In the case of fifteen pebbles, the first player wins if he first takes
two. Then when he holds an odd number and leaves 1, 8, or 9 he wins, and
when he holds an even number and leaves 4, 5, or 12 he also wins. He can
always do one or other of these things until the end of the game, and so
defeat his opponent. In the case of thirteen pebbles the first player
must lose if his opponent plays correctly. In fact, the only numbers
with which the first player ought to lose are 5 and multiples of 8 added
to 5, such as 13, 21, 29, etc.