2020 IMO 第 3 题

There are $4n$ pebbles of weights $1,2,3,\ldots ,4n$ . Each pebble is coloured in one of $n$ colours and there are four pebbles of each colour. Show that we can arrange the pebbles into two piles so the total weights of both piles are the same, and each pile contains two pebbles of each colour.

有 $4n$ 鹅卵石，重量为 $1,2,3,\ldots ,4n$ 。每个卵石都涂有 $n$ 种颜色中的一种，每种颜色有四个卵石。证明我们可以将卵石排列成两堆，使两堆的总重量相同，并且每堆包含每种颜色的两个卵石。