Number Scrabble Explained

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.

Play

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.[7] However, if all the numbers are used and no player gets exactly 15, the game is a draw.

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.. The Game of JAM: An Isomorph of Tic-Tac-Toe. The American Journal of Psychology. 1 January 1967. 80. 1. 137–140. 10.2307/1420555. 1420555. 6036351.
  2. Book: Simon. Herbert A.. The Sciences of the Artificial. 1969. MIT Press. 9780262264495. en. Here are the rules of a game, which I shall call number scrabble..
  3. Book: 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. Cazenave. Tristan. Winands. Mark H. M.. Edelkamp. Stefan. Schiffel. Stephan. Thielscher. Michael. Togelius. Julian. 2016-05-11. Springer. 9783319394022. en.
  4. Book: Ham, Ethan. Tabletop Game Design for Video Game Designers. 2015-06-19. CRC Press. 9781317536048. en.
  5. Book: Juul, Jesper. Half-Real: Video Games Between Real Rules and Fictional Worlds. 2011-08-19. MIT Press. 9780262516518. en.
  6. Web site: TicTacToe Magic. December 11, 2016. December 11, 2016.
  7. Web site: Fifteen : nrich.maths.org. nrich.maths.org. 2016-12-11.
  8. Web site: Oh Boy! I Get to do Math!: Tic-Tac-Toe as a Magic Square. Math!. Oh Boy I. Get To Do. 2015-05-30. Oh Boy! I Get to do Math!. 2016-12-11.

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Number Scrabble".

Except where otherwise indicated, Everything.Explained.Today is © Copyright 2009-2024, A B Cryer, All Rights Reserved. Cookie policy.