# Fifteen

From Math Puzzle Wiki

## Puzzle

Two friends, Sam and Lloyd, play the following game with nine ping-pong balls, numbered 1 to 9. Each boy, on their turn, takes a ball (without replacement). The winner of the game is the first one to obtain 3 balls that sum to 15. Does either player have a winning strategy in this game?

## Help

**Hint**

Try to reinterpret the game as taking place on a 3x3 grid.

**Answer**

No. At best Sam (going first) can guarantee a draw.

**Solution**

This game is actually "equivalent" to Tic Tac Toe on a 3x3 magic square (i.e. each row, column and diagonal sums to 15). Since there is no winning strategy for Tic Tac Toe neither is there for this game.