IMO 2015 Shortlist C4
Let n be a positive integer. Two players A and B play a game in which they take turns choosing positive integers k ď n. ...
Category: Combinatorics
Problem
Let n be a positive integer. Two players A and B play a game in which they take turns choosing positive integers k ď n. The rules of the game are: piq A player cannot choose a number that has been chosen by either player on any previous turn. piiq A player cannot choose a number consecutive to any of those the player has already chosen on any previous turn. piiiq The game is a draw if all numbers have been chosen; otherwise the player who cannot choose a number anymore loses the game. The player A takes the first turn. Determine the outcome of the game, assuming that both players use optimal strategies. (Finland) Shortlisted problems 5