## QUEENS AND BISHOP PUZZLE.

(

Chessboard Problems)

It will be seen that every square of the board is either occupied or

attacked. The puzzle is to substitute a bishop for the rook on the same

square, and then place the four queens on other squares so that every

square shall again be either occupied or attacked.

## Answer:

[Illustration: FIG. 1.]

[Illustration: FIG. 2.]

The bishop is on the square originally occupied by the rook, and the

four queens are so placed that every square is either occupied or

attacked by a piece. (Fig. 1.)

I pointed out in 1899 that if four queens are placed as shown in the

diagram (Fig. 2), then the fifth queen may be placed on any one of the

twelve squares marked a, b, c, d, and e; or a rook on the two squares,

c; or a bishop on the eight squares, a, b, and e; or a pawn on the

square b; or a king on the four squares, b, c, and e. The only known

arrangement for four queens and a knight is that given by Mr. J. Wallis

in _The Strand Magazine_ for August 1908, here reproduced. (Fig. 3.)

[Illustration: FIG. 3.]

I have recorded a large number of solutions with four queens and a rook,

or bishop, but the only arrangement, I believe, with three queens and

two rooks in which all the pieces are guarded is that of which I give an

illustration (Fig. 4), first published by Dr. C. Planck. But I have

since found the accompanying solution with three queens, a rook, and a

bishop, though the pieces do not protect one another. (Fig. 5.)

[Illustration: FIG. 4.]

[Illustration: FIG. 5.]