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Problem 1505

National Olympiad, first round

Combinatorics Difficulty 6.0 Find the answer BMO Round 2 · United Kingdom · 2024

Let $m < n$ be positive integers. Start with $n$ piles, each of $m$ objects. Repeatedly carry out the following operation: choose two piles and remove $n$ objects in total from the two piles.

For which $(m, n)$ is it possible to empty all the piles?

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