书学69有人能给解释一下吗？什么意思？

tress · 发表于 2010-12-28 12:06:20

69. 讲有140 张cards 分给m个人，eachperson at least get 2 cards，求the 【numbers】of possible value of m. 不记得有没有限定m>2了
选项A.five B. six C. eight D.ten E不记得
其实就把140除2得70，再考察70可被几个数整除
思路：这个应该是在探讨140的因子：（2.，70）（4,35）（5,28）（10,14）（20,7）如果有m>2就应是9个，没有的话应是10个(啥意思？)

sdcar2010 · 发表于 2010-12-28 12:24:30

140 = 2^2*5*7. Its number of factors= (2+1) * (1+1) * (1+1) = 3 * 2 * 2 = 12. They are 1, 140; 2, 70; 4, 35; 5, 28; 7, 20; 10, 14.

140 张cards 分给m个人，each person at least gets 2 cards.
Therefore 140 = m*n, whereas n>=2, and m and n are factors of 140.
Apparently, m cannot be 140, since that would force n to be 1, which is smaller than 2. But m can be any of the other 11 factors of 140 in order to make n >=2. Specifically, m could be 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, and 70.

P.S. The stimulus has to add another condition: each person receives the SAME amount of cards. Otherwise, the above analysis cannot hold.

tress · 发表于 2010-12-28 12:39:54

Thanks.

书学69有人能给解释一下吗？什么意思？

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