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two non-empty stacks of n and m coins on a table

Source: Switzerland - 2013 Swiss MO Final Round p6

January 14, 2023
combinatorics

Problem Statement

There are two non-empty stacks of nn and mm coins on a table. The following operations are allowed: ∙\bullet The same number of coins are removed from both stacks. ∙\bullet The number of coins in a stack is tripled. For which pairs (n,m)(n, m) is it possible that after finitely many operations, no coins are more available?
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