Number Scrabble
{{Short description|Mathematical game}}
Number Scrabble (also known as Pick15{{cite journal|last1=Michon|first1=John A.|title=The Game of JAM: An Isomorph of Tic-Tac-Toe|journal=The American Journal of Psychology|date=1 January 1967|volume=80|issue=1|pages=137–140|doi=10.2307/1420555|jstor=1420555|pmid=6036351}}{{cite book|last1=Simon|first1=Herbert A.|title=The Sciences of the Artificial|date=1969|publisher=MIT Press|isbn=9780262264495|url=https://books.google.com/books?id=k5Sr0nFw7psC&q=%22number+scrabble%22+%22tic+tac+toe%22&pg=PA132|language=en|quote=Here are the rules of a game, which I shall call number scrabble.}}{{Cite book|url=https://books.google.com/books?id=NLcqDAAAQBAJ&q=%22tic-tac-toe%22+%22number+scrabble%22&pg=PA168|title=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|last1=Cazenave|first1=Tristan|last2=Winands|first2=Mark H. M.|last3=Edelkamp|first3=Stefan|last4=Schiffel|first4=Stephan|last5=Thielscher|first5=Michael|last6=Togelius|first6=Julian|date=2016-05-11|publisher=Springer|isbn=9783319394022|language=en}} or 3 to 15{{Cite book|url=https://books.google.com/books?id=RpDwCQAAQBAJ&q=%223+to+15+game%22&pg=PA101|title=Tabletop Game Design for Video Game Designers|last=Ham|first=Ethan|date=2015-06-19|publisher=CRC Press|isbn=9781317536048|language=en}}) 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.{{Cite book|url=https://books.google.com/books?id=mZP6AQAAQBAJ&q=Pick+15+number+game+between+1+and+9&pg=PA51|title=Half-Real: Video Games Between Real Rules and Fictional Worlds|last=Juul|first=Jesper|date=2011-08-19|publisher=MIT Press|isbn=9780262516518|language=en}}{{Cite web|url=https://people.sc.fsu.edu/~jburkardt/m_src/exm_pdf/tictactoe.pdf|title=TicTacToe Magic|last=|first=|date=December 11, 2016|website=|publisher=|access-date=December 11, 2016}} 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.{{Cite web|url=https://nrich.maths.org/1223|title=Fifteen : nrich.maths.org|website=nrich.maths.org|access-date=2016-12-11}} 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.{{Cite web|url=http://ohboyigettodomath.blogspot.com/2015/05/tic-tac-toe-as-magic-square.html|title=Oh Boy! I Get to do Math!: Tic-Tac-Toe as a Magic Square|last=Math!|first=Oh Boy I. Get To Do|date=2015-05-30|website=Oh Boy! I Get to do Math!|access-date=2016-12-11}}
Example
As an example game between player A and player B:
- A picks 9.
- B picks 8.
- A picks 2.
- B has no choice but to pick 4 (otherwise, A could get 9+2+4=15).
- A has no choice but to pick 3 (otherwise, B could get 8+4+3=15).
- B picks 6, and thereby threatens to win by either picking 1 (8+6+1=15) or 5 (4+6+5=15).
- 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.