请教一道GWD中的题目，谢谢

greatvampirer

DS题：

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

有人可以帮忙讲一下思路吗？我看下来没一点想法

谢谢先~

IORIYAGAMI

问题：n能否被m整除

条件（1）3n能被m整除

条件（2）13n能被m整除

分析：m可以取6、9、12，这些都是3的倍数，在上述m值情况下，3n能被m整除是3在发挥因子约分的作用，比如说3×14/6=3×2×7/6=7，但是14/6则不能整除。

而13与m的所有取值并无因子上的联系，所以当13n能被m整除时，发挥因子约分作用的只可能是n，所以n一定能被m整除

greatvampirer

谢谢，把题目简化看起来果然一目了然

太感谢了