Here is an interesting little puzzle game that I used to play with an
acquaintance on the beach at Slocomb-on-Sea. Two players place an odd
number of pebbles, we will say fifteen, between them. Then each takes in
turn one, two, or three pebbles (as he chooses), and the winner is the
one who gets the odd number. Thus, if you get seven and your opponent
eight, you win. If you get six and he gets nine, he wins. Ought the
first or second player to win, and how? When you have settled the
question with fifteen pebbles try again with, say, thirteen.