## Thursday, July 16, 2015

### 487: The Fifteen Puzzle

Everyone older than ten knows that there is a way to play tic-tac-toe so that you can never lose. Any game that can be played to a draw unless someone makes a newbie's mistake, is boring once you know the secret.

Let's look at this one and see if you can find a strategy for it:

Players alternate writing a number from 1 - 9 (once used, it’s dead). First one with a set of three numbers that sum to 15 wins.

Is there a guaranteed winning strategy for Player 1?
Is there a guaranteed winning strategy for Player 2?

source:
How does his later comment help? "It’s equivalent to tic-tac-toe since any row/col/diagonal in a 3x3 magic square sums to 15, but more mathematically interesting."

#### 1 comment:

1. Consider the game in which two players alternate placing quarters on a large square table. The rules are that your quarter must be placed down fully on the table; no overlapping with others, and no hanging off of the edge. The first player to have no legal move loses.

The game described above can be won by Player 1: Take the center point on move one, and then mirror the opponent's moves thereafter.

This is a more general "strategy-stealing" idea, but it can be applied to the game at hand, too:

Player 1 should pick 5, and, thereafter, mirror their opponent's n by picking 10-n.