IMO 2022 Shortlist C4
Let n ą 3 be a positive integer. Suppose that n children are arranged in a circle, and n coins are distributed between t...
Category: Combinatorics
Problem
Let n ą 3 be a positive integer. Suppose that n children are arranged in a circle, and n 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. (Israel) Shortlisted problems 5