2020 IMO Problems/Problem 3

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Problem

There are $4n$ pebbles of weights $1, 2, 3, . . . , 4n$. Each pebble is colored in one of $n$ colors and there are four pebbles of each color. 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 color.

Video solution

https://youtu.be/bDHtM1wijbY [Video covers all day 1 problems]

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