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2 player game with a heap of n stones

Source: 1995 Bulgaria NMO, Round 4, p3

July 30, 2021
combinatoricsgamewinning strategygame strategy

Problem Statement

Two players AA and BB take stones one after the other from a heap with n≥2n \ge 2 stones. AA begins the game and takes at least one stone, but no more than n−1n -1 stones. Thereafter, a player on turn takes at least one, but no more than the other player has taken before him. The player who takes the last stone wins. Who of the players has a winning strategy?
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