I have a single chessboard and a single set of chessmen. In how many
different ways may the men be correctly set up for the beginning of a
game? I find that most people slip at a particular point in making the
calculation.


347.--COUNTING THE RECTANGLES.

Can you say correctly just how many squares and other rectangles the
chessboard contains? In other words, in how great a number of different
ways is it possible to indicate a square or other rectangle enclosed by
lines that separate the squares of the board?


348.--THE ROOKERY.

[Illustration]

The White rooks cannot move outside the little square in which they are
enclosed except on the final move, in giving checkmate. The puzzle is
how to checkmate Black in the fewest possible moves with No. 8 rook, the
other rooks being left in numerical order round the sides of their
square with the break between 1 and 7.


349.--STALEMATE.

Some years ago the puzzle was proposed to construct an imaginary game of
chess, in which White shall be stalemated in the fewest possible moves