358.--THE SIX PAWNS.

In how many different ways may I place six pawns on the chessboard so
that there shall be an even number of unoccupied squares in every row
and every column? We are not here considering the diagonals at all, and
every different six squares occupied makes a different solution, so we
have not to exclude reversals or reflections.


359.--COUNTER SOLITAIRE.

Here is a little game of solitaire that is quite easy, but not so easy
as to be uninteresting. You can either rule out the squares on a sheet
of cardboard or paper, or you can use a portion of your chessboard. I
have shown numbered counters in the illustration so as to make the
solution easy and intelligible to all, but chess pawns or draughts will
serve just as well in practice.

[Illustration]

The puzzle is to remove all the counters except one, and this one that
is left must be No. 1. You remove a counter by jumping over another
counter to the next space beyond, if that square is vacant, but you
cannot make a leap in a diagonal direction. The following moves will
make the play quite clear: 1-9, 2-10, 1-2, and so on. Here 1 jumps over
9, and you remove 9 from the board; then 2 jumps over 10, and you remove
10; then 1 jumps over 2, and you remove 2. Every move is thus a capture,
until the last capture of all is made by No. 1.