There are $4n$ pebbles of weights $1, 2, 3, \dots, 4n.$ 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:
i. The total weights of both piles are the same.
ii. Each pile contains two pebbles of each colour.
Proposed by Milan Haiman, Hungary and Carl Schildkraut, USA
IMO 2020 #3
- FuadAlAlam
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