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hard game with knight

Source: ARO 1994, Problem 11.8

June 13, 2008
analytic geometryrotationcombinatorics unsolvedcombinatorics

Problem Statement

Players A,B A,B alternately move a knight on a 1994×1994 1994\times 1994 chessboard. Player A A makes only horizontal moves, i.e. such that the knight is moved to a neighboring row, while B B makes only vertical moves. Initally player A A places the knight to an arbitrary square and makes the first move. The knight cannot be moved to a square that was already visited during the game. A player who cannot make a move loses. Prove that player A A has a winning strategy.
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