To win at this game you must, sooner or later,
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
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
As the game is started with the arrangement
o.ooooooooooo, the first player can always win, but only by knocking
the sixth or tenth kayle (counting the one already fallen as the
and this leaves in either case o.ooo.ooooooo, as the order of the
is of no importance.
Whatever the second player now does, this can
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.
whatever he does we can afterwards leave him either ooo.ooo or
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,
the case may be.
The complete analysis I can now leave for the
of the reader.