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 to amass a personal total of exactly 15 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.

References
  1. Michon, John A. (1 January 1967). "The Game of JAM: An Isomorph of Tic-Tac-Toe". The American Journal of Psychology. 80 (1): 137–140. doi:10.2307/1420555. JSTOR 1420555. PMID 6036351.
  2. Simon, Herbert A. (1969). The Sciences of the Artificial. MIT Press. ISBN 9780262264495. Here are the rules of a game, which I shall call number scrabble.
  3. Cazenave, Tristan; Winands, Mark H. M.; Edelkamp, Stefan; Schiffel, Stephan; Thielscher, Michael; Togelius, Julian (2016-05-11). Computer Games: Fourth Workshop on Computer Games, CGW 2015, and the Fourth Workshop on General Intelligence in Game-Playing Agents, GIGA 2015, Held in Conjunction with the 24th International Conference on Artificial Intelligence, IJCAI 2015, Buenos Aires, Argentina, July 26-27, 2015, Revised Selected Papers. Springer. ISBN 9783319394022.
  4. Ham, Ethan (2015-06-19). Tabletop Game Design for Video Game Designers. CRC Press. ISBN 9781317536048.
  5. Juul, Jesper (2011-08-19). Half-Real: Video Games Between Real Rules and Fictional Worlds. MIT Press. ISBN 9780262516518.
  6. "TicTacToe Magic" (PDF). December 11, 2016. Retrieved December 11, 2016.
  7. "Fifteen : nrich.maths.org". nrich.maths.org. Retrieved 2016-12-11.
  8. Math!, Oh Boy I. Get To Do (2015-05-30). "Oh Boy! I Get to do Math!: Tic-Tac-Toe as a Magic Square". Oh Boy! I Get to do Math!. Retrieved 2016-12-11.
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