ISL 2009 C1
Consider 2009 cards, each having one gold side and one black side, lying in parallel on a long table. Initially all cards show their gold sides. Two players, standing by the same long side of the table, play a game with alternating moves. Each move consists of choosing a block of 50 consecutive cards, the leftmost of which is showing gold, and turning them all over, so those which showed gold now show black and vice versa. The last player who can make a legal move wins. (a) Does the game necessarily end? (b) Does there exist a winning strategy for the starting player?
Official text Transcription from NuminaMath olympiads, checked word for word against the official paper. Quoted with source.
Official text: IMO 2009 Shortlist booklet, page 8.
Solutions
Official solution Solution 1 by the IMO Problem Selection Committee
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