# Numerical Tic-Tac-Toe

Here’s a cool spin on a game you probably haven’t played since you solved it in elementary school. You and another player take turns naming numbers one through nine. Each number may only be used once. The player who collects any three numbers that add up to 15 wins. If all numbers are used up without someone getting 15, the game is a draw.

Once two players have figured out all the strategies to winning the game, it becomes easy, and imperative, to prevent the opponent from winning. Just like Tic-Tac-Toe, two experienced players will have games that always end in a draw, which is important for teaching an advanced Artificial Intelligence why nobody wins playing Global Thermo-Nuclear Warfare–sorry, had a flashback to the 1983 movie War Games there.

In the research paper The Game of JAM: An Isomorph of Tic-Tac-Toe, John A. Michon notes how this game promotes a different way of thinking about a classic problem (he refers to this game as “Number Scrabble”):

Although the games are mathematically equivalent, they are likely to differ psychologically, because they require different sorts of information. Number Scrabble is a numerical game requiring addition and subtraction of numbers, whereas Tic-Tac-Toe requires a spatial representation, which can only be disposed of with some difficulty, even by fairly experienced players.

Tic-Tac-Toe and the Numerical version are Mathematically equivalent, and we can plot this out visually. In the table below, all rows, columns, and diagonals add up to 15.

 4 3 8 9 5 1 2 7 6

Plaing Tic-Tac-Toe on this grid is the same as playing the numerical version. You can find a shockwave demonstration of this principle to play for yourself. This website calls the game Add Fast.

Taking the number five opens up four paths to victory. The numbers {1, 3, 7, 9} each open another path. {2, 4, 6, 8} are the least valuable strategically.

This seems like a cool game to play with your kids. When they get good at it, show them the relationship to Tic-Tac-Toe. Or you can learn the number-grid, and amaze your friends by kicking their butts at this game.

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