Puzzle: Henry Dudeney’s Pebble Game

English mathematician and puzzle-meister Henry Ernest Dudeney once wrote:

“It may be said generally that a game is a contest of skill for two or more persons, into which we enter either for amusement or to win a prize. A puzzle is something to be done or solved by the individual.

“The example that I give here is apparently a game, but, as in every case one player may win if he only play correctly, it is in reality a puzzle. The interest, therefore, lies in attempting to discover the leading method of play.”

Below is the puzzle game as Dudeney explained it.

Play it for fun at first, then see if you can solve the puzzle.

The Odd Pebble Game

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.