# Difference between revisions of "2020 IMO Problems/Problem 3"

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− | Problem | + | == Problem == |

− | + | There are <math>4n</math> pebbles of weights <math>1, 2, 3, . . . , 4n</math>. Each pebble is colored in one of <math>n</math> 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: | |

− | 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 == | == Video solution == | ||

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

## Revision as of 11:25, 14 May 2021

## Problem

There are pebbles of weights . Each pebble is colored in one of 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]