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David Paulowich wrote on 2007-05-26 UTC

'A paradox, a paradox, a most ingenious paradox!'

My statement should be rephrased to read: the smallest rectangular board containing all of the pieces may increase beyond any limit. This can be demonstrated by two pairs of (opposite color) Rooks moving off, one pair in a vertical direction and one pair in a horizontal direction.

Joe Joyce's statement should be rephrased to read: any White move takes place in a playing area consisting of no more than 32 square areas (15x15) centered on the Black pieces. Black's reply must take place in a playing area consisting of no more than 32 square areas (15x15) centered on the White pieces. These 15x15 areas will overlap the previous areas centered on the White pieces.

So the game may be regarded as taking place in (no more than) 32 shifting patches of sunlight scattered across a limitless dark plain. Note that a piece may move thousands of squares in a single move, provided it starts and ends its move within the required distance from an opponent's piece.

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