Number Scrabble

Number Scrabble (also known as Pick15^[1][2][3] or 3 to 15^[4]) is a mathematical game where players take turns to select numbers from 1 to 9 without repeating any numbers previously used, and the first player with a sum of exactly 15 using any three of their number selections wins the game.^[5][6] The game is isomorphic to tic-tac-toe, as can be seen if the game is mapped onto a magic square.^[6]

Play

A 3x3 magic square of the numbers 1 through 9

Number Scrabble is played with the list of numbers between 1 and 9. Each player takes turns picking a number from the list. Once a number has been picked, it cannot be picked again. If a player has picked three numbers that add up to 15, that player wins the game.^[5][6][7] However, if all the numbers are used and no player gets exactly 15, the game is a draw.^[5][6]

The game is identical to tic-tac-toe, as can be seen by reference to a 3x3 magic square: if a player has selected three numbers which can be found in a line on a magic square, they will add up to 15. If they have selected any other three numbers, they will not.^[8]

Example

As an example game between player A and player B:

1. A picks 9.
2. B picks 8.
3. A picks 2.
4. B has no choice but to pick 4 (otherwise, A could get 9+2+4=15).
5. A has no choice but to pick 3 (otherwise, B could get 8+4+3=15).
6. B picks 6, and thereby threatens to win by either picking 1 (8+6+1=15) or 5 (4+6+5=15).
7. At this point, A has lost because the second pick (2) was a mistake, A should not pick 1, 2, 3, or 7 as second pick, or A must lose.