2020 IMO Problems/Problem 3

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Problem 3. There are 4n pebbles of weights 1, 2, 3, . . . , 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.

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