ISL 2022 C4
Let be a positive integer. Suppose that children are arranged in a circle, and coins are distributed between them (some children may have no coins). At every step, a child with at least 2 coins may give 1 coin to each of their immediate neighbours on the right and left. Determine all initial distributions of coins from which it is possible that, after a finite number of steps, each child has exactly one coin.
Dataset text NuminaMath olympiads. Quoted with source.
Official text: IMO 2022 Shortlist booklet, page 6.
Show the answer
All distributions where \sum_{i=1}^{n} i c_{i}=\frac{n(n+1)}{2}(\bmod n)
Solutions
Official solution Solution 1 by the IMO Problem Selection Committee
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