IMO 2020 #3
Posted: Fri Dec 04, 2020 2:21 pm
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
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