International Mathematical Olympiad 2020 Problem 3

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 that the following two conditions are both satisfied:

• The total weights of both piles are the same.
• Each pile contains two pebbles of each colour.