OG13的一道DS题，请教！

redredfox

A school administrator will assign each student in a group of n students to one of m classrooms. If 3 < m < 13 < n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?

(1) It is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it.

(2) It is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it.

答案是B. 网上查到的最简洁的解释是：

In simpler terms it is asking whether n/m is an integer?

(1) 3n/m is an integer.
'3/m' can be integer and the result multiplied by 'n' to get an integer
or 'n/m' can be integer and the result multiplied by '3' to get an integer.

(2) 13n/m is an integer

'13/m' cannot be integer as 'm' is less that '13'.

Hence 'n/m' is an integer.

我想知道既然ｎ＞１３而且3<m<13, 我怎么也找不到能够满足B条件的具体数字n和m。请牛牛指教。

gorgeous

1) 这句话换个角度理解就是3n可以被m整除（PS:题目意思是n/m是否为>1的整数）
因为m>3，所以m里面可以有n的因子，也可以有3为因子。因此N/m最后是否为整数是不确定的。

2)13n可以被m整除
因为m<13，所以m只能是n的因子了...所以n/m必然为整数，且>1。举例：n=14,m=7

cutey3

明白了，非常感谢！