1994 CMO 第 2 题

There are $m$ pieces of candy held in $n$ trays( $n,m\ge 4$ ). An *operation* is defined as follow: take out one piece of candy from any two trays respectively, then put them in a third tray. Determine, with proof, if we can move all candies to a single tray by finite *operations*.

$n$ 个托盘中装有 $m$ 块糖果( $n,m\ge 4$ )。一个“操作”的定义如下：从任意两个托盘中分别取出一颗糖果，然后将它们放入第三个托盘中。通过证明，确定我们是否可以通过有限的*操作*将所有糖果移动到一个托盘中。