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Two-player Quadraphage(square-eater), inventor David Silverman 1948. Moving second, if q=4 (four squares eliminated each move), one-step King from 'center'(or one of four central squares), with object to reach edge, can be 'captured' in no more than three moves on all boards 5x5 or greater. If q=3, King can be trapped on boards 6x6 up. If q=2, King escapes(with good play) on 7x7, but trapped 8x8 up. If q=1, with only one square removed each turn, can King always escape? Answer: No. On board 32x32 King escapes with best play. Starting at size 33x33, there is a strategy to remove 1 square at a time so that King is lost, never reaching edge. Of course there could be CPage variates ad infinitum. Supposing King is Wazir, then King can be trapped on 8x8 with q=1. Suppose piece is Bishop on an infinite board but finite move up to say a billion squares. If q=3, Bishop is clearly trapped(just seal the arrival squares); in fact, q=1 traps a Bishop or Rook on an infinite (square) board, in a difficult strategy. However 'q=1' enables Queen to make finite moves there forever. Does 'q=2'?