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. 294.--THE CHESSBOARD SENTENCE. +===I===I===I===I=======I=======+ | |:::| |:::| ::::| ::::| I===I...I===I...I...+===I...+===I |:::| ::::: |:::| ::::: | |...|...+===I...I...+===+...+===I | |:::| |:::| ::::| ::::| |...+===+...+===I===I===I=======I |:::: ::::: |:::| ::::: | I===========I===I...I===I===+...| | ::::: |:::| |:::| |:::| |...+===+...|...|...|...I===+...| |:::| |:::| |:::| |:::: | |...|...|...|...I===+...+===+...| | |:::| |:::| ::::: |:::| I===+...+===I...+=======I===+...| |:::: ::::| ::::: |:::: | +===========I===================+ The pieces may be fitted together, as shown in the illustration, to form a perfect chessboard. 295.--THE EIGHT ROOKS. Obviously there must be a rook in every row and every column. Starting with the top row, it is clear that we may put our first rook on any one of eight different squares. Wherever it is placed, we have the option of seven squares for the second rook in the second row. Then we have six squares from which to select the third row, five in the fourth, and so on. Therefore the number of our different ways must be 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320 (that is 8!), which is the correct answer. How many ways there are if mere reversals and reflections are not counted as different has not yet been determined; it is a difficult problem. But this point, on a smaller square, is considered in the next puzzle. 296.--THE FOUR LIONS. There are only seven different ways under the conditions. They are as follows: 1 2 3 4, 1 2 4 3, 1 3 2 4, 1 3 4 2, 1 4 3 2, 2 1 4 3, 2 4 1 3. Taking the last example, this notation means that we place a lion in the second square of first row, fourth square of second row, first square of third row, and third square of fourth row. The first example is, of course, the one we gave when setting the puzzle. 297.--BISHOPS--UNGUARDED.