8,0)",[520,8110],{"dataC":1179,"xLinkHref":8111},"#MJX-68-TEX-N-3D",[505,8113,8115],{"dataMmlNode":518,"transform":8114},"translate(2384.6,0)",[520,8116],{"dataC":522,"xLinkHref":8117},"#MJX-68-TEX-N-32",[505,8119,8121],{"dataMmlNode":7712,"transform":8120},"translate(2884.6,0)",[520,8122],{"dataC":8123,"xLinkHref":8124},"1D466","#MJX-68-TEX-I-1D466",[505,8126,8128,8130],{"dataMmlNode":518,"transform":8127},"translate(3374.6,0)",[520,8129],{"dataC":522,"xLinkHref":8117},[520,8131],{"dataC":959,"xLinkHref":8132,"transform":537},"#MJX-68-TEX-N-33",[505,8134,8136],{"dataMmlNode":7712,"transform":8135},"translate(4374.6,0)",[520,8137],{"dataC":7715,"xLinkHref":8138},"#MJX-68-TEX-I-1D465",[505,8140,8142,8147],{"dataMmlNode":7733,"transform":8141},"translate(4946.6,0)",[505,8143,8144],{"dataMmlNode":518},[520,8145],{"dataC":2255,"xLinkHref":8146},"#MJX-68-TEX-N-35",[505,8148,8150],{"dataMmlNode":526,"transform":8149,"dataMjxTexclass":528},"translate(533,-150) scale(0.707)",[505,8151,8152,8155],{"dataMmlNode":518},[520,8153],{"dataC":533,"xLinkHref":8154},"#MJX-68-TEX-N-31",[520,8156],{"dataC":2255,"xLinkHref":8146,"transform":537},[505,8158,8160],{"dataMmlNode":540,"transform":8159},"translate(6236.7,0)",[520,8161],{"dataC":8162,"xLinkHref":8163},"2C","#MJX-68-TEX-N-2C",[505,8165,8167],{"dataMmlNode":7712,"transform":8166},"translate(6681.3,0)",[520,8168],{"dataC":8169,"xLinkHref":8170},"1D441","#MJX-68-TEX-I-1D441",[505,8172,8174],{"dataMmlNode":540,"transform":8173},"translate(7847.1,0)",[520,8175],{"dataC":1179,"xLinkHref":8111},[505,8177,8179,8182],{"dataMmlNode":518,"transform":8178},"translate(8902.9,0)",[520,8180],{"dataC":599,"xLinkHref":8181},"#MJX-68-TEX-N-36",[520,8183],{"dataC":2732,"xLinkHref":8184,"transform":537},"#MJX-68-TEX-N-37",[505,8186,8188],{"dataMmlNode":7712,"transform":8187},"translate(9902.9,0)",[520,8189],{"dataC":7715,"xLinkHref":8138},[505,8191,8193],{"dataMmlNode":518,"transform":8192},"translate(10474.9,0)",[520,8194],{"dataC":2739,"xLinkHref":8195},"#MJX-68-TEX-N-39",[505,8197,8199,8203],{"dataMmlNode":7733,"transform":8198},"translate(10974.9,0)",[505,8200,8201],{"dataMmlNode":7712},[520,8202],{"dataC":8123,"xLinkHref":8124},[505,8204,8206],{"dataMmlNode":526,"transform":8205,"dataMjxTexclass":528},"translate(523,-150) scale(0.707)",[505,8207,8208,8210],{"dataMmlNode":518},[520,8209],{"dataC":533,"xLinkHref":8154},[520,8211],{"dataC":959,"xLinkHref":8132,"transform":537},"\nВ записи чисел переменными x и y обозначены допустимые в данных системах счисления неизвестные цифры. Определите наименьшее значение натурального числа A, при котором существуют такие x, y, что M + A кратно N.",[619,8214,622],{"id":8215},"решение-12",[624,8217,6830],{"id":8218},"решение-на-python-4",[6832,8220,8222],{"className":6834,"code":8221,"language":6836,"meta":6837,"style":6837},"for A in range(1, 2000):\n    for x in range(0, 13):\n        for y in range(0, 13):\n            M = 5 * 15 ** 0 + x * 15 ** 1 + 3 * 15 ** 2 + 2 * 15 ** 3 + y * 15 ** 4 + 2 * 15 ** 5\n            N = y * 13 ** 0 + 9 * 13 ** 1 + x * 13 ** 2 + 7 * 13 ** 3 + 6 * 13 ** 4\n            if (M + A) % N == 0:\n                print(A)\n",[6839,8223,8224,8246,8268,8290,8370,8435,8460],{"__ignoreMap":6837},[6842,8225,8226,8228,8231,8233,8235,8237,8239,8241,8244],{"class":6844,"line":6845},[6842,8227,7819],{"class":6852},[6842,8229,8230],{"class":6848}," A ",[6842,8232,7825],{"class":6852},[6842,8234,7828],{"class":6856},[6842,8236,7831],{"class":6848},[6842,8238,717],{"class":6856},[6842,8240,7836],{"class":6848},[6842,8242,8243],{"class":6856},"2000",[6842,8245,7842],{"class":6848},[6842,8247,8248,8251,8253,8255,8257,8259,8261,8263,8266],{"class":6844,"line":6899},[6842,8249,8250],{"class":6852},"    for",[6842,8252,7822],{"class":6848},[6842,8254,7825],{"class":6852},[6842,8256,7828],{"class":6856},[6842,8258,7831],{"class":6848},[6842,8260,508],{"class":6856},[6842,8262,7836],{"class":6848},[6842,8264,8265],{"class":6856},"13",[6842,8267,7842],{"class":6848},[6842,8269,8270,8273,8276,8278,8280,8282,8284,8286,8288],{"class":6844,"line":884},[6842,8271,8272],{"class":6852},"        for",[6842,8274,8275],{"class":6848}," y ",[6842,8277,7825],{"class":6852},[6842,8279,7828],{"class":6856},[6842,8281,7831],{"class":6848},[6842,8283,508],{"class":6856},[6842,8285,7836],{"class":6848},[6842,8287,8265],{"class":6856},[6842,8289,7842],{"class":6848},[6842,8291,8292,8295,8297,8300,8302,8304,8306,8308,8310,8312,8314,8316,8318,8320,8322,8324,8326,8328,8330,8332,8334,8336,8338,8340,8342,8344,8346,8348,8350,8352,8354,8357,8359,8361,8363,8365,8367],{"class":6844,"line":4212},[6842,8293,8294],{"class":6848},"            M ",[6842,8296,6853],{"class":6852},[6842,8298,8299],{"class":6856}," 5",[6842,8301,6860],{"class":6852},[6842,8303,7938],{"class":6856},[6842,8305,7860],{"class":6852},[6842,8307,6921],{"class":6856},[6842,8309,6872],{"class":6852},[6842,8311,7822],{"class":6848},[6842,8313,7896],{"class":6852},[6842,8315,7938],{"class":6856},[6842,8317,7860],{"class":6852},[6842,8319,7876],{"class":6856},[6842,8321,6872],{"class":6852},[6842,8323,7601],{"class":6856},[6842,8325,6860],{"class":6852},[6842,8327,7938],{"class":6856},[6842,8329,7860],{"class":6852},[6842,8331,7283],{"class":6856},[6842,8333,6872],{"class":6852},[6842,8335,7283],{"class":6856},[6842,8337,6860],{"class":6852},[6842,8339,7938],{"class":6856},[6842,8341,7860],{"class":6852},[6842,8343,7601],{"class":6856},[6842,8345,6872],{"class":6852},[6842,8347,8275],{"class":6848},[6842,8349,7896],{"class":6852},[6842,8351,7938],{"class":6856},[6842,8353,7860],{"class":6852},[6842,8355,8356],{"class":6856}," 4",[6842,8358,6872],{"class":6852},[6842,8360,7283],{"class":6856},[6842,8362,6860],{"class":6852},[6842,8364,7938],{"class":6856},[6842,8366,7860],{"class":6852},[6842,8368,8369],{"class":6856}," 5\n",[6842,8371,8372,8375,8377,8379,8381,8383,8385,8387,8389,8391,8393,8395,8397,8399,8401,8403,8405,8407,8409,8411,8413,8415,8417,8419,8421,8423,8425,8427,8429,8431,8433],{"class":6844,"line":6947},[6842,8373,8374],{"class":6848},"            N ",[6842,8376,6853],{"class":6852},[6842,8378,8275],{"class":6848},[6842,8380,7896],{"class":6852},[6842,8382,7852],{"class":6856},[6842,8384,7860],{"class":6852},[6842,8386,6921],{"class":6856},[6842,8388,6872],{"class":6852},[6842,8390,6937],{"class":6856},[6842,8392,6860],{"class":6852},[6842,8394,7852],{"class":6856},[6842,8396,7860],{"class":6852},[6842,8398,7876],{"class":6856},[6842,8400,6872],{"class":6852},[6842,8402,7822],{"class":6848},[6842,8404,7896],{"class":6852},[6842,8406,7852],{"class":6856},[6842,8408,7860],{"class":6852},[6842,8410,7283],{"class":6856},[6842,8412,6872],{"class":6852},[6842,8414,6857],{"class":6856},[6842,8416,6860],{"class":6852},[6842,8418,7852],{"class":6856},[6842,8420,7860],{"class":6852},[6842,8422,7601],{"class":6856},[6842,8424,6872],{"class":6852},[6842,8426,6891],{"class":6856},[6842,8428,6860],{"class":6852},[6842,8430,7852],{"class":6856},[6842,8432,7860],{"class":6852},[6842,8434,7915],{"class":6856},[6842,8436,8437,8440,8443,8445,8448,8450,8453,8456,8458],{"class":6844,"line":6959},[6842,8438,8439],{"class":6852},"            if",[6842,8441,8442],{"class":6848}," (M ",[6842,8444,7993],{"class":6852},[6842,8446,8447],{"class":6848}," A) ",[6842,8449,6934],{"class":6852},[6842,8451,8452],{"class":6848}," N ",[6842,8454,8455],{"class":6852},"==",[6842,8457,6921],{"class":6856},[6842,8459,6924],{"class":6848},[6842,8461,8462,8465],{"class":6844,"line":6971},[6842,8463,8464],{"class":6856},"                print",[6842,8466,8467],{"class":6848},"(A)\n",[402,8469,8470,8471,8474],{},"Нужно найти A, значит, начинаем перебирать эту переменную в цикле. ",[418,8472,8473],{},"Изначально стоит пробовать запускать цикл из небольших верхних пределов значений для range, т.к. нужно найти наименьшее значение."," Идём от 1, т.к. речь идёт о натуральных числах. Перебираем x и y. Они могут принимать значения из алфавита в 13-ой системе. Берём наименьшую систему, т.к. эти переменные есть и в первом числе, и во втором числе.",[402,8476,8477],{},"Если выполняется условие задачи, то нам интересно такое A, при котором это произошло.",[402,8479,8480],{},"В этой задаче A получается достаточно большим, поэтому верхний предел цикла по функции range удалось найти уже при значении 2000.",[402,8482,8483],{},[406,8484,8485],{},"Ответ: 1535",[444,8487,8489],{"id":8488},"задача-13-тренировочная","Задача 13 (Тренировочная)",[402,8491,8492],{},"Укажите через запятую в порядке возрастания все десятичные натуральные числа, не превосходящие 17, запись которых в троичной системе счисления оканчивается на две одинаковые цифры.",[619,8494,622],{"id":8495},"решение-13",[624,8497,6830],{"id":8498},"решение-на-python-5",[6832,8500,8502],{"className":6834,"code":8501,"language":6836,"meta":6837,"style":6837},"for i in range(3, 18):\n    # Последняя цифра в троичной системе\n    last1 = i % 3\n    # Предпоследняя цифра в троичной системе\n    x = i\n    x \u002F\u002F= 3\n    last2 = x % 3\n    if last1 == last2:\n        print(i)\n",[6839,8503,8504,8526,8532,8546,8551,8561,8569,8582,8595],{"__ignoreMap":6837},[6842,8505,8506,8508,8511,8513,8515,8517,8519,8521,8524],{"class":6844,"line":6845},[6842,8507,7819],{"class":6852},[6842,8509,8510],{"class":6848}," i ",[6842,8512,7825],{"class":6852},[6842,8514,7828],{"class":6856},[6842,8516,7831],{"class":6848},[6842,8518,7560],{"class":6856},[6842,8520,7836],{"class":6848},[6842,8522,8523],{"class":6856},"18",[6842,8525,7842],{"class":6848},[6842,8527,8528],{"class":6844,"line":6899},[6842,8529,8531],{"class":8530},"sAwPA","    # Последняя цифра в троичной системе\n",[6842,8533,8534,8537,8539,8541,8543],{"class":6844,"line":884},[6842,8535,8536],{"class":6848},"    last1 ",[6842,8538,6853],{"class":6852},[6842,8540,8510],{"class":6848},[6842,8542,6934],{"class":6852},[6842,8544,8545],{"class":6856}," 3\n",[6842,8547,8548],{"class":6844,"line":4212},[6842,8549,8550],{"class":8530},"    # Предпоследняя цифра в троичной системе\n",[6842,8552,8553,8556,8558],{"class":6844,"line":6947},[6842,8554,8555],{"class":6848},"    x ",[6842,8557,6853],{"class":6852},[6842,8559,8560],{"class":6848}," i\n",[6842,8562,8563,8565,8567],{"class":6844,"line":6959},[6842,8564,8555],{"class":6848},[6842,8566,6965],{"class":6852},[6842,8568,8545],{"class":6856},[6842,8570,8571,8574,8576,8578,8580],{"class":6844,"line":6971},[6842,8572,8573],{"class":6848},"    last2 ",[6842,8575,6853],{"class":6852},[6842,8577,7822],{"class":6848},[6842,8579,6934],{"class":6852},[6842,8581,8545],{"class":6856},[6842,8583,8585,8587,8590,8592],{"class":6844,"line":8584},8,[6842,8586,6929],{"class":6852},[6842,8588,8589],{"class":6848}," last1 ",[6842,8591,8455],{"class":6852},[6842,8593,8594],{"class":6848}," last2:\n",[6842,8596,8598,8600],{"class":6844,"line":8597},9,[6842,8599,8011],{"class":6856},[6842,8601,8602],{"class":6848},"(i)\n",[402,8604,8605],{},"Остаток от деления на 3 - это и есть последняя цифра в троичной системе. Чтобы найти предпоследнюю цифру в троичной системе, нужно выполнить целочисленное деление числа (i) на 3, потом вновь найти остаток от деления.",[402,8607,8608],{},"Используем вспомогательную переменную x, чтобы не изменять значение первоначального числа i. Если выполняется условие задачи, печатаем i, при котором это произошло.",[402,8610,8611],{},"Начинаем перебор цикла с 3, т.к. именно с этого числа представление в троичной системе будет содержать минимум 2 разряда.",[402,8613,8614],{},[406,8615,8616],{},"Ответ: 4, 8, 9, 13, 17",[444,8618,8620],{"id":8619},"задача-14-уравнение","Задача 14 (Уравнение)",[402,8622,8623],{},"Чему равно наименьшее основание позиционной системы счисления x, при котором 225x = 405y? Ответ записать в виде целого числа.",[619,8625,622],{"id":8626},"решение-14",[624,8628,6830],{"id":8629},"решение-на-python-6",[6832,8631,8633],{"className":6834,"code":8632,"language":6836,"meta":6837,"style":6837},"for x in range(2, 16):\n    for y in range(2, 16):\n        a = 5 * x**0 + 2 * x**1 + 2 * x**2\n        b = 5 * y**0 + 0 * y**1 + 4 * y**2\n        if a == b:\n            print(x)\n",[6839,8634,8635,8655,8675,8718,8760,8773],{"__ignoreMap":6837},[6842,8636,8637,8639,8641,8643,8645,8647,8649,8651,8653],{"class":6844,"line":6845},[6842,8638,7819],{"class":6852},[6842,8640,7822],{"class":6848},[6842,8642,7825],{"class":6852},[6842,8644,7828],{"class":6856},[6842,8646,7831],{"class":6848},[6842,8648,881],{"class":6856},[6842,8650,7836],{"class":6848},[6842,8652,7839],{"class":6856},[6842,8654,7842],{"class":6848},[6842,8656,8657,8659,8661,8663,8665,8667,8669,8671,8673],{"class":6844,"line":6899},[6842,8658,8250],{"class":6852},[6842,8660,8275],{"class":6848},[6842,8662,7825],{"class":6852},[6842,8664,7828],{"class":6856},[6842,8666,7831],{"class":6848},[6842,8668,881],{"class":6856},[6842,8670,7836],{"class":6848},[6842,8672,7839],{"class":6856},[6842,8674,7842],{"class":6848},[6842,8676,8677,8680,8682,8684,8686,8689,8691,8693,8695,8697,8699,8701,8703,8705,8707,8709,8711,8713,8715],{"class":6844,"line":884},[6842,8678,8679],{"class":6848},"        a ",[6842,8681,6853],{"class":6852},[6842,8683,8299],{"class":6856},[6842,8685,6860],{"class":6852},[6842,8687,8688],{"class":6848}," x",[6842,8690,6866],{"class":6852},[6842,8692,508],{"class":6856},[6842,8694,6872],{"class":6852},[6842,8696,7283],{"class":6856},[6842,8698,6860],{"class":6852},[6842,8700,8688],{"class":6848},[6842,8702,6866],{"class":6852},[6842,8704,717],{"class":6856},[6842,8706,6872],{"class":6852},[6842,8708,7283],{"class":6856},[6842,8710,6860],{"class":6852},[6842,8712,8688],{"class":6848},[6842,8714,6866],{"class":6852},[6842,8716,8717],{"class":6856},"2\n",[6842,8719,8720,8723,8725,8727,8729,8732,8734,8736,8738,8740,8742,8744,8746,8748,8750,8752,8754,8756,8758],{"class":6844,"line":4212},[6842,8721,8722],{"class":6848},"        b ",[6842,8724,6853],{"class":6852},[6842,8726,8299],{"class":6856},[6842,8728,6860],{"class":6852},[6842,8730,8731],{"class":6848}," y",[6842,8733,6866],{"class":6852},[6842,8735,508],{"class":6856},[6842,8737,6872],{"class":6852},[6842,8739,6921],{"class":6856},[6842,8741,6860],{"class":6852},[6842,8743,8731],{"class":6848},[6842,8745,6866],{"class":6852},[6842,8747,717],{"class":6856},[6842,8749,6872],{"class":6852},[6842,8751,8356],{"class":6856},[6842,8753,6860],{"class":6852},[6842,8755,8731],{"class":6848},[6842,8757,6866],{"class":6852},[6842,8759,8717],{"class":6856},[6842,8761,8762,8765,8768,8770],{"class":6844,"line":6947},[6842,8763,8764],{"class":6852},"        if",[6842,8766,8767],{"class":6848}," a ",[6842,8769,8455],{"class":6852},[6842,8771,8772],{"class":6848}," b:\n",[6842,8774,8775,8778],{"class":6844,"line":6959},[6842,8776,8777],{"class":6856},"            print",[6842,8779,8780],{"class":6848},"(x)\n",[402,8782,8783],{},"Перебираем переменные x и y в циклах в примерном диапазоне от двоичной до шестнадцатеричной систем счисления. Внутри вложенных циклов переведём одно и второе число по правилам 8 класса в десятичную систему. Если числа окажутся равны, печатаем такое значение x, при котором это произошло.",[402,8785,8786],{},[406,8787,8788],{},"Ответ: 8",[444,8790,8792],{"id":8791},"задача-15-последняя-цифра","Задача 15 (Последняя цифра)",[402,8794,8795],{},"Запись числа в девятеричной системе счисления заканчивается цифрой 4. Какой будет последняя цифра в записи этого числа в троичной системе счисления?",[619,8797,622],{"id":8798},"решение-15",[624,8800,6830],{"id":8801},"решение-на-python-7",[6832,8803,8805],{"className":6834,"code":8804,"language":6836,"meta":6837,"style":6837},"for i in range(9, 20):\n    if i % 9 == 4:\n        print(i, i % 3)\n",[6839,8806,8807,8829,8845],{"__ignoreMap":6837},[6842,8808,8809,8811,8813,8815,8817,8819,8822,8824,8827],{"class":6844,"line":6845},[6842,8810,7819],{"class":6852},[6842,8812,8510],{"class":6848},[6842,8814,7825],{"class":6852},[6842,8816,7828],{"class":6856},[6842,8818,7831],{"class":6848},[6842,8820,8821],{"class":6856},"9",[6842,8823,7836],{"class":6848},[6842,8825,8826],{"class":6856},"20",[6842,8828,7842],{"class":6848},[6842,8830,8831,8833,8835,8837,8839,8841,8843],{"class":6844,"line":6899},[6842,8832,6929],{"class":6852},[6842,8834,8510],{"class":6848},[6842,8836,6934],{"class":6852},[6842,8838,6937],{"class":6856},[6842,8840,6940],{"class":6852},[6842,8842,8356],{"class":6856},[6842,8844,6924],{"class":6848},[6842,8846,8847,8849,8852,8854,8856],{"class":6844,"line":884},[6842,8848,8011],{"class":6856},[6842,8850,8851],{"class":6848},"(i, i ",[6842,8853,6934],{"class":6852},[6842,8855,7601],{"class":6856},[6842,8857,8026],{"class":6848},[402,8859,8860],{},"Используем то, что последняя цифра числа в какой-то системе счисления - это и есть остаток от деления этого числа на основание данной системы.",[402,8862,8863],{},[406,8864,8865],{},"Ответ: 1",[444,8867,8869],{"id":8868},"задача-16-окончание-на","Задача 16 (Окончание на)",[402,8871,8872],{},"Укажите через запятую в порядке возрастания все основания систем счисления, в которых запись числа 23 оканчивается на 2.",[619,8874,622],{"id":8875},"решение-16",[624,8877,6830],{"id":8878},"решение-на-python-8",[402,8880,8881],{},"Нужно перебрать все числа от 3 до 23 и определить, какие из них при делении числа 23 дадут остаток 2.",[6832,8883,8885],{"className":6834,"code":8884,"language":6836,"meta":6837,"style":6837},"for n in range(3, 24):\n    if 23 % n == 2:\n        print(n)\n",[6839,8886,8887,8909,8927],{"__ignoreMap":6837},[6842,8888,8889,8891,8894,8896,8898,8900,8902,8904,8907],{"class":6844,"line":6845},[6842,8890,7819],{"class":6852},[6842,8892,8893],{"class":6848}," n ",[6842,8895,7825],{"class":6852},[6842,8897,7828],{"class":6856},[6842,8899,7831],{"class":6848},[6842,8901,7560],{"class":6856},[6842,8903,7836],{"class":6848},[6842,8905,8906],{"class":6856},"24",[6842,8908,7842],{"class":6848},[6842,8910,8911,8913,8916,8919,8921,8923,8925],{"class":6844,"line":6899},[6842,8912,6929],{"class":6852},[6842,8914,8915],{"class":6856}," 23",[6842,8917,8918],{"class":6852}," %",[6842,8920,8893],{"class":6848},[6842,8922,8455],{"class":6852},[6842,8924,7283],{"class":6856},[6842,8926,6924],{"class":6848},[6842,8928,8929,8931],{"class":6844,"line":884},[6842,8930,8011],{"class":6856},[6842,8932,8933],{"class":6848},"(n)\n",[402,8935,8936],{},[406,8937,8938],{},"Ответ: 3, 7, 21",[444,8940,8942],{"id":8941},"задача-17-равенство","Задача 17 (Равенство)",[402,8944,8945],{},"В какой системе счисления выполняется равенство 12 · 13 = 222? В ответе укажите число – основание системы счисления.",[619,8947,622],{"id":8948},"решение-17",[624,8950,6830],{"id":8951},"решение-на-python-9",[402,8953,8954],{},"Если бы мы находились в десятичной системе, то последней цифрой была бы 6 (2 * 3). Но у нас 2! Т.е. cистема счисления меньше или равна 6 и больше или равна 4, т.к. если бы система счисления была больше 6, то у нас была бы 6 последняя цифра.",[6832,8956,8958],{"className":6834,"code":8957,"language":6836,"meta":6837,"style":6837},"def F(num, n):\n    s = ''\n    while num > 0:\n        s += str(num % n)\n        num \u002F\u002F= n\n    return s[::-1]\n\n\nfor x in range(4, 6):\n    a = int(\"12\", x)\n    b = int(\"13\", x)\n    n = F(a * b, x)\n    if n == '222':\n        print(x)\n",[6839,8959,8960,8972,8983,8997,9015,9025,9041,9047,9051,9073,9091,9107,9123,9137],{"__ignoreMap":6837},[6842,8961,8962,8965,8969],{"class":6844,"line":6845},[6842,8963,8964],{"class":6852},"def",[6842,8966,8968],{"class":8967},"s7eDp"," F",[6842,8970,8971],{"class":6848},"(num, n):\n",[6842,8973,8974,8977,8979],{"class":6844,"line":6899},[6842,8975,8976],{"class":6848},"    s ",[6842,8978,6853],{"class":6852},[6842,8980,8982],{"class":8981},"sYBdl"," ''\n",[6842,8984,8985,8988,8991,8993,8995],{"class":6844,"line":884},[6842,8986,8987],{"class":6852},"    while",[6842,8989,8990],{"class":6848}," num ",[6842,8992,6918],{"class":6852},[6842,8994,6921],{"class":6856},[6842,8996,6924],{"class":6848},[6842,8998,8999,9002,9004,9007,9010,9012],{"class":6844,"line":4212},[6842,9000,9001],{"class":6848},"        s ",[6842,9003,6953],{"class":6852},[6842,9005,9006],{"class":6856}," str",[6842,9008,9009],{"class":6848},"(num ",[6842,9011,6934],{"class":6852},[6842,9013,9014],{"class":6848}," n)\n",[6842,9016,9017,9020,9022],{"class":6844,"line":6947},[6842,9018,9019],{"class":6848},"        num ",[6842,9021,6965],{"class":6852},[6842,9023,9024],{"class":6848}," n\n",[6842,9026,9027,9030,9033,9036,9038],{"class":6844,"line":6959},[6842,9028,9029],{"class":6852},"    return",[6842,9031,9032],{"class":6848}," s[::",[6842,9034,9035],{"class":6852},"-",[6842,9037,717],{"class":6856},[6842,9039,9040],{"class":6848},"]\n",[6842,9042,9043],{"class":6844,"line":6971},[6842,9044,9046],{"emptyLinePlaceholder":9045},true,"\n",[6842,9048,9049],{"class":6844,"line":8584},[6842,9050,9046],{"emptyLinePlaceholder":9045},[6842,9052,9053,9055,9057,9059,9061,9063,9066,9068,9071],{"class":6844,"line":8597},[6842,9054,7819],{"class":6852},[6842,9056,7822],{"class":6848},[6842,9058,7825],{"class":6852},[6842,9060,7828],{"class":6856},[6842,9062,7831],{"class":6848},[6842,9064,9065],{"class":6856},"4",[6842,9067,7836],{"class":6848},[6842,9069,9070],{"class":6856},"6",[6842,9072,7842],{"class":6848},[6842,9074,9076,9078,9080,9083,9085,9088],{"class":6844,"line":9075},10,[6842,9077,7847],{"class":6848},[6842,9079,6853],{"class":6852},[6842,9081,9082],{"class":6856}," int",[6842,9084,7831],{"class":6848},[6842,9086,9087],{"class":8981},"\"12\"",[6842,9089,9090],{"class":6848},", x)\n",[6842,9092,9094,9096,9098,9100,9102,9105],{"class":6844,"line":9093},11,[6842,9095,7920],{"class":6848},[6842,9097,6853],{"class":6852},[6842,9099,9082],{"class":6856},[6842,9101,7831],{"class":6848},[6842,9103,9104],{"class":8981},"\"13\"",[6842,9106,9090],{"class":6848},[6842,9108,9110,9113,9115,9118,9120],{"class":6844,"line":9109},12,[6842,9111,9112],{"class":6848},"    n ",[6842,9114,6853],{"class":6852},[6842,9116,9117],{"class":6848}," F(a ",[6842,9119,7896],{"class":6852},[6842,9121,9122],{"class":6848}," b, x)\n",[6842,9124,9126,9128,9130,9132,9135],{"class":6844,"line":9125},13,[6842,9127,6929],{"class":6852},[6842,9129,8893],{"class":6848},[6842,9131,8455],{"class":6852},[6842,9133,9134],{"class":8981}," '222'",[6842,9136,6924],{"class":6848},[6842,9138,9140,9142],{"class":6844,"line":9139},14,[6842,9141,8011],{"class":6856},[6842,9143,8780],{"class":6848},[402,9145,9146],{},"Шестёрка не \"поместилась\" в младший разряд, от неё осталось только 2. Остальные 4 единицы ушли в более старший разряд. Если 4 единицы составляют единицу более старшего разряда, то значит, мы находимся в четверичной системе.",[402,9148,9149],{},[406,9150,9151],{},"Ответ: 4",[444,9153,9155],{"id":9154},"задача-18-основание-системы","Задача 18 (Основание системы)",[402,9157,9158],{},"Запись числа 338 в системе счисления с основанием N содержит 3 цифры и оканчивается на 2. Чему равно максимально возможное основание системы счисления?",[619,9160,622],{"id":9161},"решение-18",[624,9163,6830],{"id":9164},"решение-на-python-10",[6832,9166,9168],{"className":6834,"code":9167,"language":6836,"meta":6837,"style":6837},"def F(num, n):\n    s = ''\n    while num > 0:\n        s += str(num % n)\n        num \u002F\u002F= n\n    return s[::-1]\n\n\nfor x in range(20, 2, -1):\n    num = 338\n    n = F(num, x)\n    if len(n) == 3 and n[-1] == '2':\n        print(x, n)\n        break\n",[6839,9169,9170,9178,9186,9198,9212,9220,9232,9236,9240,9266,9276,9285,9319,9326],{"__ignoreMap":6837},[6842,9171,9172,9174,9176],{"class":6844,"line":6845},[6842,9173,8964],{"class":6852},[6842,9175,8968],{"class":8967},[6842,9177,8971],{"class":6848},[6842,9179,9180,9182,9184],{"class":6844,"line":6899},[6842,9181,8976],{"class":6848},[6842,9183,6853],{"class":6852},[6842,9185,8982],{"class":8981},[6842,9187,9188,9190,9192,9194,9196],{"class":6844,"line":884},[6842,9189,8987],{"class":6852},[6842,9191,8990],{"class":6848},[6842,9193,6918],{"class":6852},[6842,9195,6921],{"class":6856},[6842,9197,6924],{"class":6848},[6842,9199,9200,9202,9204,9206,9208,9210],{"class":6844,"line":4212},[6842,9201,9001],{"class":6848},[6842,9203,6953],{"class":6852},[6842,9205,9006],{"class":6856},[6842,9207,9009],{"class":6848},[6842,9209,6934],{"class":6852},[6842,9211,9014],{"class":6848},[6842,9213,9214,9216,9218],{"class":6844,"line":6947},[6842,9215,9019],{"class":6848},[6842,9217,6965],{"class":6852},[6842,9219,9024],{"class":6848},[6842,9221,9222,9224,9226,9228,9230],{"class":6844,"line":6959},[6842,9223,9029],{"class":6852},[6842,9225,9032],{"class":6848},[6842,9227,9035],{"class":6852},[6842,9229,717],{"class":6856},[6842,9231,9040],{"class":6848},[6842,9233,9234],{"class":6844,"line":6971},[6842,9235,9046],{"emptyLinePlaceholder":9045},[6842,9237,9238],{"class":6844,"line":8584},[6842,9239,9046],{"emptyLinePlaceholder":9045},[6842,9241,9242,9244,9246,9248,9250,9252,9254,9256,9258,9260,9262,9264],{"class":6844,"line":8597},[6842,9243,7819],{"class":6852},[6842,9245,7822],{"class":6848},[6842,9247,7825],{"class":6852},[6842,9249,7828],{"class":6856},[6842,9251,7831],{"class":6848},[6842,9253,8826],{"class":6856},[6842,9255,7836],{"class":6848},[6842,9257,881],{"class":6856},[6842,9259,7836],{"class":6848},[6842,9261,9035],{"class":6852},[6842,9263,717],{"class":6856},[6842,9265,7842],{"class":6848},[6842,9267,9268,9271,9273],{"class":6844,"line":9075},[6842,9269,9270],{"class":6848},"    num ",[6842,9272,6853],{"class":6852},[6842,9274,9275],{"class":6856}," 338\n",[6842,9277,9278,9280,9282],{"class":6844,"line":9093},[6842,9279,9112],{"class":6848},[6842,9281,6853],{"class":6852},[6842,9283,9284],{"class":6848}," F(num, x)\n",[6842,9286,9287,9289,9292,9295,9297,9299,9302,9305,9307,9309,9312,9314,9317],{"class":6844,"line":9109},[6842,9288,6929],{"class":6852},[6842,9290,9291],{"class":6856}," len",[6842,9293,9294],{"class":6848},"(n) ",[6842,9296,8455],{"class":6852},[6842,9298,7601],{"class":6856},[6842,9300,9301],{"class":6852}," and",[6842,9303,9304],{"class":6848}," n[",[6842,9306,9035],{"class":6852},[6842,9308,717],{"class":6856},[6842,9310,9311],{"class":6848},"] ",[6842,9313,8455],{"class":6852},[6842,9315,9316],{"class":8981}," '2'",[6842,9318,6924],{"class":6848},[6842,9320,9321,9323],{"class":6844,"line":9125},[6842,9322,8011],{"class":6856},[6842,9324,9325],{"class":6848},"(x, n)\n",[6842,9327,9328],{"class":6844,"line":9139},[6842,9329,9330],{"class":6852},"        break\n",[624,9332,627],{"id":9333},"решение-аналитическое-8",[402,9335,9336,9337,9400],{},"В данной задаче можно применить формулу: ",[452,9338,9340],{"className":9339,"jax":456},[455],[458,9341,9346,9364],{"style":9342,"xmlns":461,"width":9343,"height":9344,"role":464,"focusable":465,"viewBox":9345,"xmlnsXLink":467},"vertical-align: -0.439ex;","8.25ex","1.984ex","0 -683 3646.5 877",[469,9347,9348,9351,9355,9358,9361],{},[472,9349],{"id":9350,"d":8086},"MJX-69-TEX-I-1D441",[472,9352],{"id":9353,"d":9354},"MJX-69-TEX-I-1D45A","M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z",[472,9356],{"id":9357,"d":491},"MJX-69-TEX-N-2212",[472,9359],{"id":9360,"d":479},"MJX-69-TEX-N-31",[472,9362],{"id":9363,"d":8082},"MJX-69-TEX-N-2C",[505,9365,9366],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,9367,9368,9382,9388,9394],{"dataMmlNode":512},[505,9369,9370,9375],{"dataMmlNode":515},[505,9371,9372],{"dataMmlNode":7712},[520,9373],{"dataC":8169,"xLinkHref":9374},"#MJX-69-TEX-I-1D441",[505,9376,9378],{"dataMmlNode":7712,"transform":9377},"translate(975.3,363) scale(0.707)",[520,9379],{"dataC":9380,"xLinkHref":9381},"1D45A","#MJX-69-TEX-I-1D45A",[505,9383,9385],{"dataMmlNode":540,"transform":9384},"translate(1868.3,0)",[520,9386],{"dataC":568,"xLinkHref":9387},"#MJX-69-TEX-N-2212",[505,9389,9391],{"dataMmlNode":518,"transform":9390},"translate(2868.5,0)",[520,9392],{"dataC":533,"xLinkHref":9393},"#MJX-69-TEX-N-31",[505,9395,9397],{"dataMmlNode":540,"transform":9396},"translate(3368.5,0)",[520,9398],{"dataC":8162,"xLinkHref":9399},"#MJX-69-TEX-N-2C"," где N - основание системы, m - количество разрядов.\nПримером для данной формулы можно взять два разряда в двоичной системе. Максимальное число c двумя разрядами в двоичной системе равно 11. А в десятичной системе это число равно 3, т.е. 2 в 2 степени - 1.",[402,9402,9403,9404,9481,9542,9543,9659],{},"338 число будет точно больше, чем двухзначное число с основанием N. Получается неравенство:\n",[452,9405,9407],{"className":9406,"jax":456},[455],[458,9408,9411,9435],{"style":460,"xmlns":461,"width":9409,"height":463,"role":464,"focusable":465,"viewBox":9410,"xmlnsXLink":467},"13.427ex","0 -833.9 5934.8 915.9",[469,9412,9413,9416,9419,9423,9426,9429,9432],{},[472,9414],{"id":9415,"d":922},"MJX-70-TEX-N-33",[472,9417],{"id":9418,"d":495},"MJX-70-TEX-N-38",[472,9420],{"id":9421,"d":9422},"MJX-70-TEX-N-3E","M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z",[472,9424],{"id":9425,"d":8086},"MJX-70-TEX-I-1D441",[472,9427],{"id":9428,"d":475},"MJX-70-TEX-N-32",[472,9430],{"id":9431,"d":491},"MJX-70-TEX-N-2212",[472,9433],{"id":9434,"d":479},"MJX-70-TEX-N-31",[505,9436,9437],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,9438,9439,9449,9456,9469,9475],{"dataMmlNode":512},[505,9440,9441,9444,9446],{"dataMmlNode":518},[520,9442],{"dataC":959,"xLinkHref":9443},"#MJX-70-TEX-N-33",[520,9445],{"dataC":959,"xLinkHref":9443,"transform":537},[520,9447],{"dataC":581,"xLinkHref":9448,"transform":965},"#MJX-70-TEX-N-38",[505,9450,9452],{"dataMmlNode":540,"transform":9451},"translate(1777.8,0)",[520,9453],{"dataC":9454,"xLinkHref":9455},"3E","#MJX-70-TEX-N-3E",[505,9457,9459,9464],{"dataMmlNode":515,"transform":9458},"translate(2833.6,0)",[505,9460,9461],{"dataMmlNode":7712},[520,9462],{"dataC":8169,"xLinkHref":9463},"#MJX-70-TEX-I-1D441",[505,9465,9466],{"dataMmlNode":518,"transform":9377},[520,9467],{"dataC":522,"xLinkHref":9468},"#MJX-70-TEX-N-32",[505,9470,9472],{"dataMmlNode":540,"transform":9471},"translate(4434.6,0)",[520,9473],{"dataC":568,"xLinkHref":9474},"#MJX-70-TEX-N-2212",[505,9476,9478],{"dataMmlNode":518,"transform":9477},"translate(5434.8,0)",[520,9479],{"dataC":533,"xLinkHref":9480},"#MJX-70-TEX-N-31",[452,9482,9484],{"className":9483,"jax":456},[455],[458,9485,9490,9508],{"style":9486,"xmlns":461,"width":9487,"height":9488,"role":464,"focusable":465,"viewBox":9489,"xmlnsXLink":467},"vertical-align: -0.09ex;","9.53ex","1.977ex","0 -833.9 4212.4 873.9",[469,9491,9492,9495,9498,9502,9505],{},[472,9493],{"id":9494,"d":8086},"MJX-71-TEX-I-1D441",[472,9496],{"id":9497,"d":475},"MJX-71-TEX-N-32",[472,9499],{"id":9500,"d":9501},"MJX-71-TEX-N-3C","M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z",[472,9503],{"id":9504,"d":922},"MJX-71-TEX-N-33",[472,9506],{"id":9507,"d":2686},"MJX-71-TEX-N-39",[505,9509,9510],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,9511,9512,9524,9531],{"dataMmlNode":512},[505,9513,9514,9519],{"dataMmlNode":515},[505,9515,9516],{"dataMmlNode":7712},[520,9517],{"dataC":8169,"xLinkHref":9518},"#MJX-71-TEX-I-1D441",[505,9520,9521],{"dataMmlNode":518,"transform":9377},[520,9522],{"dataC":522,"xLinkHref":9523},"#MJX-71-TEX-N-32",[505,9525,9527],{"dataMmlNode":540,"transform":9526},"translate(1656.6,0)",[520,9528],{"dataC":9529,"xLinkHref":9530},"3C","#MJX-71-TEX-N-3C",[505,9532,9534,9537,9539],{"dataMmlNode":518,"transform":9533},"translate(2712.4,0)",[520,9535],{"dataC":959,"xLinkHref":9536},"#MJX-71-TEX-N-33",[520,9538],{"dataC":959,"xLinkHref":9536,"transform":537},[520,9540],{"dataC":2739,"xLinkHref":9541,"transform":965},"#MJX-71-TEX-N-39","\nN - положительное целое число. Тогда:\n",[452,9544,9546],{"className":9545,"jax":456},[455],[458,9547,9551,9585],{"style":9342,"xmlns":461,"width":9548,"height":9549,"role":464,"focusable":465,"viewBox":9550,"xmlnsXLink":467},"17.766ex","2.587ex","0 -949.5 7852.8 1143.5",[469,9552,9553,9556,9559,9563,9566,9569,9573,9576,9579,9582],{},[472,9554],{"id":9555,"d":8086},"MJX-72-TEX-I-1D441",[472,9557],{"id":9558,"d":9501},"MJX-72-TEX-N-3C",[472,9560],{"id":9561,"d":9562},"MJX-72-TEX-N-221A","M95 178Q89 178 81 186T72 200T103 230T169 280T207 309Q209 311 212 311H213Q219 311 227 294T281 177Q300 134 312 108L397 -77Q398 -77 501 136T707 565T814 786Q820 800 834 800Q841 800 846 794T853 782V776L620 293L385 -193Q381 -200 366 -200Q357 -200 354 -197Q352 -195 256 15L160 225L144 214Q129 202 113 190T95 178Z",[472,9564],{"id":9565,"d":922},"MJX-72-TEX-N-33",[472,9567],{"id":9568,"d":2686},"MJX-72-TEX-N-39",[472,9570],{"id":9571,"d":9572},"MJX-72-TEX-N-2248","M55 319Q55 360 72 393T114 444T163 472T205 482Q207 482 213 482T223 483Q262 483 296 468T393 413L443 381Q502 346 553 346Q609 346 649 375T694 454Q694 465 698 474T708 483Q722 483 722 452Q722 386 675 338T555 289Q514 289 468 310T388 357T308 404T224 426Q164 426 125 393T83 318Q81 289 69 289Q55 289 55 319ZM55 85Q55 126 72 159T114 210T163 238T205 248Q207 248 213 248T223 249Q262 249 296 234T393 179L443 147Q502 112 553 112Q609 112 649 141T694 220Q694 249 708 249T722 217Q722 153 675 104T555 55Q514 55 468 76T388 123T308 170T224 192Q164 192 125 159T83 84Q80 55 69 55Q55 55 55 85Z",[472,9574],{"id":9575,"d":479},"MJX-72-TEX-N-31",[472,9577],{"id":9578,"d":495},"MJX-72-TEX-N-38",[472,9580],{"id":9581,"d":8082},"MJX-72-TEX-N-2C",[472,9583],{"id":9584,"d":926},"MJX-72-TEX-N-34",[505,9586,9587],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,9588,9589,9594,9600,9631,9638,9647,9653],{"dataMmlNode":512},[505,9590,9591],{"dataMmlNode":7712},[520,9592],{"dataC":8169,"xLinkHref":9593},"#MJX-72-TEX-I-1D441",[505,9595,9597],{"dataMmlNode":540,"transform":9596},"translate(1165.8,0)",[520,9598],{"dataC":9529,"xLinkHref":9599},"#MJX-72-TEX-N-3C",[505,9601,9604,9617,9624],{"dataMmlNode":9602,"transform":9603},"msqrt","translate(2221.6,0)",[505,9605,9607],{"transform":9606},"translate(853,0)",[505,9608,9609,9612,9614],{"dataMmlNode":518},[520,9610],{"dataC":959,"xLinkHref":9611},"#MJX-72-TEX-N-33",[520,9613],{"dataC":959,"xLinkHref":9611,"transform":537},[520,9615],{"dataC":2739,"xLinkHref":9616,"transform":965},"#MJX-72-TEX-N-39",[505,9618,9620],{"dataMmlNode":540,"transform":9619},"translate(0,89.5)",[520,9621],{"dataC":9622,"xLinkHref":9623},"221A","#MJX-72-TEX-N-221A",[9625,9626],"rect",{"width":9627,"height":9628,"x":9629,"y":9630},1500,60,"853","829.5",[505,9632,9634],{"dataMmlNode":540,"transform":9633},"translate(4852.3,0)",[520,9635],{"dataC":9636,"xLinkHref":9637},"2248","#MJX-72-TEX-N-2248",[505,9639,9641,9644],{"dataMmlNode":518,"transform":9640},"translate(5908.1,0)",[520,9642],{"dataC":533,"xLinkHref":9643},"#MJX-72-TEX-N-31",[520,9645],{"dataC":581,"xLinkHref":9646,"transform":537},"#MJX-72-TEX-N-38",[505,9648,9650],{"dataMmlNode":540,"transform":9649},"translate(6908.1,0)",[520,9651],{"dataC":8162,"xLinkHref":9652},"#MJX-72-TEX-N-2C",[505,9654,9656],{"dataMmlNode":518,"transform":9655},"translate(7352.8,0)",[520,9657],{"dataC":963,"xLinkHref":9658},"#MJX-72-TEX-N-34",[452,9660,9662],{"className":9661,"jax":456},[455],[458,9663,9668,9683],{"style":9664,"xmlns":461,"width":9665,"height":9666,"role":464,"focusable":465,"viewBox":9667,"xmlnsXLink":467},"vertical-align: -0.312ex;","7.289ex","1.857ex","0 -683 3221.6 821",[469,9669,9670,9673,9677,9680],{},[472,9671],{"id":9672,"d":8086},"MJX-73-TEX-I-1D441",[472,9674],{"id":9675,"d":9676},"MJX-73-TEX-N-2264","M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z",[472,9678],{"id":9679,"d":479},"MJX-73-TEX-N-31",[472,9681],{"id":9682,"d":495},"MJX-73-TEX-N-38",[505,9684,9685],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,9686,9687,9692,9698],{"dataMmlNode":512},[505,9688,9689],{"dataMmlNode":7712},[520,9690],{"dataC":8169,"xLinkHref":9691},"#MJX-73-TEX-I-1D441",[505,9693,9694],{"dataMmlNode":540,"transform":9596},[520,9695],{"dataC":9696,"xLinkHref":9697},"2264","#MJX-73-TEX-N-2264",[505,9699,9700,9703],{"dataMmlNode":518,"transform":9603},[520,9701],{"dataC":533,"xLinkHref":9702},"#MJX-73-TEX-N-31",[520,9704],{"dataC":581,"xLinkHref":9705,"transform":537},"#MJX-73-TEX-N-38",[402,9707,9708],{},"Сказано, что число в системе с основанием N оканчивается на 2. Поэтому первый остаток должен быть равен 2!",[402,9710,9711],{},[464,9712],{"alt":9713,"src":9714},"Задача 18 Решение","\u002Fimages\u002Fblog\u002Fege\u002Ftask14\u002Fimg1.png",[402,9716,9717],{},"Будем идти вниз от числа 18 и проверять, на что делится 336.",[402,9719,9720],{},"Число 336 должно делится на N.",[402,9722,9723],{},"Подошло число 16 (16 * 21 = 336!)",[402,9725,9726],{},[406,9727,9728],{},"Ответ: 16",[444,9730,9732],{"id":9731},"задача-19-выражение-с-x","Задача 19 (Выражение с X)",[402,9734,5379,9735,9831],{},[452,9736,9738],{"className":9737,"jax":456},[455],[458,9739,9742,9769],{"style":460,"xmlns":461,"width":9740,"height":2790,"role":464,"focusable":465,"viewBox":9741,"xmlnsXLink":467},"17.856ex","0 -864 7892.4 946",[469,9743,9744,9747,9750,9753,9756,9759,9762,9765],{},[472,9745],{"id":9746,"d":475},"MJX-74-TEX-N-32",[472,9748],{"id":9749,"d":479},"MJX-74-TEX-N-31",[472,9751],{"id":9752,"d":499},"MJX-74-TEX-N-36",[472,9754],{"id":9755,"d":2199},"MJX-74-TEX-N-35",[472,9757],{"id":9758,"d":483},"MJX-74-TEX-N-2B",[472,9760],{"id":9761,"d":922},"MJX-74-TEX-N-33",[472,9763],{"id":9764,"d":491},"MJX-74-TEX-N-2212",[472,9766],{"id":9767,"d":9768},"MJX-74-TEX-I-1D44B","M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z",[505,9770,9771],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,9772,9773,9792,9797,9808,9814,9819,9824],{"dataMmlNode":512},[505,9774,9775,9786],{"dataMmlNode":515},[505,9776,9777,9780,9783],{"dataMmlNode":518},[520,9778],{"dataC":522,"xLinkHref":9779},"#MJX-74-TEX-N-32",[520,9781],{"dataC":533,"xLinkHref":9782,"transform":537},"#MJX-74-TEX-N-31",[520,9784],{"dataC":599,"xLinkHref":9785,"transform":965},"#MJX-74-TEX-N-36",[505,9787,9789],{"dataMmlNode":518,"transform":9788},"translate(1533,393.1) scale(0.707)",[520,9790],{"dataC":2255,"xLinkHref":9791},"#MJX-74-TEX-N-35",[505,9793,9794],{"dataMmlNode":540,"transform":5437},[520,9795],{"dataC":544,"xLinkHref":9796},"#MJX-74-TEX-N-2B",[505,9798,9799,9803],{"dataMmlNode":515,"transform":5443},[505,9800,9801],{"dataMmlNode":518},[520,9802],{"dataC":599,"xLinkHref":9785},[505,9804,9805],{"dataMmlNode":518,"transform":527},[520,9806],{"dataC":959,"xLinkHref":9807},"#MJX-74-TEX-N-33",[505,9809,9811],{"dataMmlNode":540,"transform":9810},"translate(4317.8,0)",[520,9812],{"dataC":568,"xLinkHref":9813},"#MJX-74-TEX-N-2212",[505,9815,9817],{"dataMmlNode":518,"transform":9816},"translate(5318,0)",[520,9818],{"dataC":533,"xLinkHref":9782},[505,9820,9822],{"dataMmlNode":540,"transform":9821},"translate(6040.2,0)",[520,9823],{"dataC":568,"xLinkHref":9813},[505,9825,9827],{"dataMmlNode":7712,"transform":9826},"translate(7040.4,0)",[520,9828],{"dataC":9829,"xLinkHref":9830},"1D44B","#MJX-74-TEX-I-1D44B"," записали в системе счисления с основанием 6, при этом в записи оказалось 12 цифр 5. При каком минимальном целом положительном X это возможно?",[619,9833,622],{"id":9834},"решение-19",[624,9836,6830],{"id":9837},"решение-на-python-11",[402,9839,9840],{},"Идея алгоритма:",[632,9842,9843,9846,9849,9852,9855,9858,9861],{},[635,9844,9845],{},"Вычисляем исходное многоразрядное число k без учёта вычитания X;",[635,9847,9848],{},"Организуем при помощи цикла while перебор значений X от 1 до величины числа k;",[635,9850,9851],{},"Вычисляем интересующее нас значение k1 = k - X;",[635,9853,9854],{},"При помощи типового алгоритма разбора числа на цифры подсчитываем количество имеющихся в числе k1 цифр \"5\";",[635,9856,9857],{},"Если количество цифр \"5\" оказалось равно 12, то прерываем цикл командой break — остаётся текущее значение X (так как перебор производился с 1 в сторону увеличения, это наименьшее значение X);",[635,9859,9860],{},"Добавляем в код логическую переменную flag(флаг), которой изначально присваиваем значение False(ложь), а при обнаружении решения и выходе из цикла по break значение флага меняется на True(истина);",[635,9862,9863],{},"В конце программы проверяем состояние \"флага\"(переменной flag) и выводим при успешном решении значение X.",[6832,9865,9867],{"className":6834,"code":9866,"language":6836,"meta":6837,"style":6837},"k = 216**5 + 6**3 - 1\nflag = False\nX = 1\nwhile X \u003C k:\n    n = 0\n    k1 = k - X\n    while k1 > 0:\n        if k1 % 6 == 5:\n            n += 1\n        k1 \u002F\u002F= 6\n    if n == 12:\n        flag = True\n        break\n    X += 1\nif flag:\n    print(X)\n",[6839,9868,9869,9896,9906,9915,9928,9936,9951,9964,9980,9989,9999,10011,10021,10025,10034,10043],{"__ignoreMap":6837},[6842,9870,9871,9874,9876,9879,9881,9884,9886,9888,9890,9892,9894],{"class":6844,"line":6845},[6842,9872,9873],{"class":6848},"k ",[6842,9875,6853],{"class":6852},[6842,9877,9878],{"class":6856}," 216",[6842,9880,6866],{"class":6852},[6842,9882,9883],{"class":6856},"5",[6842,9885,6872],{"class":6852},[6842,9887,6891],{"class":6856},[6842,9889,6866],{"class":6852},[6842,9891,7560],{"class":6856},[6842,9893,6888],{"class":6852},[6842,9895,6956],{"class":6856},[6842,9897,9898,9901,9903],{"class":6844,"line":6899},[6842,9899,9900],{"class":6848},"flag ",[6842,9902,6853],{"class":6852},[6842,9904,9905],{"class":6856}," False\n",[6842,9907,9908,9911,9913],{"class":6844,"line":884},[6842,9909,9910],{"class":6848},"X ",[6842,9912,6853],{"class":6852},[6842,9914,6956],{"class":6856},[6842,9916,9917,9919,9922,9925],{"class":6844,"line":4212},[6842,9918,6912],{"class":6852},[6842,9920,9921],{"class":6848}," X ",[6842,9923,9924],{"class":6852},"\u003C",[6842,9926,9927],{"class":6848}," k:\n",[6842,9929,9930,9932,9934],{"class":6844,"line":6947},[6842,9931,9112],{"class":6848},[6842,9933,6853],{"class":6852},[6842,9935,6907],{"class":6856},[6842,9937,9938,9941,9943,9946,9948],{"class":6844,"line":6959},[6842,9939,9940],{"class":6848},"    k1 ",[6842,9942,6853],{"class":6852},[6842,9944,9945],{"class":6848}," k ",[6842,9947,9035],{"class":6852},[6842,9949,9950],{"class":6848}," X\n",[6842,9952,9953,9955,9958,9960,9962],{"class":6844,"line":6971},[6842,9954,8987],{"class":6852},[6842,9956,9957],{"class":6848}," k1 ",[6842,9959,6918],{"class":6852},[6842,9961,6921],{"class":6856},[6842,9963,6924],{"class":6848},[6842,9965,9966,9968,9970,9972,9974,9976,9978],{"class":6844,"line":8584},[6842,9967,8764],{"class":6852},[6842,9969,9957],{"class":6848},[6842,9971,6934],{"class":6852},[6842,9973,6891],{"class":6856},[6842,9975,6940],{"class":6852},[6842,9977,8299],{"class":6856},[6842,9979,6924],{"class":6848},[6842,9981,9982,9985,9987],{"class":6844,"line":8597},[6842,9983,9984],{"class":6848},"            n ",[6842,9986,6953],{"class":6852},[6842,9988,6956],{"class":6856},[6842,9990,9991,9994,9996],{"class":6844,"line":9075},[6842,9992,9993],{"class":6848},"        k1 ",[6842,9995,6965],{"class":6852},[6842,9997,9998],{"class":6856}," 6\n",[6842,10000,10001,10003,10005,10007,10009],{"class":6844,"line":9093},[6842,10002,6929],{"class":6852},[6842,10004,8893],{"class":6848},[6842,10006,8455],{"class":6852},[6842,10008,7963],{"class":6856},[6842,10010,6924],{"class":6848},[6842,10012,10013,10016,10018],{"class":6844,"line":9109},[6842,10014,10015],{"class":6848},"        flag ",[6842,10017,6853],{"class":6852},[6842,10019,10020],{"class":6856}," True\n",[6842,10022,10023],{"class":6844,"line":9125},[6842,10024,9330],{"class":6852},[6842,10026,10027,10030,10032],{"class":6844,"line":9139},[6842,10028,10029],{"class":6848},"    X ",[6842,10031,6953],{"class":6852},[6842,10033,6956],{"class":6856},[6842,10035,10037,10040],{"class":6844,"line":10036},15,[6842,10038,10039],{"class":6852},"if",[6842,10041,10042],{"class":6848}," flag:\n",[6842,10044,10046,10049],{"class":6844,"line":10045},16,[6842,10047,10048],{"class":6856},"    print",[6842,10050,10051],{"class":6848},"(X)\n",[402,10053,10054],{},[406,10055,10056],{},"Ответ: 259",[444,10058,10060],{"id":10059},"задача-20-из-егэ-2024","Задача 20 (из ЕГЭ 2024)",[402,10062,4235,10063,10132],{},[406,10064,10065],{},[452,10066,10068],{"className":10067,"jax":456},[455],[458,10069,10073,10093],{"style":9342,"xmlns":461,"width":10070,"height":10071,"role":464,"focusable":465,"viewBox":10072,"xmlnsXLink":467},"8.407ex","2.326ex","0 -833.9 3716.1 1027.9",[469,10074,10075,10078,10081,10084,10087,10090],{},[472,10076],{"id":10077,"d":922},"MJX-75-TEX-N-33",[472,10079],{"id":10080,"d":479},"MJX-75-TEX-N-31",[472,10082],{"id":10083,"d":487},"MJX-75-TEX-N-30",[472,10085],{"id":10086,"d":491},"MJX-75-TEX-N-2212",[472,10088],{"id":10089,"d":7667},"MJX-75-TEX-I-1D465",[472,10091],{"id":10092,"d":8082},"MJX-75-TEX-N-2C",[505,10094,10095],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,10096,10097,10116,10121,10126],{"dataMmlNode":512},[505,10098,10099,10104],{"dataMmlNode":515},[505,10100,10101],{"dataMmlNode":518},[520,10102],{"dataC":959,"xLinkHref":10103},"#MJX-75-TEX-N-33",[505,10105,10106],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,10107,10108,10111,10114],{"dataMmlNode":518},[520,10109],{"dataC":533,"xLinkHref":10110},"#MJX-75-TEX-N-31",[520,10112],{"dataC":561,"xLinkHref":10113,"transform":537},"#MJX-75-TEX-N-30",[520,10115],{"dataC":561,"xLinkHref":10113,"transform":965},[505,10117,10118],{"dataMmlNode":540,"transform":2847},[520,10119],{"dataC":568,"xLinkHref":10120},"#MJX-75-TEX-N-2212",[505,10122,10123],{"dataMmlNode":7712,"transform":2853},[520,10124],{"dataC":7715,"xLinkHref":10125},"#MJX-75-TEX-I-1D465",[505,10127,10129],{"dataMmlNode":540,"transform":10128},"translate(3438.1,0)",[520,10130],{"dataC":8162,"xLinkHref":10131},"#MJX-75-TEX-N-2C"," где х — целое положительное число, не превышающее 2030, записали в троичной системе счисления. Определите наибольшее значение х, при котором в троичной записи числа, являющегося значением данного арифметического выражения, содержится ровно пять нулей.",[402,10134,10135],{},"В ответе запишите число в десятичной системе счисления.",[619,10137,622],{"id":10138},"решение-20",[624,10140,6830],{"id":10141},"решение-на-python-12",[402,10143,10144],{},"Напишем программу на языке Python аналогичную в предыдущей задаче. Заменим выражение, обернув его в цикл for вместо while. Также поменяем условия внутри while при переборе всех разрядов у числа. И наконец, условие выхода из цикла тоже поменяем.",[6832,10146,10148],{"className":6834,"code":10147,"language":6836,"meta":6837,"style":6837},"# По условию X не больше 2030. range начинаем с 2030 до 1, т.к. ищем наибольший x.\n# третий параметр -1 отвечает за шаг, т.е. мы уменьшаем число в последовательности с 2030\nfor x in range(2030, 1, -1):\n    f = 3 ** 100 - x\n    # Счётчик нулей\n    k1 = 0\n    # Перебираем цифры в троичной системе\n    while f > 0:\n        if f % 3 == 0:\n            k1 += 1\n        f \u002F\u002F= 3\n    if k1 == 5:\n        print(x)\n        break\n",[6839,10149,10150,10155,10160,10187,10205,10210,10218,10223,10235,10251,10260,10269,10281,10287],{"__ignoreMap":6837},[6842,10151,10152],{"class":6844,"line":6845},[6842,10153,10154],{"class":8530},"# По условию X не больше 2030. range начинаем с 2030 до 1, т.к. ищем наибольший x.\n",[6842,10156,10157],{"class":6844,"line":6899},[6842,10158,10159],{"class":8530},"# третий параметр -1 отвечает за шаг, т.е. мы уменьшаем число в последовательности с 2030\n",[6842,10161,10162,10164,10166,10168,10170,10172,10175,10177,10179,10181,10183,10185],{"class":6844,"line":884},[6842,10163,7819],{"class":6852},[6842,10165,7822],{"class":6848},[6842,10167,7825],{"class":6852},[6842,10169,7828],{"class":6856},[6842,10171,7831],{"class":6848},[6842,10173,10174],{"class":6856},"2030",[6842,10176,7836],{"class":6848},[6842,10178,717],{"class":6856},[6842,10180,7836],{"class":6848},[6842,10182,9035],{"class":6852},[6842,10184,717],{"class":6856},[6842,10186,7842],{"class":6848},[6842,10188,10189,10191,10193,10195,10197,10200,10202],{"class":6844,"line":4212},[6842,10190,6962],{"class":6848},[6842,10192,6853],{"class":6852},[6842,10194,7601],{"class":6856},[6842,10196,7860],{"class":6852},[6842,10198,10199],{"class":6856}," 100",[6842,10201,6888],{"class":6852},[6842,10203,10204],{"class":6848}," x\n",[6842,10206,10207],{"class":6844,"line":6947},[6842,10208,10209],{"class":8530},"    # Счётчик нулей\n",[6842,10211,10212,10214,10216],{"class":6844,"line":6959},[6842,10213,9940],{"class":6848},[6842,10215,6853],{"class":6852},[6842,10217,6907],{"class":6856},[6842,10219,10220],{"class":6844,"line":6971},[6842,10221,10222],{"class":8530},"    # Перебираем цифры в троичной системе\n",[6842,10224,10225,10227,10229,10231,10233],{"class":6844,"line":8584},[6842,10226,8987],{"class":6852},[6842,10228,6915],{"class":6848},[6842,10230,6918],{"class":6852},[6842,10232,6921],{"class":6856},[6842,10234,6924],{"class":6848},[6842,10236,10237,10239,10241,10243,10245,10247,10249],{"class":6844,"line":8597},[6842,10238,8764],{"class":6852},[6842,10240,6915],{"class":6848},[6842,10242,6934],{"class":6852},[6842,10244,7601],{"class":6856},[6842,10246,6940],{"class":6852},[6842,10248,6921],{"class":6856},[6842,10250,6924],{"class":6848},[6842,10252,10253,10256,10258],{"class":6844,"line":9075},[6842,10254,10255],{"class":6848},"            k1 ",[6842,10257,6953],{"class":6852},[6842,10259,6956],{"class":6856},[6842,10261,10262,10265,10267],{"class":6844,"line":9093},[6842,10263,10264],{"class":6848},"        f ",[6842,10266,6965],{"class":6852},[6842,10268,8545],{"class":6856},[6842,10270,10271,10273,10275,10277,10279],{"class":6844,"line":9109},[6842,10272,6929],{"class":6852},[6842,10274,9957],{"class":6848},[6842,10276,8455],{"class":6852},[6842,10278,8299],{"class":6856},[6842,10280,6924],{"class":6848},[6842,10282,10283,10285],{"class":6844,"line":9125},[6842,10284,8011],{"class":6856},[6842,10286,8780],{"class":6848},[6842,10288,10289],{"class":6844,"line":9139},[6842,10290,9330],{"class":6852},[402,10292,10293],{},[406,10294,10295],{},"Ответ: 2024",[444,10297,10299],{"id":10298},"задача-21-добьём-14-задание-из-егэ-по-информатике","Задача 21 (Добьём 14 задание из ЕГЭ по информатике)",[402,10301,10302],{},"В некоторой системе счисления записи десятичных чисел 66 и 40 заканчиваются на 1. Определите основание системы счисления.",[619,10304,622],{"id":10305},"решение-21",[402,10307,10308],{},"Ещё раз про основания.\nНужно найти такое число, чтобы числа 66 и 40 при делении на него давали остаток 1. Первый остаток при делении на основание системы - это и есть последняя цифра числа в этой системе счисления.",[402,10310,10311],{},"Искомое число должно быть делителем чисел 65 (66-1) и 39 (40-1). У числа 39 не так много делителей: 1, 3, 13, 39.",[402,10313,10314],{},"Видим, что число 65 делится на 13 (65 : 13 = 5).",[402,10316,10317],{},"Поэтому искомое число равно 13.",[624,10319,6830],{"id":10320},"решение-на-python-13",[6832,10322,10324],{"className":6834,"code":10323,"language":6836,"meta":6837,"style":6837},"for n in range(2, 40):\n    if 66 % n == 1 and 40 % n == 1:\n        print(n)\n        break\n",[6839,10325,10326,10347,10377,10383],{"__ignoreMap":6837},[6842,10327,10328,10330,10332,10334,10336,10338,10340,10342,10345],{"class":6844,"line":6845},[6842,10329,7819],{"class":6852},[6842,10331,8893],{"class":6848},[6842,10333,7825],{"class":6852},[6842,10335,7828],{"class":6856},[6842,10337,7831],{"class":6848},[6842,10339,881],{"class":6856},[6842,10341,7836],{"class":6848},[6842,10343,10344],{"class":6856},"40",[6842,10346,7842],{"class":6848},[6842,10348,10349,10351,10354,10356,10358,10360,10362,10364,10367,10369,10371,10373,10375],{"class":6844,"line":6899},[6842,10350,6929],{"class":6852},[6842,10352,10353],{"class":6856}," 66",[6842,10355,8918],{"class":6852},[6842,10357,8893],{"class":6848},[6842,10359,8455],{"class":6852},[6842,10361,7876],{"class":6856},[6842,10363,9301],{"class":6852},[6842,10365,10366],{"class":6856}," 40",[6842,10368,8918],{"class":6852},[6842,10370,8893],{"class":6848},[6842,10372,8455],{"class":6852},[6842,10374,7876],{"class":6856},[6842,10376,6924],{"class":6848},[6842,10378,10379,10381],{"class":6844,"line":884},[6842,10380,8011],{"class":6856},[6842,10382,8933],{"class":6848},[6842,10384,10385],{"class":6844,"line":4212},[6842,10386,9330],{"class":6852},[402,10388,10389],{},[406,10390,10391],{},"Ответ: 13",[444,10393,10395],{"id":10394},"задача-22-демоверсия-2024","Задача 22 (Демоверсия 2024)",[402,10397,10398,10399,10514],{},"Операнды арифметического выражения записаны в системе счисления с основанием 19. ",[452,10400,10402],{"className":10401,"jax":456},[455],[458,10403,10406,10432],{"style":7655,"xmlns":461,"width":10404,"height":1816,"role":464,"focusable":465,"viewBox":10405,"xmlnsXLink":467},"21.373ex","0 -676 9446.7 841.6",[469,10407,10408,10411,10414,10417,10420,10423,10426,10429],{},[472,10409],{"id":10410,"d":2686},"MJX-76-TEX-N-39",[472,10412],{"id":10413,"d":495},"MJX-76-TEX-N-38",[472,10415],{"id":10416,"d":2679},"MJX-76-TEX-N-37",[472,10418],{"id":10419,"d":7667},"MJX-76-TEX-I-1D465",[472,10421],{"id":10422,"d":475},"MJX-76-TEX-N-32",[472,10424],{"id":10425,"d":479},"MJX-76-TEX-N-31",[472,10427],{"id":10428,"d":483},"MJX-76-TEX-N-2B",[472,10430],{"id":10431,"d":922},"MJX-76-TEX-N-33",[505,10433,10434],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,10435,10436,10451,10457,10477,10483,10488,10493],{"dataMmlNode":512},[505,10437,10438,10441,10444,10446,10448],{"dataMmlNode":518},[520,10439],{"dataC":2739,"xLinkHref":10440},"#MJX-76-TEX-N-39",[520,10442],{"dataC":581,"xLinkHref":10443,"transform":537},"#MJX-76-TEX-N-38",[520,10445],{"dataC":581,"xLinkHref":10443,"transform":965},[520,10447],{"dataC":2739,"xLinkHref":10440,"transform":968},[520,10449],{"dataC":2732,"xLinkHref":10450,"transform":1489},"#MJX-76-TEX-N-37",[505,10452,10454],{"dataMmlNode":7712,"transform":10453},"translate(2500,0)",[520,10455],{"dataC":7715,"xLinkHref":10456},"#MJX-76-TEX-I-1D465",[505,10458,10460,10468],{"dataMmlNode":7733,"transform":10459},"translate(3072,0)",[505,10461,10462,10465],{"dataMmlNode":518},[520,10463],{"dataC":522,"xLinkHref":10464},"#MJX-76-TEX-N-32",[520,10466],{"dataC":533,"xLinkHref":10467,"transform":537},"#MJX-76-TEX-N-31",[505,10469,10471],{"dataMmlNode":526,"transform":10470,"dataMjxTexclass":528},"translate(1033,-150) scale(0.707)",[505,10472,10473,10475],{"dataMmlNode":518},[520,10474],{"dataC":533,"xLinkHref":10467},[520,10476],{"dataC":2739,"xLinkHref":10440,"transform":537},[505,10478,10480],{"dataMmlNode":540,"transform":10479},"translate(5084.3,0)",[520,10481],{"dataC":544,"xLinkHref":10482},"#MJX-76-TEX-N-2B",[505,10484,10486],{"dataMmlNode":518,"transform":10485},"translate(6084.6,0)",[520,10487],{"dataC":522,"xLinkHref":10464},[505,10489,10491],{"dataMmlNode":7712,"transform":10490},"translate(6584.6,0)",[520,10492],{"dataC":7715,"xLinkHref":10456},[505,10494,10496,10505],{"dataMmlNode":7733,"transform":10495},"translate(7156.6,0)",[505,10497,10498,10500,10502],{"dataMmlNode":518},[520,10499],{"dataC":2739,"xLinkHref":10440},[520,10501],{"dataC":522,"xLinkHref":10464,"transform":537},[520,10503],{"dataC":959,"xLinkHref":10504,"transform":965},"#MJX-76-TEX-N-33",[505,10506,10508],{"dataMmlNode":526,"transform":10507,"dataMjxTexclass":528},"translate(1533,-150) scale(0.707)",[505,10509,10510,10512],{"dataMmlNode":518},[520,10511],{"dataC":533,"xLinkHref":10467},[520,10513],{"dataC":2739,"xLinkHref":10440,"transform":537},"\nВ записи чисел переменной x обозначена неизвестная цифра из алфавита 19-ричной системы счисления. Определите наибольшее значение x, при котором значение данного арифметического выражения кратно 18.\nДля найденного x вычислите частное от деления значения арифметического выражения на 18 и укажите его в ответе в десятичной системе счисления. Основание системы счисления указывать не нужно.",[619,10516,10518],{"id":10517},"или",[406,10519,10520],{},"ИЛИ",[402,10522,10523,10524,10527,10755],{},"Значение арифметического выражения",[10525,10526],"br",{},[452,10528,10530],{"className":10529,"jax":456},[455],[458,10531,10535,10574],{"style":460,"xmlns":461,"width":10532,"height":10533,"role":464,"focusable":465,"viewBox":10534,"xmlnsXLink":467},"51.697ex","2.158ex","0 -871.8 22849.9 953.8",[469,10536,10537,10540,10543,10546,10549,10552,10555,10558,10561,10564,10568,10571],{},[472,10538],{"id":10539,"d":922},"MJX-77-TEX-N-33",[472,10541],{"id":10542,"d":7018},"MJX-77-TEX-N-2219",[472,10544],{"id":10545,"d":479},"MJX-77-TEX-N-31",[472,10547],{"id":10548,"d":475},"MJX-77-TEX-N-32",[472,10550],{"id":10551,"d":2199},"MJX-77-TEX-N-35",[472,10553],{"id":10554,"d":495},"MJX-77-TEX-N-38",[472,10556],{"id":10557,"d":483},"MJX-77-TEX-N-2B",[472,10559],{"id":10560,"d":499},"MJX-77-TEX-N-36",[472,10562],{"id":10563,"d":2679},"MJX-77-TEX-N-37",[472,10565],{"id":10566,"d":10567},"MJX-77-TEX-N-2013","M0 248V285H499V248H0Z",[472,10569],{"id":10570,"d":926},"MJX-77-TEX-N-34",[472,10572],{"id":10573,"d":487},"MJX-77-TEX-N-30",[505,10575,10576],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,10577,10578,10583,10588,10608,10614,10619,10624,10641,10650,10656,10661,10676,10681,10686,10691,10706,10713,10718,10723,10736,10743],{"dataMmlNode":512},[505,10579,10580],{"dataMmlNode":518},[520,10581],{"dataC":959,"xLinkHref":10582},"#MJX-77-TEX-N-33",[505,10584,10585],{"dataMmlNode":540,"transform":2713},[520,10586],{"dataC":7065,"xLinkHref":10587},"#MJX-77-TEX-N-2219",[505,10589,10590,10603],{"dataMmlNode":515,"transform":7069},[505,10591,10592,10594,10597,10600],{"dataMmlNode":518},[520,10593],{"dataC":959,"xLinkHref":10582},[520,10595],{"dataC":533,"xLinkHref":10596,"transform":537},"#MJX-77-TEX-N-31",[520,10598],{"dataC":522,"xLinkHref":10599,"transform":965},"#MJX-77-TEX-N-32",[520,10601],{"dataC":2255,"xLinkHref":10602,"transform":968},"#MJX-77-TEX-N-35",[505,10604,10605],{"dataMmlNode":518,"transform":6748},[520,10606],{"dataC":581,"xLinkHref":10607},"#MJX-77-TEX-N-38",[505,10609,10611],{"dataMmlNode":540,"transform":10610},"translate(4103.2,0)",[520,10612],{"dataC":544,"xLinkHref":10613},"#MJX-77-TEX-N-2B",[505,10615,10617],{"dataMmlNode":518,"transform":10616},"translate(5103.4,0)",[520,10618],{"dataC":522,"xLinkHref":10599},[505,10620,10622],{"dataMmlNode":540,"transform":10621},"translate(5825.7,0)",[520,10623],{"dataC":7065,"xLinkHref":10587},[505,10625,10627,10636],{"dataMmlNode":515,"transform":10626},"translate(6547.9,0)",[505,10628,10629,10632,10634],{"dataMmlNode":518},[520,10630],{"dataC":599,"xLinkHref":10631},"#MJX-77-TEX-N-36",[520,10633],{"dataC":522,"xLinkHref":10599,"transform":537},[520,10635],{"dataC":2255,"xLinkHref":10602,"transform":965},[505,10637,10638],{"dataMmlNode":518,"transform":9788},[520,10639],{"dataC":2732,"xLinkHref":10640},"#MJX-77-TEX-N-37",[505,10642,10644],{"dataMmlNode":526,"dataMjxTexclass":528,"transform":10643},"translate(8484.4,0)",[505,10645,10646],{"dataMmlNode":540},[520,10647],{"dataC":10648,"xLinkHref":10649},"2013","#MJX-77-TEX-N-2013",[505,10651,10653],{"dataMmlNode":518,"transform":10652},"translate(8984.4,0)",[520,10654],{"dataC":963,"xLinkHref":10655},"#MJX-77-TEX-N-34",[505,10657,10659],{"dataMmlNode":540,"transform":10658},"translate(9706.7,0)",[520,10660],{"dataC":7065,"xLinkHref":10587},[505,10662,10664,10672],{"dataMmlNode":515,"transform":10663},"translate(10428.9,0)",[505,10665,10666,10668,10670],{"dataMmlNode":518},[520,10667],{"dataC":599,"xLinkHref":10631},[520,10669],{"dataC":522,"xLinkHref":10599,"transform":537},[520,10671],{"dataC":2255,"xLinkHref":10602,"transform":965},[505,10673,10674],{"dataMmlNode":518,"transform":9788},[520,10675],{"dataC":599,"xLinkHref":10631},[505,10677,10679],{"dataMmlNode":540,"transform":10678},"translate(12587.7,0)",[520,10680],{"dataC":544,"xLinkHref":10613},[505,10682,10684],{"dataMmlNode":518,"transform":10683},"translate(13587.9,0)",[520,10685],{"dataC":959,"xLinkHref":10582},[505,10687,10689],{"dataMmlNode":540,"transform":10688},"translate(14310.1,0)",[520,10690],{"dataC":7065,"xLinkHref":10587},[505,10692,10694,10702],{"dataMmlNode":515,"transform":10693},"translate(15032.3,0)",[505,10695,10696,10698,10700],{"dataMmlNode":518},[520,10697],{"dataC":533,"xLinkHref":10596},[520,10699],{"dataC":522,"xLinkHref":10599,"transform":537},[520,10701],{"dataC":2255,"xLinkHref":10602,"transform":965},[505,10703,10704],{"dataMmlNode":518,"transform":9788},[520,10705],{"dataC":2255,"xLinkHref":10602},[505,10707,10709],{"dataMmlNode":526,"dataMjxTexclass":528,"transform":10708},"translate(16968.9,0)",[505,10710,10711],{"dataMmlNode":540},[520,10712],{"dataC":10648,"xLinkHref":10649},[505,10714,10716],{"dataMmlNode":518,"transform":10715},"translate(17468.9,0)",[520,10717],{"dataC":522,"xLinkHref":10599},[505,10719,10721],{"dataMmlNode":540,"transform":10720},"translate(18191.1,0)",[520,10722],{"dataC":7065,"xLinkHref":10587},[505,10724,10726,10732],{"dataMmlNode":515,"transform":10725},"translate(18913.3,0)",[505,10727,10728,10730],{"dataMmlNode":518},[520,10729],{"dataC":522,"xLinkHref":10599},[520,10731],{"dataC":2255,"xLinkHref":10602,"transform":537},[505,10733,10734],{"dataMmlNode":518,"transform":2863},[520,10735],{"dataC":963,"xLinkHref":10655},[505,10737,10739],{"dataMmlNode":526,"dataMjxTexclass":528,"transform":10738},"translate(20349.9,0)",[505,10740,10741],{"dataMmlNode":540},[520,10742],{"dataC":10648,"xLinkHref":10649},[505,10744,10746,10748,10751,10753],{"dataMmlNode":518,"transform":10745},"translate(20849.9,0)",[520,10747],{"dataC":522,"xLinkHref":10599},[520,10749],{"dataC":561,"xLinkHref":10750,"transform":537},"#MJX-77-TEX-N-30",[520,10752],{"dataC":522,"xLinkHref":10599,"transform":965},[520,10754],{"dataC":963,"xLinkHref":10655,"transform":968},"\nзаписали в системе счисления с основанием 25. Сколько значащих нулей содержится в этой записи?",[619,10757,622],{"id":10758},"решение-22",[402,10760,10761],{},"В задании сказано, что x - это число в 19-ичной системе. Значит нам нужно перебрать все x от 18 до 0 в цикле и подставить в выражение. Расписав отдельно между операцией + значения чисел в развёрнутой форме в десятичной системе - сохраним результат в переменные значения a и b. Далее условие if проверяет(как по условию), что результат всего выражения(a+b) делится без остатка на 18. Команда print будет выводить все такие варианты и остаётся только выбрать в консоли ответ как наибольшее значение x.",[624,10763,6830],{"id":10764},"решение-на-python-14",[6832,10766,10768],{"className":6834,"code":10767,"language":6836,"meta":6837,"style":6837},"for x in range(18, -1, -1):\n    a = 1*19**0 + 2*19**1 + x*19**2 + 7*19**3 + 9*19**4 + 8*19**5 + 8*19**6 + 9*19**7\n    b = 3*19**0 + 2*19**1 + 9*19**2 + x*19**3 + 2*19**4\n    if (a + b) % 18 == 0:\n        print(x, (a + b) \u002F\u002F 18)\n        break # т.к. ищем максимальный x и идём в цикле от наибольшего x можно уже прервать цикл\n",[6839,10769,10770,10798,10900,10965,10986,11002],{"__ignoreMap":6837},[6842,10771,10772,10774,10776,10778,10780,10782,10784,10786,10788,10790,10792,10794,10796],{"class":6844,"line":6845},[6842,10773,7819],{"class":6852},[6842,10775,7822],{"class":6848},[6842,10777,7825],{"class":6852},[6842,10779,7828],{"class":6856},[6842,10781,7831],{"class":6848},[6842,10783,8523],{"class":6856},[6842,10785,7836],{"class":6848},[6842,10787,9035],{"class":6852},[6842,10789,717],{"class":6856},[6842,10791,7836],{"class":6848},[6842,10793,9035],{"class":6852},[6842,10795,717],{"class":6856},[6842,10797,7842],{"class":6848},[6842,10799,10800,10802,10804,10806,10808,10811,10813,10815,10817,10819,10821,10823,10825,10827,10829,10831,10833,10835,10837,10839,10841,10843,10845,10847,10849,10851,10853,10855,10857,10859,10861,10863,10865,10867,10869,10871,10873,10875,10877,10879,10881,10883,10885,10887,10889,10891,10893,10895,10897],{"class":6844,"line":6899},[6842,10801,7847],{"class":6848},[6842,10803,6853],{"class":6852},[6842,10805,7876],{"class":6856},[6842,10807,7896],{"class":6852},[6842,10809,10810],{"class":6856},"19",[6842,10812,6866],{"class":6852},[6842,10814,508],{"class":6856},[6842,10816,6872],{"class":6852},[6842,10818,7283],{"class":6856},[6842,10820,7896],{"class":6852},[6842,10822,10810],{"class":6856},[6842,10824,6866],{"class":6852},[6842,10826,717],{"class":6856},[6842,10828,6872],{"class":6852},[6842,10830,8688],{"class":6848},[6842,10832,7896],{"class":6852},[6842,10834,10810],{"class":6856},[6842,10836,6866],{"class":6852},[6842,10838,881],{"class":6856},[6842,10840,6872],{"class":6852},[6842,10842,6857],{"class":6856},[6842,10844,7896],{"class":6852},[6842,10846,10810],{"class":6856},[6842,10848,6866],{"class":6852},[6842,10850,7560],{"class":6856},[6842,10852,6872],{"class":6852},[6842,10854,6937],{"class":6856},[6842,10856,7896],{"class":6852},[6842,10858,10810],{"class":6856},[6842,10860,6866],{"class":6852},[6842,10862,9065],{"class":6856},[6842,10864,6872],{"class":6852},[6842,10866,6875],{"class":6856},[6842,10868,7896],{"class":6852},[6842,10870,10810],{"class":6856},[6842,10872,6866],{"class":6852},[6842,10874,9883],{"class":6856},[6842,10876,6872],{"class":6852},[6842,10878,6875],{"class":6856},[6842,10880,7896],{"class":6852},[6842,10882,10810],{"class":6856},[6842,10884,6866],{"class":6852},[6842,10886,9070],{"class":6856},[6842,10888,6872],{"class":6852},[6842,10890,6937],{"class":6856},[6842,10892,7896],{"class":6852},[6842,10894,10810],{"class":6856},[6842,10896,6866],{"class":6852},[6842,10898,10899],{"class":6856},"7\n",[6842,10901,10902,10904,10906,10908,10910,10912,10914,10916,10918,10920,10922,10924,10926,10928,10930,10932,10934,10936,10938,10940,10942,10944,10946,10948,10950,10952,10954,10956,10958,10960,10962],{"class":6844,"line":884},[6842,10903,7920],{"class":6848},[6842,10905,6853],{"class":6852},[6842,10907,7601],{"class":6856},[6842,10909,7896],{"class":6852},[6842,10911,10810],{"class":6856},[6842,10913,6866],{"class":6852},[6842,10915,508],{"class":6856},[6842,10917,6872],{"class":6852},[6842,10919,7283],{"class":6856},[6842,10921,7896],{"class":6852},[6842,10923,10810],{"class":6856},[6842,10925,6866],{"class":6852},[6842,10927,717],{"class":6856},[6842,10929,6872],{"class":6852},[6842,10931,6937],{"class":6856},[6842,10933,7896],{"class":6852},[6842,10935,10810],{"class":6856},[6842,10937,6866],{"class":6852},[6842,10939,881],{"class":6856},[6842,10941,6872],{"class":6852},[6842,10943,8688],{"class":6848},[6842,10945,7896],{"class":6852},[6842,10947,10810],{"class":6856},[6842,10949,6866],{"class":6852},[6842,10951,7560],{"class":6856},[6842,10953,6872],{"class":6852},[6842,10955,7283],{"class":6856},[6842,10957,7896],{"class":6852},[6842,10959,10810],{"class":6856},[6842,10961,6866],{"class":6852},[6842,10963,10964],{"class":6856},"4\n",[6842,10966,10967,10969,10971,10973,10975,10977,10980,10982,10984],{"class":6844,"line":4212},[6842,10968,6929],{"class":6852},[6842,10970,7990],{"class":6848},[6842,10972,7993],{"class":6852},[6842,10974,7996],{"class":6848},[6842,10976,6934],{"class":6852},[6842,10978,10979],{"class":6856}," 18",[6842,10981,6940],{"class":6852},[6842,10983,6921],{"class":6856},[6842,10985,6924],{"class":6848},[6842,10987,10988,10990,10992,10994,10996,10998,11000],{"class":6844,"line":6947},[6842,10989,8011],{"class":6856},[6842,10991,8014],{"class":6848},[6842,10993,7993],{"class":6852},[6842,10995,7996],{"class":6848},[6842,10997,8021],{"class":6852},[6842,10999,10979],{"class":6856},[6842,11001,8026],{"class":6848},[6842,11003,11004,11007],{"class":6844,"line":6959},[6842,11005,11006],{"class":6852},"        break",[6842,11008,11009],{"class":8530}," # т.к. ищем максимальный x и идём в цикле от наибольшего x можно уже прервать цикл\n",[402,11011,11012],{},[406,11013,11014],{},"Ответ: 469034148",[619,11016,11018],{"id":11017},"решение-или","Решение ИЛИ:",[402,11020,11021],{},"Второй вариант ИЛИ решить даже легче. В переменную R сначала сохраним результат вычисления данного в задании выражения. Далее переменная k служит счётчиком, отвечающим в конце на вопрос задачи в print. Далее запускаем цикл по условию пока результат выражения больше нуля -> мы будем остаток от деления на 25 и сокращать кол-во разрядов у числа целочисленным делением на 25. Тем самым в условии if мы посчитаем количество значащих нулей в результате выражения, так как, если бы этот результат был записан в 25-ичной системе счисления.",[624,11023,6830],{"id":11024},"решение-на-python-15",[6832,11026,11028],{"className":6834,"code":11027,"language":6836,"meta":6837,"style":6837},"R = 3*3125**8 + 2*625**7 - 4*625**6 + 3*125**5 - 2*25**4 - 2024\nk = 0\nwhile R > 0:\n    if R % 25 == 0:\n        k += 1\n    R = R \u002F\u002F 25\nprint(k)\n",[6839,11029,11030,11105,11113,11126,11143,11152,11166],{"__ignoreMap":6837},[6842,11031,11032,11035,11037,11039,11041,11044,11046,11049,11051,11053,11055,11058,11060,11063,11065,11067,11069,11071,11073,11075,11077,11079,11081,11084,11086,11088,11090,11092,11094,11097,11099,11101,11103],{"class":6844,"line":6845},[6842,11033,11034],{"class":6848},"R ",[6842,11036,6853],{"class":6852},[6842,11038,7601],{"class":6856},[6842,11040,7896],{"class":6852},[6842,11042,11043],{"class":6856},"3125",[6842,11045,6866],{"class":6852},[6842,11047,11048],{"class":6856},"8",[6842,11050,6872],{"class":6852},[6842,11052,7283],{"class":6856},[6842,11054,7896],{"class":6852},[6842,11056,11057],{"class":6856},"625",[6842,11059,6866],{"class":6852},[6842,11061,11062],{"class":6856},"7",[6842,11064,6888],{"class":6852},[6842,11066,8356],{"class":6856},[6842,11068,7896],{"class":6852},[6842,11070,11057],{"class":6856},[6842,11072,6866],{"class":6852},[6842,11074,9070],{"class":6856},[6842,11076,6872],{"class":6852},[6842,11078,7601],{"class":6856},[6842,11080,7896],{"class":6852},[6842,11082,11083],{"class":6856},"125",[6842,11085,6866],{"class":6852},[6842,11087,9883],{"class":6856},[6842,11089,6888],{"class":6852},[6842,11091,7283],{"class":6856},[6842,11093,7896],{"class":6852},[6842,11095,11096],{"class":6856},"25",[6842,11098,6866],{"class":6852},[6842,11100,9065],{"class":6856},[6842,11102,6888],{"class":6852},[6842,11104,7352],{"class":6856},[6842,11106,11107,11109,11111],{"class":6844,"line":6899},[6842,11108,9873],{"class":6848},[6842,11110,6853],{"class":6852},[6842,11112,6907],{"class":6856},[6842,11114,11115,11117,11120,11122,11124],{"class":6844,"line":884},[6842,11116,6912],{"class":6852},[6842,11118,11119],{"class":6848}," R ",[6842,11121,6918],{"class":6852},[6842,11123,6921],{"class":6856},[6842,11125,6924],{"class":6848},[6842,11127,11128,11130,11132,11134,11137,11139,11141],{"class":6844,"line":4212},[6842,11129,6929],{"class":6852},[6842,11131,11119],{"class":6848},[6842,11133,6934],{"class":6852},[6842,11135,11136],{"class":6856}," 25",[6842,11138,6940],{"class":6852},[6842,11140,6921],{"class":6856},[6842,11142,6924],{"class":6848},[6842,11144,11145,11148,11150],{"class":6844,"line":6947},[6842,11146,11147],{"class":6848},"        k ",[6842,11149,6953],{"class":6852},[6842,11151,6956],{"class":6856},[6842,11153,11154,11157,11159,11161,11163],{"class":6844,"line":6959},[6842,11155,11156],{"class":6848},"    R ",[6842,11158,6853],{"class":6852},[6842,11160,11119],{"class":6848},[6842,11162,8021],{"class":6852},[6842,11164,11165],{"class":6856}," 25\n",[6842,11167,11168,11170],{"class":6844,"line":6971},[6842,11169,6974],{"class":6856},[6842,11171,11172],{"class":6848},"(k)\n",[402,11174,11175],{},[406,11176,5956],{},[444,11178,11180],{"id":11179},"задача-23-демоверсия-2025","Задача 23 (Демоверсия 2025)",[402,11182,11183],{},"1 вариант задания остался прежним как в демоверсии 2024 года.",[402,11185,11186],{},"Изменился совсем незначительно вариант ИЛИ. И добавился ещё второй вариант ИЛИ.",[619,11188,10520],{"id":11189},"или-1",[402,11191,10523,11192,11194,10755],{},[10525,11193],{},[452,11195,11197],{"className":11196,"jax":456},[455],[458,11198,11199,11237],{"style":460,"xmlns":461,"width":10532,"height":10533,"role":464,"focusable":465,"viewBox":10534,"xmlnsXLink":467},[469,11200,11201,11204,11207,11210,11213,11216,11219,11222,11225,11228,11231,11234],{},[472,11202],{"id":11203,"d":922},"MJX-78-TEX-N-33",[472,11205],{"id":11206,"d":7018},"MJX-78-TEX-N-2219",[472,11208],{"id":11209,"d":479},"MJX-78-TEX-N-31",[472,11211],{"id":11212,"d":475},"MJX-78-TEX-N-32",[472,11214],{"id":11215,"d":2199},"MJX-78-TEX-N-35",[472,11217],{"id":11218,"d":495},"MJX-78-TEX-N-38",[472,11220],{"id":11221,"d":483},"MJX-78-TEX-N-2B",[472,11223],{"id":11224,"d":499},"MJX-78-TEX-N-36",[472,11226],{"id":11227,"d":2679},"MJX-78-TEX-N-37",[472,11229],{"id":11230,"d":10567},"MJX-78-TEX-N-2013",[472,11232],{"id":11233,"d":926},"MJX-78-TEX-N-34",[472,11235],{"id":11236,"d":487},"MJX-78-TEX-N-30",[505,11238,11239],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,11240,11241,11246,11251,11271,11276,11280,11284,11300,11307,11312,11316,11330,11334,11338,11342,11356,11362,11366,11370,11382,11388],{"dataMmlNode":512},[505,11242,11243],{"dataMmlNode":518},[520,11244],{"dataC":959,"xLinkHref":11245},"#MJX-78-TEX-N-33",[505,11247,11248],{"dataMmlNode":540,"transform":2713},[520,11249],{"dataC":7065,"xLinkHref":11250},"#MJX-78-TEX-N-2219",[505,11252,11253,11266],{"dataMmlNode":515,"transform":7069},[505,11254,11255,11257,11260,11263],{"dataMmlNode":518},[520,11256],{"dataC":959,"xLinkHref":11245},[520,11258],{"dataC":533,"xLinkHref":11259,"transform":537},"#MJX-78-TEX-N-31",[520,11261],{"dataC":522,"xLinkHref":11262,"transform":965},"#MJX-78-TEX-N-32",[520,11264],{"dataC":2255,"xLinkHref":11265,"transform":968},"#MJX-78-TEX-N-35",[505,11267,11268],{"dataMmlNode":518,"transform":6748},[520,11269],{"dataC":581,"xLinkHref":11270},"#MJX-78-TEX-N-38",[505,11272,11273],{"dataMmlNode":540,"transform":10610},[520,11274],{"dataC":544,"xLinkHref":11275},"#MJX-78-TEX-N-2B",[505,11277,11278],{"dataMmlNode":518,"transform":10616},[520,11279],{"dataC":522,"xLinkHref":11262},[505,11281,11282],{"dataMmlNode":540,"transform":10621},[520,11283],{"dataC":7065,"xLinkHref":11250},[505,11285,11286,11295],{"dataMmlNode":515,"transform":10626},[505,11287,11288,11291,11293],{"dataMmlNode":518},[520,11289],{"dataC":599,"xLinkHref":11290},"#MJX-78-TEX-N-36",[520,11292],{"dataC":522,"xLinkHref":11262,"transform":537},[520,11294],{"dataC":2255,"xLinkHref":11265,"transform":965},[505,11296,11297],{"dataMmlNode":518,"transform":9788},[520,11298],{"dataC":2732,"xLinkHref":11299},"#MJX-78-TEX-N-37",[505,11301,11302],{"dataMmlNode":526,"dataMjxTexclass":528,"transform":10643},[505,11303,11304],{"dataMmlNode":540},[520,11305],{"dataC":10648,"xLinkHref":11306},"#MJX-78-TEX-N-2013",[505,11308,11309],{"dataMmlNode":518,"transform":10652},[520,11310],{"dataC":963,"xLinkHref":11311},"#MJX-78-TEX-N-34",[505,11313,11314],{"dataMmlNode":540,"transform":10658},[520,11315],{"dataC":7065,"xLinkHref":11250},[505,11317,11318,11326],{"dataMmlNode":515,"transform":10663},[505,11319,11320,11322,11324],{"dataMmlNode":518},[520,11321],{"dataC":599,"xLinkHref":11290},[520,11323],{"dataC":522,"xLinkHref":11262,"transform":537},[520,11325],{"dataC":2255,"xLinkHref":11265,"transform":965},[505,11327,11328],{"dataMmlNode":518,"transform":9788},[520,11329],{"dataC":599,"xLinkHref":11290},[505,11331,11332],{"dataMmlNode":540,"transform":10678},[520,11333],{"dataC":544,"xLinkHref":11275},[505,11335,11336],{"dataMmlNode":518,"transform":10683},[520,11337],{"dataC":959,"xLinkHref":11245},[505,11339,11340],{"dataMmlNode":540,"transform":10688},[520,11341],{"dataC":7065,"xLinkHref":11250},[505,11343,11344,11352],{"dataMmlNode":515,"transform":10693},[505,11345,11346,11348,11350],{"dataMmlNode":518},[520,11347],{"dataC":533,"xLinkHref":11259},[520,11349],{"dataC":522,"xLinkHref":11262,"transform":537},[520,11351],{"dataC":2255,"xLinkHref":11265,"transform":965},[505,11353,11354],{"dataMmlNode":518,"transform":9788},[520,11355],{"dataC":2255,"xLinkHref":11265},[505,11357,11358],{"dataMmlNode":526,"dataMjxTexclass":528,"transform":10708},[505,11359,11360],{"dataMmlNode":540},[520,11361],{"dataC":10648,"xLinkHref":11306},[505,11363,11364],{"dataMmlNode":518,"transform":10715},[520,11365],{"dataC":522,"xLinkHref":11262},[505,11367,11368],{"dataMmlNode":540,"transform":10720},[520,11369],{"dataC":7065,"xLinkHref":11250},[505,11371,11372,11378],{"dataMmlNode":515,"transform":10725},[505,11373,11374,11376],{"dataMmlNode":518},[520,11375],{"dataC":522,"xLinkHref":11262},[520,11377],{"dataC":2255,"xLinkHref":11265,"transform":537},[505,11379,11380],{"dataMmlNode":518,"transform":2863},[520,11381],{"dataC":963,"xLinkHref":11311},[505,11383,11384],{"dataMmlNode":526,"dataMjxTexclass":528,"transform":10738},[505,11385,11386],{"dataMmlNode":540},[520,11387],{"dataC":10648,"xLinkHref":11306},[505,11389,11390,11392,11395,11397],{"dataMmlNode":518,"transform":10745},[520,11391],{"dataC":522,"xLinkHref":11262},[520,11393],{"dataC":561,"xLinkHref":11394,"transform":537},"#MJX-78-TEX-N-30",[520,11396],{"dataC":522,"xLinkHref":11262,"transform":965},[520,11398],{"dataC":2255,"xLinkHref":11265,"transform":968},[619,11400,11402],{"id":11401},"ещё-или","ЕЩЁ ИЛИ",[402,11404,4235,11405,11500],{},[452,11406,11408],{"className":11407,"jax":456},[455],[458,11409,11413,11436],{"style":9342,"xmlns":461,"width":11410,"height":11411,"role":464,"focusable":465,"viewBox":11412,"xmlnsXLink":467},"13.257ex","2.342ex","0 -841 5859.8 1035",[469,11414,11415,11418,11421,11424,11427,11430,11433],{},[472,11416],{"id":11417,"d":2679},"MJX-79-TEX-N-37",[472,11419],{"id":11420,"d":479},"MJX-79-TEX-N-31",[472,11422],{"id":11423,"d":487},"MJX-79-TEX-N-30",[472,11425],{"id":11426,"d":483},"MJX-79-TEX-N-2B",[472,11428],{"id":11429,"d":10567},"MJX-79-TEX-N-2013",[472,11431],{"id":11432,"d":7667},"MJX-79-TEX-I-1D465",[472,11434],{"id":11435,"d":8082},"MJX-79-TEX-N-2C",[505,11437,11438],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,11439,11440,11459,11464,11480,11488,11494],{"dataMmlNode":512},[505,11441,11442,11447],{"dataMmlNode":515},[505,11443,11444],{"dataMmlNode":518},[520,11445],{"dataC":2732,"xLinkHref":11446},"#MJX-79-TEX-N-37",[505,11448,11449],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,11450,11451,11454,11456],{"dataMmlNode":518},[520,11452],{"dataC":533,"xLinkHref":11453},"#MJX-79-TEX-N-31",[520,11455],{"dataC":2732,"xLinkHref":11446,"transform":537},[520,11457],{"dataC":561,"xLinkHref":11458,"transform":965},"#MJX-79-TEX-N-30",[505,11460,11461],{"dataMmlNode":540,"transform":2847},[520,11462],{"dataC":544,"xLinkHref":11463},"#MJX-79-TEX-N-2B",[505,11465,11466,11470],{"dataMmlNode":515,"transform":2853},[505,11467,11468],{"dataMmlNode":518},[520,11469],{"dataC":2732,"xLinkHref":11446},[505,11471,11472],{"dataMmlNode":526,"transform":527,"dataMjxTexclass":528},[505,11473,11474,11476,11478],{"dataMmlNode":518},[520,11475],{"dataC":533,"xLinkHref":11453},[520,11477],{"dataC":561,"xLinkHref":11458,"transform":537},[520,11479],{"dataC":561,"xLinkHref":11458,"transform":965},[505,11481,11483],{"dataMmlNode":526,"dataMjxTexclass":528,"transform":11482},"translate(4509.8,0)",[505,11484,11485],{"dataMmlNode":540},[520,11486],{"dataC":10648,"xLinkHref":11487},"#MJX-79-TEX-N-2013",[505,11489,11491],{"dataMmlNode":7712,"transform":11490},"translate(5009.8,0)",[520,11492],{"dataC":7715,"xLinkHref":11493},"#MJX-79-TEX-I-1D465",[505,11495,11497],{"dataMmlNode":540,"transform":11496},"translate(5581.8,0)",[520,11498],{"dataC":8162,"xLinkHref":11499},"#MJX-79-TEX-N-2C"," где x – целое положительное число, не превышающее 2030, записали в 7-ричной системе счисления.\nОпределите наибольшее значение x, при котором в 7-ричной записи числа, являющегося значением данного арифметического выражения, содержится ровно 71 нуль.\nВ ответе запишите число в десятичной системе счисления.",[619,11502,622],{"id":11503},"решение-23",[402,11505,11506],{},"Приведу ещё одно своё решение этого задания.",[402,11508,11509],{},"В задании сказано, что x - это число в 19-ичной системе. Значит нам нужно перебрать все x от 0 до 18 в цикле и подставить в выражение. Расписав отдельно между операцией + значения чисел в развёрнутой форме в десятичной системе - сохраним результат в переменные значения a и b. Далее условие if проверяет(как по условию), что результат всего выражения(a+b) делится без остатка на 18. Команда results.add будет добавлять все такие варианты в список. В конце остаётся только вывести в консоли ответ, как наибольшее значение(max).",[624,11511,6830],{"id":11512},"решение-на-python-16",[402,11514,11515],{},"Через \"сохранение\" всех значений в списке.",[6832,11517,11519],{"className":6834,"code":11518,"language":6836,"meta":6837,"style":6837},"results = []\nfor x in range(0, 19):\n    a = 9 * 19 ** 7 + 8 * 19 ** 6 + 8 * 19 ** 5 + 9 * 19 ** 4 + 7 * 19 ** 3 + x * 19 ** 2 + 2 * 19 ** 1 + 1 * 19 ** 0\n    b = 2 * 19 ** 4 + x * 19 ** 3 + 9 * 19 ** 2 + 2 * 19 ** 1 + 3 * 19 ** 0\n    if (a + b) % 18 == 0:\n        results.append((a + b) \u002F\u002F 18)\nprint(max(results))\n",[6839,11520,11521,11531,11551,11652,11716,11736,11751],{"__ignoreMap":6837},[6842,11522,11523,11526,11528],{"class":6844,"line":6845},[6842,11524,11525],{"class":6848},"results ",[6842,11527,6853],{"class":6852},[6842,11529,11530],{"class":6848}," []\n",[6842,11532,11533,11535,11537,11539,11541,11543,11545,11547,11549],{"class":6844,"line":6899},[6842,11534,7819],{"class":6852},[6842,11536,7822],{"class":6848},[6842,11538,7825],{"class":6852},[6842,11540,7828],{"class":6856},[6842,11542,7831],{"class":6848},[6842,11544,508],{"class":6856},[6842,11546,7836],{"class":6848},[6842,11548,10810],{"class":6856},[6842,11550,7842],{"class":6848},[6842,11552,11553,11555,11557,11559,11561,11564,11566,11568,11570,11572,11574,11576,11578,11580,11582,11584,11586,11588,11590,11592,11594,11596,11598,11600,11602,11604,11606,11608,11610,11612,11614,11616,11618,11620,11622,11624,11626,11628,11630,11632,11634,11636,11638,11640,11642,11644,11646,11648,11650],{"class":6844,"line":884},[6842,11554,7847],{"class":6848},[6842,11556,6853],{"class":6852},[6842,11558,6937],{"class":6856},[6842,11560,6860],{"class":6852},[6842,11562,11563],{"class":6856}," 19",[6842,11565,7860],{"class":6852},[6842,11567,6857],{"class":6856},[6842,11569,6872],{"class":6852},[6842,11571,6875],{"class":6856},[6842,11573,6860],{"class":6852},[6842,11575,11563],{"class":6856},[6842,11577,7860],{"class":6852},[6842,11579,6891],{"class":6856},[6842,11581,6872],{"class":6852},[6842,11583,6875],{"class":6856},[6842,11585,6860],{"class":6852},[6842,11587,11563],{"class":6856},[6842,11589,7860],{"class":6852},[6842,11591,8299],{"class":6856},[6842,11593,6872],{"class":6852},[6842,11595,6937],{"class":6856},[6842,11597,6860],{"class":6852},[6842,11599,11563],{"class":6856},[6842,11601,7860],{"class":6852},[6842,11603,8356],{"class":6856},[6842,11605,6872],{"class":6852},[6842,11607,6857],{"class":6856},[6842,11609,6860],{"class":6852},[6842,11611,11563],{"class":6856},[6842,11613,7860],{"class":6852},[6842,11615,7601],{"class":6856},[6842,11617,6872],{"class":6852},[6842,11619,7822],{"class":6848},[6842,11621,7896],{"class":6852},[6842,11623,11563],{"class":6856},[6842,11625,7860],{"class":6852},[6842,11627,7283],{"class":6856},[6842,11629,6872],{"class":6852},[6842,11631,7283],{"class":6856},[6842,11633,6860],{"class":6852},[6842,11635,11563],{"class":6856},[6842,11637,7860],{"class":6852},[6842,11639,7876],{"class":6856},[6842,11641,6872],{"class":6852},[6842,11643,7876],{"class":6856},[6842,11645,6860],{"class":6852},[6842,11647,11563],{"class":6856},[6842,11649,7860],{"class":6852},[6842,11651,6907],{"class":6856},[6842,11653,11654,11656,11658,11660,11662,11664,11666,11668,11670,11672,11674,11676,11678,11680,11682,11684,11686,11688,11690,11692,11694,11696,11698,11700,11702,11704,11706,11708,11710,11712,11714],{"class":6844,"line":4212},[6842,11655,7920],{"class":6848},[6842,11657,6853],{"class":6852},[6842,11659,7283],{"class":6856},[6842,11661,6860],{"class":6852},[6842,11663,11563],{"class":6856},[6842,11665,7860],{"class":6852},[6842,11667,8356],{"class":6856},[6842,11669,6872],{"class":6852},[6842,11671,7822],{"class":6848},[6842,11673,7896],{"class":6852},[6842,11675,11563],{"class":6856},[6842,11677,7860],{"class":6852},[6842,11679,7601],{"class":6856},[6842,11681,6872],{"class":6852},[6842,11683,6937],{"class":6856},[6842,11685,6860],{"class":6852},[6842,11687,11563],{"class":6856},[6842,11689,7860],{"class":6852},[6842,11691,7283],{"class":6856},[6842,11693,6872],{"class":6852},[6842,11695,7283],{"class":6856},[6842,11697,6860],{"class":6852},[6842,11699,11563],{"class":6856},[6842,11701,7860],{"class":6852},[6842,11703,7876],{"class":6856},[6842,11705,6872],{"class":6852},[6842,11707,7601],{"class":6856},[6842,11709,6860],{"class":6852},[6842,11711,11563],{"class":6856},[6842,11713,7860],{"class":6852},[6842,11715,6907],{"class":6856},[6842,11717,11718,11720,11722,11724,11726,11728,11730,11732,11734],{"class":6844,"line":6947},[6842,11719,6929],{"class":6852},[6842,11721,7990],{"class":6848},[6842,11723,7993],{"class":6852},[6842,11725,7996],{"class":6848},[6842,11727,6934],{"class":6852},[6842,11729,10979],{"class":6856},[6842,11731,6940],{"class":6852},[6842,11733,6921],{"class":6856},[6842,11735,6924],{"class":6848},[6842,11737,11738,11741,11743,11745,11747,11749],{"class":6844,"line":6959},[6842,11739,11740],{"class":6848},"        results.append((a ",[6842,11742,7993],{"class":6852},[6842,11744,7996],{"class":6848},[6842,11746,8021],{"class":6852},[6842,11748,10979],{"class":6856},[6842,11750,8026],{"class":6848},[6842,11752,11753,11755,11757,11760],{"class":6844,"line":6971},[6842,11754,6974],{"class":6856},[6842,11756,7831],{"class":6848},[6842,11758,11759],{"class":6856},"max",[6842,11761,11762],{"class":6848},"(results))\n",[402,11764,11765],{},[406,11766,11014],{},[619,11768,11018],{"id":11769},"решение-или-1",[402,11771,11021],{},[624,11773,6830],{"id":11774},"решение-на-python-17",[6832,11776,11778],{"className":6834,"code":11777,"language":6836,"meta":6837,"style":6837},"R = 3*3125**8 + 2*625**7 - 4*625**6 + 3*125**5 - 2*25**4 - 2025 \ncounter = 0\nwhile R > 0:\n    if R % 25 == 0:\n        counter += 1\n    R \u002F\u002F= 25\nprint(counter)\n",[6839,11779,11780,11852,11861,11873,11889,11898,11906],{"__ignoreMap":6837},[6842,11781,11782,11784,11786,11788,11790,11792,11794,11796,11798,11800,11802,11804,11806,11808,11810,11812,11814,11816,11818,11820,11822,11824,11826,11828,11830,11832,11834,11836,11838,11840,11842,11844,11846,11849],{"class":6844,"line":6845},[6842,11783,11034],{"class":6848},[6842,11785,6853],{"class":6852},[6842,11787,7601],{"class":6856},[6842,11789,7896],{"class":6852},[6842,11791,11043],{"class":6856},[6842,11793,6866],{"class":6852},[6842,11795,11048],{"class":6856},[6842,11797,6872],{"class":6852},[6842,11799,7283],{"class":6856},[6842,11801,7896],{"class":6852},[6842,11803,11057],{"class":6856},[6842,11805,6866],{"class":6852},[6842,11807,11062],{"class":6856},[6842,11809,6888],{"class":6852},[6842,11811,8356],{"class":6856},[6842,11813,7896],{"class":6852},[6842,11815,11057],{"class":6856},[6842,11817,6866],{"class":6852},[6842,11819,9070],{"class":6856},[6842,11821,6872],{"class":6852},[6842,11823,7601],{"class":6856},[6842,11825,7896],{"class":6852},[6842,11827,11083],{"class":6856},[6842,11829,6866],{"class":6852},[6842,11831,9883],{"class":6856},[6842,11833,6888],{"class":6852},[6842,11835,7283],{"class":6856},[6842,11837,7896],{"class":6852},[6842,11839,11096],{"class":6856},[6842,11841,6866],{"class":6852},[6842,11843,9065],{"class":6856},[6842,11845,6888],{"class":6852},[6842,11847,11848],{"class":6856}," 2025",[6842,11850,11851],{"class":6848}," \n",[6842,11853,11854,11857,11859],{"class":6844,"line":6899},[6842,11855,11856],{"class":6848},"counter ",[6842,11858,6853],{"class":6852},[6842,11860,6907],{"class":6856},[6842,11862,11863,11865,11867,11869,11871],{"class":6844,"line":884},[6842,11864,6912],{"class":6852},[6842,11866,11119],{"class":6848},[6842,11868,6918],{"class":6852},[6842,11870,6921],{"class":6856},[6842,11872,6924],{"class":6848},[6842,11874,11875,11877,11879,11881,11883,11885,11887],{"class":6844,"line":4212},[6842,11876,6929],{"class":6852},[6842,11878,11119],{"class":6848},[6842,11880,6934],{"class":6852},[6842,11882,11136],{"class":6856},[6842,11884,6940],{"class":6852},[6842,11886,6921],{"class":6856},[6842,11888,6924],{"class":6848},[6842,11890,11891,11894,11896],{"class":6844,"line":6947},[6842,11892,11893],{"class":6848},"        counter ",[6842,11895,6953],{"class":6852},[6842,11897,6956],{"class":6856},[6842,11899,11900,11902,11904],{"class":6844,"line":6959},[6842,11901,11156],{"class":6848},[6842,11903,6965],{"class":6852},[6842,11905,11165],{"class":6856},[6842,11907,11908,11910],{"class":6844,"line":6971},[6842,11909,6974],{"class":6856},[6842,11911,11912],{"class":6848},"(counter)\n",[402,11914,11915],{},[406,11916,11917],{},"Ответ: 10",[619,11919,11921],{"id":11920},"решение-ещё-или","Решение ЕЩЁ ИЛИ:",[624,11923,6830],{"id":11924},"решение-на-python-18",[402,11926,11927],{},"Также через \"сохранение\" всех значений в списке.",[6832,11929,11931],{"className":6834,"code":11930,"language":6836,"meta":6837,"style":6837},"results = []\nfor x in range(1, 2031):  # x не должен превысить значение 2030\n    R = 7 ** 170 + 7 ** 100 - x\n    # Счётчик нулей\n    counter = 0\n    # Перебираем цифры все цифры в числе\n    while R > 0:\n        if R % 7 == 0:  # Условие проверки для 7-ичной системы\n            counter += 1  # считаем нули\n        R \u002F\u002F= 7  # Уменьшение разряда числа в 7-ичной системе\n\n    if counter == 71:\n        results.append(x)  # Добавить в список x удовлетворяющий условию задачи по количеству нулей\nprint(max(results))  # Выводим ответ как сохранившейся в списке максимальный x\n",[6839,11932,11933,11941,11966,11991,11995,12004,12009,12021,12041,12053,12065,12069,12083,12091],{"__ignoreMap":6837},[6842,11934,11935,11937,11939],{"class":6844,"line":6845},[6842,11936,11525],{"class":6848},[6842,11938,6853],{"class":6852},[6842,11940,11530],{"class":6848},[6842,11942,11943,11945,11947,11949,11951,11953,11955,11957,11960,11963],{"class":6844,"line":6899},[6842,11944,7819],{"class":6852},[6842,11946,7822],{"class":6848},[6842,11948,7825],{"class":6852},[6842,11950,7828],{"class":6856},[6842,11952,7831],{"class":6848},[6842,11954,717],{"class":6856},[6842,11956,7836],{"class":6848},[6842,11958,11959],{"class":6856},"2031",[6842,11961,11962],{"class":6848},"):  ",[6842,11964,11965],{"class":8530},"# x не должен превысить значение 2030\n",[6842,11967,11968,11970,11972,11974,11976,11979,11981,11983,11985,11987,11989],{"class":6844,"line":884},[6842,11969,11156],{"class":6848},[6842,11971,6853],{"class":6852},[6842,11973,6857],{"class":6856},[6842,11975,7860],{"class":6852},[6842,11977,11978],{"class":6856}," 170",[6842,11980,6872],{"class":6852},[6842,11982,6857],{"class":6856},[6842,11984,7860],{"class":6852},[6842,11986,10199],{"class":6856},[6842,11988,6888],{"class":6852},[6842,11990,10204],{"class":6848},[6842,11992,11993],{"class":6844,"line":4212},[6842,11994,10209],{"class":8530},[6842,11996,11997,12000,12002],{"class":6844,"line":6947},[6842,11998,11999],{"class":6848},"    counter ",[6842,12001,6853],{"class":6852},[6842,12003,6907],{"class":6856},[6842,12005,12006],{"class":6844,"line":6959},[6842,12007,12008],{"class":8530},"    # Перебираем цифры все цифры в числе\n",[6842,12010,12011,12013,12015,12017,12019],{"class":6844,"line":6971},[6842,12012,8987],{"class":6852},[6842,12014,11119],{"class":6848},[6842,12016,6918],{"class":6852},[6842,12018,6921],{"class":6856},[6842,12020,6924],{"class":6848},[6842,12022,12023,12025,12027,12029,12031,12033,12035,12038],{"class":6844,"line":8584},[6842,12024,8764],{"class":6852},[6842,12026,11119],{"class":6848},[6842,12028,6934],{"class":6852},[6842,12030,6857],{"class":6856},[6842,12032,6940],{"class":6852},[6842,12034,6921],{"class":6856},[6842,12036,12037],{"class":6848},":  ",[6842,12039,12040],{"class":8530},"# Условие проверки для 7-ичной системы\n",[6842,12042,12043,12046,12048,12050],{"class":6844,"line":8597},[6842,12044,12045],{"class":6848},"            counter ",[6842,12047,6953],{"class":6852},[6842,12049,7876],{"class":6856},[6842,12051,12052],{"class":8530},"  # считаем нули\n",[6842,12054,12055,12058,12060,12062],{"class":6844,"line":9075},[6842,12056,12057],{"class":6848},"        R ",[6842,12059,6965],{"class":6852},[6842,12061,6857],{"class":6856},[6842,12063,12064],{"class":8530},"  # Уменьшение разряда числа в 7-ичной системе\n",[6842,12066,12067],{"class":6844,"line":9093},[6842,12068,9046],{"emptyLinePlaceholder":9045},[6842,12070,12071,12073,12076,12078,12081],{"class":6844,"line":9109},[6842,12072,6929],{"class":6852},[6842,12074,12075],{"class":6848}," counter ",[6842,12077,8455],{"class":6852},[6842,12079,12080],{"class":6856}," 71",[6842,12082,6924],{"class":6848},[6842,12084,12085,12088],{"class":6844,"line":9125},[6842,12086,12087],{"class":6848},"        results.append(x)  ",[6842,12089,12090],{"class":8530},"# Добавить в список x удовлетворяющий условию задачи по количеству нулей\n",[6842,12092,12093,12095,12097,12099,12102],{"class":6844,"line":9139},[6842,12094,6974],{"class":6856},[6842,12096,7831],{"class":6848},[6842,12098,11759],{"class":6856},[6842,12100,12101],{"class":6848},"(results))  ",[6842,12103,12104],{"class":8530},"# Выводим ответ как сохранившейся в списке максимальный x\n",[402,12106,12107],{},[406,12108,12109],{},"Ответ: 2029",[2923,12111,12112],{},[402,12113,12114],{},"p.s. Вариантов и способов решения этого и подобных заданий № 14 в коде на python всегда может быть несколько: \"замудренных\", изящных, коротких и не очень.",[444,12116,12118],{"id":12117},"задача-24-демоверсия-2026","Задача 24 (Демоверсия 2026)",[402,12120,10523],{},[402,12122,12123],{},[452,12124,12126],{"className":12125,"jax":456},[455],[458,12127,12130,12171],{"style":460,"xmlns":461,"width":12128,"height":7008,"role":464,"focusable":465,"viewBox":12129,"xmlnsXLink":467},"56.028ex","0 -881.8 24764.3 963.8",[469,12131,12132,12135,12138,12141,12144,12147,12150,12153,12156,12159,12162,12165,12168],{},[472,12133],{"id":12134,"d":475},"MJX-80-TEX-N-32",[472,12136],{"id":12137,"d":7018},"MJX-80-TEX-N-2219",[472,12139],{"id":12140,"d":479},"MJX-80-TEX-N-31",[472,12142],{"id":12143,"d":495},"MJX-80-TEX-N-38",[472,12145],{"id":12146,"d":2679},"MJX-80-TEX-N-37",[472,12148],{"id":12149,"d":487},"MJX-80-TEX-N-30",[472,12151],{"id":12152,"d":483},"MJX-80-TEX-N-2B",[472,12154],{"id":12155,"d":2686},"MJX-80-TEX-N-39",[472,12157],{"id":12158,"d":10567},"MJX-80-TEX-N-2013",[472,12160],{"id":12161,"d":926},"MJX-80-TEX-N-34",[472,12163],{"id":12164,"d":922},"MJX-80-TEX-N-33",[472,12166],{"id":12167,"d":499},"MJX-80-TEX-N-36",[472,12169],{"id":12170,"d":2199},"MJX-80-TEX-N-35",[505,12172,12173],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,12174,12175,12180,12185,12214,12220,12244,12252,12257,12262,12287,12292,12313,12320,12325,12330,12351,12358],{"dataMmlNode":512},[505,12176,12177],{"dataMmlNode":518},[520,12178],{"dataC":522,"xLinkHref":12179},"#MJX-80-TEX-N-32",[505,12181,12182],{"dataMmlNode":540,"transform":2713},[520,12183],{"dataC":7065,"xLinkHref":12184},"#MJX-80-TEX-N-2219",[505,12186,12187,12200],{"dataMmlNode":515,"transform":7069},[505,12188,12189,12191,12194,12197],{"dataMmlNode":518},[520,12190],{"dataC":522,"xLinkHref":12179},[520,12192],{"dataC":533,"xLinkHref":12193,"transform":537},"#MJX-80-TEX-N-31",[520,12195],{"dataC":581,"xLinkHref":12196,"transform":965},"#MJX-80-TEX-N-38",[520,12198],{"dataC":2732,"xLinkHref":12199,"transform":968},"#MJX-80-TEX-N-37",[505,12201,12203],{"dataMmlNode":526,"transform":12202,"dataMjxTexclass":528},"translate(2033,403.1) scale(0.707)",[505,12204,12205,12207,12210,12212],{"dataMmlNode":518},[520,12206],{"dataC":522,"xLinkHref":12179},[520,12208],{"dataC":561,"xLinkHref":12209,"transform":537},"#MJX-80-TEX-N-30",[520,12211],{"dataC":522,"xLinkHref":12179,"transform":965},[520,12213],{"dataC":561,"xLinkHref":12209,"transform":968},[505,12215,12217],{"dataMmlNode":540,"transform":12216},"translate(5163.9,0)",[520,12218],{"dataC":544,"xLinkHref":12219},"#MJX-80-TEX-N-2B",[505,12221,12223,12232],{"dataMmlNode":515,"transform":12222},"translate(6164.1,0)",[505,12224,12225,12227,12229],{"dataMmlNode":518},[520,12226],{"dataC":2732,"xLinkHref":12199},[520,12228],{"dataC":522,"xLinkHref":12179,"transform":537},[520,12230],{"dataC":2739,"xLinkHref":12231,"transform":965},"#MJX-80-TEX-N-39",[505,12233,12234],{"dataMmlNode":526,"transform":6788,"dataMjxTexclass":528},[505,12235,12236,12238,12240,12242],{"dataMmlNode":518},[520,12237],{"dataC":522,"xLinkHref":12179},[520,12239],{"dataC":561,"xLinkHref":12209,"transform":537},[520,12241],{"dataC":522,"xLinkHref":12179,"transform":965},[520,12243],{"dataC":533,"xLinkHref":12193,"transform":968},[505,12245,12247],{"dataMmlNode":526,"dataMjxTexclass":528,"transform":12246},"translate(9161.3,0)",[505,12248,12249],{"dataMmlNode":540},[520,12250],{"dataC":10648,"xLinkHref":12251},"#MJX-80-TEX-N-2013",[505,12253,12255],{"dataMmlNode":518,"transform":12254},"translate(9661.3,0)",[520,12256],{"dataC":522,"xLinkHref":12179},[505,12258,12260],{"dataMmlNode":540,"transform":12259},"translate(10383.5,0)",[520,12261],{"dataC":7065,"xLinkHref":12184},[505,12263,12265,12275],{"dataMmlNode":515,"transform":12264},"translate(11105.8,0)",[505,12266,12267,12269,12272],{"dataMmlNode":518},[520,12268],{"dataC":522,"xLinkHref":12179},[520,12270],{"dataC":963,"xLinkHref":12271,"transform":537},"#MJX-80-TEX-N-34",[520,12273],{"dataC":959,"xLinkHref":12274,"transform":965},"#MJX-80-TEX-N-33",[505,12276,12277],{"dataMmlNode":526,"transform":4833,"dataMjxTexclass":528},[505,12278,12279,12281,12283,12285],{"dataMmlNode":518},[520,12280],{"dataC":522,"xLinkHref":12179},[520,12282],{"dataC":561,"xLinkHref":12209,"transform":537},[520,12284],{"dataC":522,"xLinkHref":12179,"transform":965},[520,12286],{"dataC":522,"xLinkHref":12179,"transform":968},[505,12288,12290],{"dataMmlNode":540,"transform":12289},"translate(14325.2,0)",[520,12291],{"dataC":544,"xLinkHref":12219},[505,12293,12295,12301],{"dataMmlNode":515,"transform":12294},"translate(15325.4,0)",[505,12296,12297,12299],{"dataMmlNode":518},[520,12298],{"dataC":581,"xLinkHref":12196},[520,12300],{"dataC":533,"xLinkHref":12193,"transform":537},[505,12302,12303],{"dataMmlNode":526,"transform":2863,"dataMjxTexclass":528},[505,12304,12305,12307,12309,12311],{"dataMmlNode":518},[520,12306],{"dataC":522,"xLinkHref":12179},[520,12308],{"dataC":561,"xLinkHref":12209,"transform":537},[520,12310],{"dataC":522,"xLinkHref":12179,"transform":965},[520,12312],{"dataC":959,"xLinkHref":12274,"transform":968},[505,12314,12316],{"dataMmlNode":526,"dataMjxTexclass":528,"transform":12315},"translate(17822.6,0)",[505,12317,12318],{"dataMmlNode":540},[520,12319],{"dataC":10648,"xLinkHref":12251},[505,12321,12323],{"dataMmlNode":518,"transform":12322},"translate(18322.6,0)",[520,12324],{"dataC":522,"xLinkHref":12179},[505,12326,12328],{"dataMmlNode":540,"transform":12327},"translate(19044.9,0)",[520,12329],{"dataC":7065,"xLinkHref":12184},[505,12331,12333,12339],{"dataMmlNode":515,"transform":12332},"translate(19767.1,0)",[505,12334,12335,12337],{"dataMmlNode":518},[520,12336],{"dataC":522,"xLinkHref":12179},[520,12338],{"dataC":2732,"xLinkHref":12199,"transform":537},[505,12340,12341],{"dataMmlNode":526,"transform":7200,"dataMjxTexclass":528},[505,12342,12343,12345,12347,12349],{"dataMmlNode":518},[520,12344],{"dataC":522,"xLinkHref":12179},[520,12346],{"dataC":561,"xLinkHref":12209,"transform":537},[520,12348],{"dataC":522,"xLinkHref":12179,"transform":965},[520,12350],{"dataC":963,"xLinkHref":12271,"transform":968},[505,12352,12354],{"dataMmlNode":526,"dataMjxTexclass":528,"transform":12353},"translate(22264.3,0)",[505,12355,12356],{"dataMmlNode":540},[520,12357],{"dataC":10648,"xLinkHref":12251},[505,12359,12361,12364,12367,12369],{"dataMmlNode":518,"transform":12360},"translate(22764.3,0)",[520,12362],{"dataC":599,"xLinkHref":12363},"#MJX-80-TEX-N-36",[520,12365],{"dataC":2255,"xLinkHref":12366,"transform":537},"#MJX-80-TEX-N-35",[520,12368],{"dataC":599,"xLinkHref":12363,"transform":965},[520,12370],{"dataC":533,"xLinkHref":12193,"transform":968},[402,12372,12373],{},"записали в системе счисления с основанием 27.\nОпределите в 27-ричной записи числа количество цифр с числовым значением, превышающим 9.",[444,12375,622],{"id":12376},"решение-24",[6832,12378,12380],{"className":6834,"code":12379,"language":6836,"meta":6837,"style":6837},"R = 2 * 2187 ** 2020 + 729 ** 2021 - 2 * 243 ** 2022 + 81 ** 2023 - 2 * 27 ** 2024 - 6561\ncounter = 0\nwhile R > 0:\n    if R % 27 > 9:\n        counter += 1 \n    R \u002F\u002F= 27 \nprint(counter)\n",[6839,12381,12382,12449,12457,12469,12485,12495,12505],{"__ignoreMap":6837},[6842,12383,12384,12386,12388,12390,12392,12395,12397,12400,12402,12404,12406,12409,12411,12413,12415,12417,12419,12422,12424,12426,12428,12431,12433,12435,12437,12439,12441,12444,12446],{"class":6844,"line":6845},[6842,12385,11034],{"class":6848},[6842,12387,6853],{"class":6852},[6842,12389,7283],{"class":6856},[6842,12391,6860],{"class":6852},[6842,12393,12394],{"class":6856}," 2187",[6842,12396,7860],{"class":6852},[6842,12398,12399],{"class":6856}," 2020",[6842,12401,6872],{"class":6852},[6842,12403,6880],{"class":6856},[6842,12405,7860],{"class":6852},[6842,12407,12408],{"class":6856}," 2021",[6842,12410,6888],{"class":6852},[6842,12412,7283],{"class":6856},[6842,12414,6860],{"class":6852},[6842,12416,7301],{"class":6856},[6842,12418,7860],{"class":6852},[6842,12420,12421],{"class":6856}," 2022",[6842,12423,6872],{"class":6852},[6842,12425,7315],{"class":6856},[6842,12427,7860],{"class":6852},[6842,12429,12430],{"class":6856}," 2023",[6842,12432,6888],{"class":6852},[6842,12434,7283],{"class":6856},[6842,12436,6860],{"class":6852},[6842,12438,7329],{"class":6856},[6842,12440,7860],{"class":6852},[6842,12442,12443],{"class":6856}," 2024",[6842,12445,6888],{"class":6852},[6842,12447,12448],{"class":6856}," 6561\n",[6842,12450,12451,12453,12455],{"class":6844,"line":6899},[6842,12452,11856],{"class":6848},[6842,12454,6853],{"class":6852},[6842,12456,6907],{"class":6856},[6842,12458,12459,12461,12463,12465,12467],{"class":6844,"line":884},[6842,12460,6912],{"class":6852},[6842,12462,11119],{"class":6848},[6842,12464,6918],{"class":6852},[6842,12466,6921],{"class":6856},[6842,12468,6924],{"class":6848},[6842,12470,12471,12473,12475,12477,12479,12481,12483],{"class":6844,"line":4212},[6842,12472,6929],{"class":6852},[6842,12474,11119],{"class":6848},[6842,12476,6934],{"class":6852},[6842,12478,7329],{"class":6856},[6842,12480,7385],{"class":6852},[6842,12482,6937],{"class":6856},[6842,12484,6924],{"class":6848},[6842,12486,12487,12489,12491,12493],{"class":6844,"line":6947},[6842,12488,11893],{"class":6848},[6842,12490,6953],{"class":6852},[6842,12492,7876],{"class":6856},[6842,12494,11851],{"class":6848},[6842,12496,12497,12499,12501,12503],{"class":6844,"line":6959},[6842,12498,11156],{"class":6848},[6842,12500,6965],{"class":6852},[6842,12502,7329],{"class":6856},[6842,12504,11851],{"class":6848},[6842,12506,12507,12509],{"class":6844,"line":6971},[6842,12508,6974],{"class":6856},[6842,12510,11912],{"class":6848},[402,12512,12513],{},[406,12514,12515],{},"Ответ: 3367",[619,12517,10520],{"id":12518},"или-2",[402,12520,12521],{},"Операнды арифметического выражения записаны в системе счисления\nс основанием 29.",[402,12523,12524],{},[452,12525,12527],{"className":12526,"jax":456},[455],[458,12528,12532,12567],{"style":7655,"xmlns":461,"width":12529,"height":12530,"role":464,"focusable":465,"viewBox":12531,"xmlnsXLink":467},"23.635ex","1.906ex","0 -677 10446.7 842.6",[469,12533,12534,12537,12540,12543,12546,12549,12552,12555,12558,12561,12564],{},[472,12535],{"id":12536,"d":2686},"MJX-81-TEX-N-39",[472,12538],{"id":12539,"d":475},"MJX-81-TEX-N-32",[472,12541],{"id":12542,"d":922},"MJX-81-TEX-N-33",[472,12544],{"id":12545,"d":7667},"MJX-81-TEX-I-1D465",[472,12547],{"id":12548,"d":495},"MJX-81-TEX-N-38",[472,12550],{"id":12551,"d":2679},"MJX-81-TEX-N-37",[472,12553],{"id":12554,"d":926},"MJX-81-TEX-N-34",[472,12556],{"id":12557,"d":483},"MJX-81-TEX-N-2B",[472,12559],{"id":12560,"d":2199},"MJX-81-TEX-N-35",[472,12562],{"id":12563,"d":499},"MJX-81-TEX-N-36",[472,12565],{"id":12566,"d":479},"MJX-81-TEX-N-31",[505,12568,12569],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,12570,12571,12582,12587,12609,12615,12625,12630],{"dataMmlNode":512},[505,12572,12573,12576,12579],{"dataMmlNode":518},[520,12574],{"dataC":2739,"xLinkHref":12575},"#MJX-81-TEX-N-39",[520,12577],{"dataC":522,"xLinkHref":12578,"transform":537},"#MJX-81-TEX-N-32",[520,12580],{"dataC":959,"xLinkHref":12581,"transform":965},"#MJX-81-TEX-N-33",[505,12583,12584],{"dataMmlNode":7712,"transform":968},[520,12585],{"dataC":7715,"xLinkHref":12586},"#MJX-81-TEX-I-1D465",[505,12588,12590,12601],{"dataMmlNode":7733,"transform":12589},"translate(2072,0)",[505,12591,12592,12595,12598],{"dataMmlNode":518},[520,12593],{"dataC":581,"xLinkHref":12594},"#MJX-81-TEX-N-38",[520,12596],{"dataC":2732,"xLinkHref":12597,"transform":537},"#MJX-81-TEX-N-37",[520,12599],{"dataC":963,"xLinkHref":12600,"transform":965},"#MJX-81-TEX-N-34",[505,12602,12603],{"dataMmlNode":526,"transform":10507,"dataMjxTexclass":528},[505,12604,12605,12607],{"dataMmlNode":518},[520,12606],{"dataC":522,"xLinkHref":12578},[520,12608],{"dataC":2739,"xLinkHref":12575,"transform":537},[505,12610,12612],{"dataMmlNode":540,"transform":12611},"translate(4584.3,0)",[520,12613],{"dataC":544,"xLinkHref":12614},"#MJX-81-TEX-N-2B",[505,12616,12618,12621,12623],{"dataMmlNode":518,"transform":12617},"translate(5584.6,0)",[520,12619],{"dataC":2255,"xLinkHref":12620},"#MJX-81-TEX-N-35",[520,12622],{"dataC":522,"xLinkHref":12578,"transform":537},[520,12624],{"dataC":963,"xLinkHref":12600,"transform":965},[505,12626,12628],{"dataMmlNode":7712,"transform":12627},"translate(7084.6,0)",[520,12629],{"dataC":7715,"xLinkHref":12586},[505,12631,12633,12645],{"dataMmlNode":7733,"transform":12632},"translate(7656.6,0)",[505,12634,12635,12638,12641,12643],{"dataMmlNode":518},[520,12636],{"dataC":599,"xLinkHref":12637},"#MJX-81-TEX-N-36",[520,12639],{"dataC":533,"xLinkHref":12640,"transform":537},"#MJX-81-TEX-N-31",[520,12642],{"dataC":2255,"xLinkHref":12620,"transform":965},[520,12644],{"dataC":522,"xLinkHref":12578,"transform":968},[505,12646,12648],{"dataMmlNode":526,"transform":12647,"dataMjxTexclass":528},"translate(2033,-150) scale(0.707)",[505,12649,12650,12652],{"dataMmlNode":518},[520,12651],{"dataC":522,"xLinkHref":12578},[520,12653],{"dataC":2739,"xLinkHref":12575,"transform":537},[402,12655,12656],{},"В записи чисел переменной x обозначена неизвестная цифра из алфавита 29-ричной системы счисления.\nОпределите наибольшее значение x, при котором значение данного арифметического выражения кратно 28.\nДля найденного x вычислите частное от деления значения арифметического выражения на 28 и укажите его в ответе в десятичной системе счисления.\nОснование системы счисления указывать не нужно.",[619,12658,11018],{"id":12659},"решение-или-2",[6832,12661,12663],{"className":6834,"code":12662,"language":6836,"meta":6837,"style":6837},"for x in range(28, -1, -1):\n    a = 4 * 29 ** 0 + 7 * 29 ** 1 + 8 * 29 ** 2 + x * 29 ** 3 + 3 * 29 ** 4 + 2 * 29 ** 5 + 9 * 29 ** 6\n    b = 2 * 29 ** 0 + 5 * 29 ** 1 + 1 * 29 ** 2 + 6 * 29 ** 3 + x * 29 ** 4 + 4 * 29 ** 5 + 2 * 29 ** 6 + 5 * 29 ** 7\n    if (a + b) % 28 == 0:\n        print(x, (a + b) \u002F\u002F 28)\n        break # т.к. ищем максимальный x и идём в цикле от наибольшего x можно уже прервать цикл\n",[6839,12664,12665,12693,12782,12882,12903,12919],{"__ignoreMap":6837},[6842,12666,12667,12669,12671,12673,12675,12677,12679,12681,12683,12685,12687,12689,12691],{"class":6844,"line":6845},[6842,12668,7819],{"class":6852},[6842,12670,7822],{"class":6848},[6842,12672,7825],{"class":6852},[6842,12674,7828],{"class":6856},[6842,12676,7831],{"class":6848},[6842,12678,1229],{"class":6856},[6842,12680,7836],{"class":6848},[6842,12682,9035],{"class":6852},[6842,12684,717],{"class":6856},[6842,12686,7836],{"class":6848},[6842,12688,9035],{"class":6852},[6842,12690,717],{"class":6856},[6842,12692,7842],{"class":6848},[6842,12694,12695,12697,12699,12701,12703,12706,12708,12710,12712,12714,12716,12718,12720,12722,12724,12726,12728,12730,12732,12734,12736,12738,12740,12742,12744,12746,12748,12750,12752,12754,12756,12758,12760,12762,12764,12766,12768,12770,12772,12774,12776,12778,12780],{"class":6844,"line":6899},[6842,12696,7847],{"class":6848},[6842,12698,6853],{"class":6852},[6842,12700,8356],{"class":6856},[6842,12702,6860],{"class":6852},[6842,12704,12705],{"class":6856}," 29",[6842,12707,7860],{"class":6852},[6842,12709,6921],{"class":6856},[6842,12711,6872],{"class":6852},[6842,12713,6857],{"class":6856},[6842,12715,6860],{"class":6852},[6842,12717,12705],{"class":6856},[6842,12719,7860],{"class":6852},[6842,12721,7876],{"class":6856},[6842,12723,6872],{"class":6852},[6842,12725,6875],{"class":6856},[6842,12727,6860],{"class":6852},[6842,12729,12705],{"class":6856},[6842,12731,7860],{"class":6852},[6842,12733,7283],{"class":6856},[6842,12735,6872],{"class":6852},[6842,12737,7822],{"class":6848},[6842,12739,7896],{"class":6852},[6842,12741,12705],{"class":6856},[6842,12743,7860],{"class":6852},[6842,12745,7601],{"class":6856},[6842,12747,6872],{"class":6852},[6842,12749,7601],{"class":6856},[6842,12751,6860],{"class":6852},[6842,12753,12705],{"class":6856},[6842,12755,7860],{"class":6852},[6842,12757,8356],{"class":6856},[6842,12759,6872],{"class":6852},[6842,12761,7283],{"class":6856},[6842,12763,6860],{"class":6852},[6842,12765,12705],{"class":6856},[6842,12767,7860],{"class":6852},[6842,12769,8299],{"class":6856},[6842,12771,6872],{"class":6852},[6842,12773,6937],{"class":6856},[6842,12775,6860],{"class":6852},[6842,12777,12705],{"class":6856},[6842,12779,7860],{"class":6852},[6842,12781,9998],{"class":6856},[6842,12783,12784,12786,12788,12790,12792,12794,12796,12798,12800,12802,12804,12806,12808,12810,12812,12814,12816,12818,12820,12822,12824,12826,12828,12830,12832,12834,12836,12838,12840,12842,12844,12846,12848,12850,12852,12854,12856,12858,12860,12862,12864,12866,12868,12870,12872,12874,12876,12878,12880],{"class":6844,"line":884},[6842,12785,7920],{"class":6848},[6842,12787,6853],{"class":6852},[6842,12789,7283],{"class":6856},[6842,12791,6860],{"class":6852},[6842,12793,12705],{"class":6856},[6842,12795,7860],{"class":6852},[6842,12797,6921],{"class":6856},[6842,12799,6872],{"class":6852},[6842,12801,8299],{"class":6856},[6842,12803,6860],{"class":6852},[6842,12805,12705],{"class":6856},[6842,12807,7860],{"class":6852},[6842,12809,7876],{"class":6856},[6842,12811,6872],{"class":6852},[6842,12813,7876],{"class":6856},[6842,12815,6860],{"class":6852},[6842,12817,12705],{"class":6856},[6842,12819,7860],{"class":6852},[6842,12821,7283],{"class":6856},[6842,12823,6872],{"class":6852},[6842,12825,6891],{"class":6856},[6842,12827,6860],{"class":6852},[6842,12829,12705],{"class":6856},[6842,12831,7860],{"class":6852},[6842,12833,7601],{"class":6856},[6842,12835,6872],{"class":6852},[6842,12837,7822],{"class":6848},[6842,12839,7896],{"class":6852},[6842,12841,12705],{"class":6856},[6842,12843,7860],{"class":6852},[6842,12845,8356],{"class":6856},[6842,12847,6872],{"class":6852},[6842,12849,8356],{"class":6856},[6842,12851,6860],{"class":6852},[6842,12853,12705],{"class":6856},[6842,12855,7860],{"class":6852},[6842,12857,8299],{"class":6856},[6842,12859,6872],{"class":6852},[6842,12861,7283],{"class":6856},[6842,12863,6860],{"class":6852},[6842,12865,12705],{"class":6856},[6842,12867,7860],{"class":6852},[6842,12869,6891],{"class":6856},[6842,12871,6872],{"class":6852},[6842,12873,8299],{"class":6856},[6842,12875,6860],{"class":6852},[6842,12877,12705],{"class":6856},[6842,12879,7860],{"class":6852},[6842,12881,7617],{"class":6856},[6842,12883,12884,12886,12888,12890,12892,12894,12897,12899,12901],{"class":6844,"line":4212},[6842,12885,6929],{"class":6852},[6842,12887,7990],{"class":6848},[6842,12889,7993],{"class":6852},[6842,12891,7996],{"class":6848},[6842,12893,6934],{"class":6852},[6842,12895,12896],{"class":6856}," 28",[6842,12898,6940],{"class":6852},[6842,12900,6921],{"class":6856},[6842,12902,6924],{"class":6848},[6842,12904,12905,12907,12909,12911,12913,12915,12917],{"class":6844,"line":6947},[6842,12906,8011],{"class":6856},[6842,12908,8014],{"class":6848},[6842,12910,7993],{"class":6852},[6842,12912,7996],{"class":6848},[6842,12914,8021],{"class":6852},[6842,12916,12896],{"class":6856},[6842,12918,8026],{"class":6848},[6842,12920,12921,12923],{"class":6844,"line":6959},[6842,12922,11006],{"class":6852},[6842,12924,11009],{"class":8530},[402,12926,12927],{},[406,12928,12929],{},"Ответ: 3319197720",[619,12931,12933],{"id":12932},"или-2-1","ИЛИ 2",[402,12935,12936,12937,13072,13073,13075],{},"Значение арифметического выражения\n",[452,12938,12940],{"className":12939,"jax":456},[455],[458,12941,12945,12980],{"style":9342,"xmlns":461,"width":12942,"height":12943,"role":464,"focusable":465,"viewBox":12944,"xmlnsXLink":467},"22.056ex","2.394ex","0 -864 9748.7 1058",[469,12946,12947,12950,12953,12956,12959,12962,12965,12968,12971,12974,12977],{},[472,12948],{"id":12949,"d":2686},"MJX-82-TEX-N-39",[472,12951],{"id":12952,"d":7018},"MJX-82-TEX-N-2219",[472,12954],{"id":12955,"d":479},"MJX-82-TEX-N-31",[472,12957],{"id":12958,"d":475},"MJX-82-TEX-N-32",[472,12960],{"id":12961,"d":487},"MJX-82-TEX-N-30",[472,12963],{"id":12964,"d":483},"MJX-82-TEX-N-2B",[472,12966],{"id":12967,"d":495},"MJX-82-TEX-N-38",[472,12969],{"id":12970,"d":2199},"MJX-82-TEX-N-35",[472,12972],{"id":12973,"d":10567},"MJX-82-TEX-N-2013",[472,12975],{"id":12976,"d":7667},"MJX-82-TEX-I-1D465",[472,12978],{"id":12979,"d":8082},"MJX-82-TEX-N-2C",[505,12981,12982],{"stroke":507,"fill":507,"stroke-width":508,"transform":509},[505,12983,12984,12989,12994,13015,13021,13027,13032,13052,13060,13066],{"dataMmlNode":512},[505,12985,12986],{"dataMmlNode":518},[520,12987],{"dataC":2739,"xLinkHref":12988},"#MJX-82-TEX-N-39",[505,12990,12991],{"dataMmlNode":540,"transform":2713},[520,12992],{"dataC":7065,"xLinkHref":12993},"#MJX-82-TEX-N-2219",[505,12995,12996,13003],{"dataMmlNode":515,"transform":7069},[505,12997,12998,13001],{"dataMmlNode":518},[520,12999],{"dataC":533,"xLinkHref":13000},"#MJX-82-TEX-N-31",[520,13002],{"dataC":533,"xLinkHref":13000,"transform":537},[505,13004,13005],{"dataMmlNode":526,"transform":2863,"dataMjxTexclass":528},[505,13006,13007,13010,13012],{"dataMmlNode":518},[520,13008],{"dataC":522,"xLinkHref":13009},"#MJX-82-TEX-N-32",[520,13011],{"dataC":533,"xLinkHref":13000,"transform":537},[520,13013],{"dataC":561,"xLinkHref":13014,"transform":965},"#MJX-82-TEX-N-30",[505,13016,13018],{"dataMmlNode":540,"transform":13017},"translate(3810.3,0)",[520,13019],{"dataC":544,"xLinkHref":13020},"#MJX-82-TEX-N-2B",[505,13022,13024],{"dataMmlNode":518,"transform":13023},"translate(4810.5,0)",[520,13025],{"dataC":581,"xLinkHref":13026},"#MJX-82-TEX-N-38",[505,13028,13030],{"dataMmlNode":540,"transform":13029},"translate(5532.8,0)",[520,13031],{"dataC":7065,"xLinkHref":12993},[505,13033,13035,13041],{"dataMmlNode":515,"transform":13034},"translate(6255,0)",[505,13036,13037,13039],{"dataMmlNode":518},[520,13038],{"dataC":533,"xLinkHref":13000},[520,13040],{"dataC":533,"xLinkHref":13000,"transform":537},[505,13042,13043],{"dataMmlNode":526,"transform":2863,"dataMjxTexclass":528},[505,13044,13045,13047,13050],{"dataMmlNode":518},[520,13046],{"dataC":533,"xLinkHref":13000},[520,13048],{"dataC":2255,"xLinkHref":13049,"transform":537},"#MJX-82-TEX-N-35",[520,13051],{"dataC":561,"xLinkHref":13014,"transform":965},[505,13053,13055],{"dataMmlNode":526,"dataMjxTexclass":528,"transform":13054},"translate(8398.7,0)",[505,13056,13057],{"dataMmlNode":540},[520,13058],{"dataC":10648,"xLinkHref":13059},"#MJX-82-TEX-N-2013",[505,13061,13063],{"dataMmlNode":7712,"transform":13062},"translate(8898.7,0)",[520,13064],{"dataC":7715,"xLinkHref":13065},"#MJX-82-TEX-I-1D465",[505,13067,13069],{"dataMmlNode":540,"transform":13068},"translate(9470.7,0)",[520,13070],{"dataC":8162,"xLinkHref":13071},"#MJX-82-TEX-N-2C","\nгде x – целое положительное число, не превышающее 3000, записали в 11-ричной системе счисления.\nОпределите наибольшее значение x, при котором в 11-ричной записи числа, являющегося значением данного арифметического выражения,\nсодержится ровно 60 нулей.",[10525,13074],{},"\nВ ответе запишите число в десятичной системе счисления.",[619,13077,13079],{"id":13078},"решение-или-2-1","Решение ИЛИ 2:",[6832,13081,13083],{"className":6834,"code":13082,"language":6836,"meta":6837,"style":6837},"results = []\nfor x in range(1, 3001):  # x не должен превысить значение 3000\n    R = 9 * 11 ** 210 + 8 * 11 ** 150 - x\n    # Счётчик нулей\n    counter = 0\n    # Перебираем цифры все цифры в числе\n    while R > 0:\n        if R % 11 == 0:  # Условие проверки для 11-ичной системы\n            counter += 1  # считаем нули\n        R \u002F\u002F= 11  # Уменьшение разряда числа в 7-ичной системе\n\n    if counter == 60:  # насчитали ровно 60 нулей\n        results.append(x)  # Добавить в список x удовлетворяющий условию задачи по количеству нулей\nprint(max(results))  # Выводим ответ как сохранившейся в списке максимальный x\n",[6839,13084,13085,13093,13117,13151,13155,13163,13167,13179,13198,13208,13218,13222,13238,13244],{"__ignoreMap":6837},[6842,13086,13087,13089,13091],{"class":6844,"line":6845},[6842,13088,11525],{"class":6848},[6842,13090,6853],{"class":6852},[6842,13092,11530],{"class":6848},[6842,13094,13095,13097,13099,13101,13103,13105,13107,13109,13112,13114],{"class":6844,"line":6899},[6842,13096,7819],{"class":6852},[6842,13098,7822],{"class":6848},[6842,13100,7825],{"class":6852},[6842,13102,7828],{"class":6856},[6842,13104,7831],{"class":6848},[6842,13106,717],{"class":6856},[6842,13108,7836],{"class":6848},[6842,13110,13111],{"class":6856},"3001",[6842,13113,11962],{"class":6848},[6842,13115,13116],{"class":8530},"# x не должен превысить значение 3000\n",[6842,13118,13119,13121,13123,13125,13127,13129,13131,13134,13136,13138,13140,13142,13144,13147,13149],{"class":6844,"line":884},[6842,13120,11156],{"class":6848},[6842,13122,6853],{"class":6852},[6842,13124,6937],{"class":6856},[6842,13126,6860],{"class":6852},[6842,13128,7881],{"class":6856},[6842,13130,7860],{"class":6852},[6842,13132,13133],{"class":6856}," 210",[6842,13135,6872],{"class":6852},[6842,13137,6875],{"class":6856},[6842,13139,6860],{"class":6852},[6842,13141,7881],{"class":6856},[6842,13143,7860],{"class":6852},[6842,13145,13146],{"class":6856}," 150",[6842,13148,6888],{"class":6852},[6842,13150,10204],{"class":6848},[6842,13152,13153],{"class":6844,"line":4212},[6842,13154,10209],{"class":8530},[6842,13156,13157,13159,13161],{"class":6844,"line":6947},[6842,13158,11999],{"class":6848},[6842,13160,6853],{"class":6852},[6842,13162,6907],{"class":6856},[6842,13164,13165],{"class":6844,"line":6959},[6842,13166,12008],{"class":8530},[6842,13168,13169,13171,13173,13175,13177],{"class":6844,"line":6971},[6842,13170,8987],{"class":6852},[6842,13172,11119],{"class":6848},[6842,13174,6918],{"class":6852},[6842,13176,6921],{"class":6856},[6842,13178,6924],{"class":6848},[6842,13180,13181,13183,13185,13187,13189,13191,13193,13195],{"class":6844,"line":8584},[6842,13182,8764],{"class":6852},[6842,13184,11119],{"class":6848},[6842,13186,6934],{"class":6852},[6842,13188,7881],{"class":6856},[6842,13190,6940],{"class":6852},[6842,13192,6921],{"class":6856},[6842,13194,12037],{"class":6848},[6842,13196,13197],{"class":8530},"# Условие проверки для 11-ичной системы\n",[6842,13199,13200,13202,13204,13206],{"class":6844,"line":8597},[6842,13201,12045],{"class":6848},[6842,13203,6953],{"class":6852},[6842,13205,7876],{"class":6856},[6842,13207,12052],{"class":8530},[6842,13209,13210,13212,13214,13216],{"class":6844,"line":9075},[6842,13211,12057],{"class":6848},[6842,13213,6965],{"class":6852},[6842,13215,7881],{"class":6856},[6842,13217,12064],{"class":8530},[6842,13219,13220],{"class":6844,"line":9093},[6842,13221,9046],{"emptyLinePlaceholder":9045},[6842,13223,13224,13226,13228,13230,13233,13235],{"class":6844,"line":9109},[6842,13225,6929],{"class":6852},[6842,13227,12075],{"class":6848},[6842,13229,8455],{"class":6852},[6842,13231,13232],{"class":6856}," 60",[6842,13234,12037],{"class":6848},[6842,13236,13237],{"class":8530},"# насчитали ровно 60 нулей\n",[6842,13239,13240,13242],{"class":6844,"line":9125},[6842,13241,12087],{"class":6848},[6842,13243,12090],{"class":8530},[6842,13245,13246,13248,13250,13252,13254],{"class":6844,"line":9139},[6842,13247,6974],{"class":6856},[6842,13249,7831],{"class":6848},[6842,13251,11759],{"class":6856},[6842,13253,12101],{"class":6848},[6842,13255,12104],{"class":8530},[402,13257,13258],{},[406,13259,13260],{},"Ответ: 2992",[402,13262,13263,13264,13267,13268,13271],{},"Попробуйте сами запустить код в окне ниже с интерпретатором Python и повторите примеры из статьи чтобы самим увидеть и понять как всё это работает. Для этого в ячейке с кодом нажмите клавиши на клавиатуре ",[406,13265,13266],{},"Shift+Enter"," или запустите код через ",[406,13269,13270],{},"кнопку Run"," по значку ▶.",[13273,13274],"jypiter",{},[13276,13277,13278],"style",{},"\nmjx-container[jax=\"SVG\"] {\n  direction: ltr;\n}\n\nmjx-container[jax=\"SVG\"] > svg {\n  overflow: visible;\n  min-height: 1px;\n  min-width: 1px;\n}\n\nmjx-container[jax=\"SVG\"] > svg a {\n  fill: blue;\n  stroke: blue;\n}\n\nmjx-container[jax=\"SVG\"][display=\"true\"] {\n  display: block;\n  text-align: center;\n  margin: 1em 0;\n}\n\nmjx-container[jax=\"SVG\"][display=\"true\"][width=\"full\"] {\n  display: flex;\n}\n\nmjx-container[jax=\"SVG\"][justify=\"left\"] {\n  text-align: left;\n}\n\nmjx-container[jax=\"SVG\"][justify=\"right\"] {\n  text-align: right;\n}\n\ng[data-mml-node=\"merror\"] > g {\n  fill: red;\n  stroke: red;\n}\n\ng[data-mml-node=\"merror\"] > rect[data-background] {\n  fill: yellow;\n  stroke: none;\n}\n\ng[data-mml-node=\"mtable\"] > line[data-line], svg[data-table] > g > line[data-line] {\n  stroke-width: 70px;\n  fill: none;\n}\n\ng[data-mml-node=\"mtable\"] > rect[data-frame], svg[data-table] > g > rect[data-frame] {\n  stroke-width: 70px;\n  fill: none;\n}\n\ng[data-mml-node=\"mtable\"] > .mjx-dashed, svg[data-table] > g > .mjx-dashed {\n  stroke-dasharray: 140;\n}\n\ng[data-mml-node=\"mtable\"] > .mjx-dotted, svg[data-table] > g > .mjx-dotted {\n  stroke-linecap: round;\n  stroke-dasharray: 0,140;\n}\n\ng[data-mml-node=\"mtable\"] > g > svg {\n  overflow: visible;\n}\n\n[jax=\"SVG\"] mjx-tool {\n  display: inline-block;\n  position: relative;\n  width: 0;\n  height: 0;\n}\n\n[jax=\"SVG\"] mjx-tool > mjx-tip {\n  position: absolute;\n  top: 0;\n  left: 0;\n}\n\nmjx-tool > mjx-tip {\n  display: inline-block;\n  padding: .2em;\n  border: 1px solid #888;\n  font-size: 70%;\n  background-color: #F8F8F8;\n  color: black;\n  box-shadow: 2px 2px 5px 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