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Eighteen is the maximum number of pieces. I give two solutions. The numbered diagram is so cut that the eighteenth piece has the largest area--eight squares--that is possible under the conditions. The second diagram was prepared under the added condition that no piece should contain more than five squares.
No. 74 in _The Canterbury Puzzles_ shows how to cut the board into twelve pieces, all different, each containing five squares, with one square piece of four squares.
