ers solution, makes the shortest
jump of all--a little distance between the two rows; George and
Wilhelmina leap from the ends of the lower row to some distance N. by
N.W. and N. by N.E. respectively; while the frog in the middle of the
lower row, whose name the Professor forgot to state, goes direct S.

73.--_The Game of Kayles._

To win at this game you must, sooner or later, leave your opponent an
even number of similar groups. Then whatever he does in one group you
repeat in a similar group. Suppose, for example, that you leave him these
groups: o.o.ooo.ooo. Now, if he knocks down a single, you knock down a
single; if he knocks down two in one triplet, you knock down two in the
other triplet; if he knocks down the central kayle in a triplet, you
knock down the central one in the other triplet. In this way you must
eventually win. As the game is started with the arrangement
o.ooooooooooo, the first player can always win, but only by knocking down
the sixth or tenth kayle (counting the one already fallen as the second),
and this leaves in either case o.ooo.ooooooo, as the order of the groups
is of no importance. Whatever the second player now does, this can always
be resolved into an even number of equal groups. Let us suppose that he
knocks down the single one; then we play to leave him oo.ooooooo. Now,
whatever he does we can afterwards leave him either ooo.ooo or o.oo.ooo.
We know why the former wins, and the latter wins also; because, however
he may play, we can always leave him either o.o, or o.o.o.o, or oo.oo, as
the case may be. The complete analysis I can now leave for the amusement
of the reader.

74.--_The Broken Chessboard._

The illustration will show how the thirteen pieces can be put together so
as to construct the perfect board, and the reverse problem of cutting
these particular pieces out will be found equally entertaining.

[Illustration]

Compare with Nos. 293 and 294 in _A. in M._

75.--_The Spider and the Fly._

Though this problem was much discussed in the _Daily Mail_ from 18th
January to 7th February 1905, when it appeared to create great public
interest, it was actually first propounded by me in the _Weekly Dispatch_
of 14th June 1903.

Imagine the room to be a cardboard box. Then the box may be cut in
various different ways, so that the cardboard may be laid flat on the
table. I show four of these ways, and indicate in every case the relative
positions of the spid