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[组合] 竞赛一题(80个数中取数)

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realnumber posted 2016-5-9 09:41 |Read mode
从1.2.3···.80这80个数中至少取出多少个数,才能保证在取出的数中一定有两个数,一个数是另一个数的倍数。

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original poster realnumber posted 2016-5-11 19:28
41,42,...,80共40个数,最大的80都不到最小的41的2倍。所以40不对。
还得用抽屉原理说明41可以,
穷举法把1~80划入40个集合,....
{1,2,4,8,16,32,64}---1个
{3,6,12,24,48}
{5,10,20,40,80}---2个
{7,14,28,56}
{9,18,36,72}---2个
{11,22,44}
{13,26,52}
{15,30,60}
{17,34,68}
{19,38,76}---5个
{21,42}
{23,46}
{25,50}
{27,54}
{29,58}
{31,62}
{33,66}
{35,70}
{37,74}
{39,78}---10个
{41},{43},.....,{79}---20个

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isee posted 2016-5-21 10:01
回复 2# realnumber


  很厉害

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