Playing Clobber on a Cycle
Vincent D. Blondel, Cristobald de Kerchove D'Exaerde, Julien M. Hendrickx, Raphaël M. Jungers · 2007
Abstract We present the combinatorial 2-player game clobber and its 1-player version solitaire clobber. We present some old and recent results on both games. 1 What is Clobber? The combinatorial game clobber was introduced by Albert, Grossman, Nowakowski and Wolfe in 2002 [1]. It is played with black and white pawns as in the game of Draughts. White begins and moves a white pawn onto an adjacent black pawn and removes this black pawn from the game. The place formerly occupied by the white pawn is then empty and cannot be occupied anymore. Then Black plays similarly with the black pawns, etc. The player making the last move wins the game. As this game admits no draw and only a bounded number of moves, it can be proved that for any initial position there exists a winning strategy