Editing Tic-tac-toe (section)

== Variations ==
{{Main|Tic-tac-toe variants}}Many [[board game]]s share the element of trying to be the first to get ''n''-in-a-row, including [[three men's morris]], [[nine men's morris]], [[pente]], [[gomoku]], [[Qubic]], [[Connect Four]], [[Quarto (board game)|Quarto]], [[Gobblet]], [[Order and Chaos]], [[Toss Across]], and [[Mojo (board game)|Mojo]]. Tic-tac-toe is  an instance of an [[m,n,k-game]], where two players alternate taking turns on an ''m''×''n'' board until one of them gets ''k'' in a row. [[Harary's generalized tic-tac-toe]] is an even broader generalization. The game can be generalised even further by playing on an arbitrary [[hypergraph]], where rows are [[hyperedges]] and cells are [[vertex (graph theory)|vertices]].

Other variations of tic-tac-toe include:
* 3-dimensional tic-tac-toe on a 3×3×3 board. In this game, the first player has an easy win by playing in the centre if 2 people are playing.
One can play on a board of 4x4 squares, winning in several ways. Winning can include: 4 in a straight line, 4 in a diagonal line, 4 in a diamond, or 4 to make a square.

Another variant, [[Qubic]], is played on a 4×4×4 board; it was [[Solved board games|solved]] by [[Oren Patashnik]] in 1980 (the first player can force a win).<ref>{{Cite journal|last=Patashnik|first=Oren|date=September 1, 1980|title=Qubic: 4 × 4 × 4 Tic-Tac-Toe|journal=Mathematics Magazine|volume=53|issue=4|pages=202–216|doi=10.2307/2689613|issn=0025-570X|jstor=2689613}}</ref> Higher dimensional variations are also possible.<ref name="gh02" />
* In [[misère]] tic-tac-toe, the player wins if the opponent gets ''n'' in a row.<ref>{{cite book|last1=Averbach|first1=Bonnie|author1-link=Bonnie Averbach|last2=Chein|first2=Orin|title=Problem Solving Through Recreational Mathematics|title-link=Problem Solving Through Recreational Mathematics|page=[https://books.google.com/books?id=xRJxJ7L9sq8C&pg=PA252 252]|year=2000|publisher=Dover Publications|isbn=978-0-486-40917-7}}</ref> A 3×3 game is a draw. More generally, the first player can draw or win on any board (of any dimension) whose side length is odd, by playing first in the central cell and then mirroring the opponent's moves.<ref name="gh02">{{cite journal | first1=Solomon W. | url=http://library.msri.org/books/Book42/files/golomb.pdf | title=Hypercube tic-tac-toe | publisher=Cambridge Univ. Press | first2=Alfred W. | journal=More Games of No Chance (Berkeley, CA, 2000) | last1=Golomb | last2=Hales | mr=1973012 | series=Math. Sci. Res. Inst. Publ. | year=2002 | volume=42 | pages=167–182 | archive-url=https://web.archive.org/web/20110206014531/http://library.msri.org/books/Book42/files/golomb.pdf | archive-date=February 6, 2011 | url-status=live }}</ref>
[[File:Magicsquareexample.svg|right|100x100px]]
* In [[Wild tic-tac-toe|"wild" tic-tac-toe]], players can choose to place either X or O on each move.<ref>{{cite book|last=Mendelson|first=Elliott|title=Introducing Game Theory and its Applications|url=https://books.google.com/books?id=akCBCwAAQBAJ&pg=PA19|year=2016|publisher=CRC Press|isbn=978-1-4822-8587-1|page=19}}</ref><ref name=":02">{{cite web | title=Wild Tic-Tac-Toe | website=Puzzles in Education | date=December 11, 2007 | url=http://puzzles.com/puzzlesineducation/HandsOnPuzzles/WildTicTacToe.htm | access-date=August 29, 2019}}</ref><ref name=":1">{{cite book|last=Epstein|first=Richard A.|title=The Theory of Gambling and Statistical Logic|url=https://books.google.com/books?id=g5YWIpHTTW8C&pg=PA450|date=December 28, 2012|publisher=Academic Press|isbn=978-0-12-397870-7|page=450}}</ref>
* [[Number Scrabble]] or Pick15<ref name=":8">{{cite book|last=Juul|first=Jesper|title=Half-Real: Video Games Between Real Rules and Fictional Worlds|url=https://books.google.com/books?id=mZP6AQAAQBAJ&pg=PA51|year=2011|publisher=MIT Press|isbn=978-0-262-51651-8|page=51}}</ref> is [[isomorphic]] to tic-tac-toe but on the surface appears completely different.<ref>{{Cite journal|last=Michon|first=John A.|date=January 1, 1967|title=The Game of JAM: An Isomorph of Tic-Tac-Toe|jstor=1420555|journal=The American Journal of Psychology|volume=80|issue=1|pages=137–140|doi=10.2307/1420555|pmid=6036351}}</ref> Two players in turn say a number between one and nine. A particular number may not be repeated. The game is won by the player who has said three numbers whose sum is 15.<ref name=":8" /><ref>{{Cite web|url=https://people.sc.fsu.edu/~jburkardt/m_src/exm_pdf/tictactoe.pdf|title=TicTacToe Magic|access-date=December 17, 2016|archive-url=https://web.archive.org/web/20161220110529/https://people.sc.fsu.edu/~jburkardt/m_src/exm_pdf/tictactoe.pdf|archive-date=December 20, 2016|url-status=dead}}</ref> If all the numbers are used and no one gets three numbers that add up to 15 then the game is a draw.<ref name=":8" /> Plotting these numbers on a 3×3 [[magic square]] shows that the game exactly corresponds with tic-tac-toe, since three numbers will be arranged in a straight line if and only if they total 15.<ref>{{cite web | title=Tic-Tac-Toe as a Magic Square | website=Oh Boy! I Get to do Math! | date=May 30, 2015 | url=http://ohboyigettodomath.blogspot.com/2015/05/tic-tac-toe-as-magic-square.html | access-date=August 29, 2019}}</ref>
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* Another isomorphic game uses a list of nine carefully chosen words, for instance "try", "be", "on", "any", "boat", "by", "ten", "or", and "fear". Each player picks one word in turn and to win, a player must select three words with the same letter. The words may be plotted on a tic-tac-toe grid in such a way that a three-in-a-row line wins.<ref>{{cite book|last=Schumer|first=Peter D.|title=Mathematical Journeys|url=https://books.google.com/books?id=tV__OQ8LZcgC&pg=PA71|year=2004|publisher=John Wiley & Sons|isbn=978-0-471-22066-4|pages=71–72}}</ref>
* Numerical tic-tac-toe is a variation invented by the mathematician [[Ronald Graham]]. The numbers 1 to 9 are used in this game. The first player plays with the odd numbers, and the second player plays with the even numbers. All numbers can be used only once. The player who puts down 15 points in a line wins (sum of 3 numbers).
* In the 1970s, there was a two-player game made by [[Tri-ang]] Toys & Games called ''Check Lines'', in which the board consisted of eleven holes arranged in a [[geometrical]] pattern of twelve straight lines each containing three of the holes. Each player had exactly five tokens and played in turn placing one token in any of the holes. The winner was the first player whose tokens were arranged in two lines of three (which by definition were [[Line-line intersection|intersecting]] lines).  If neither player had won by the tenth turn, subsequent turns consisted of moving one of one's own tokens to the remaining empty hole, with the constraint that this move could only be from an adjacent hole.<ref>{{cite web | title=Check Lines | website=BoardGameGeek | url=https://boardgamegeek.com/boardgame/19584/check-lines | access-date=August 29, 2019}}</ref>
* There is also a variant of the game with the classic 3×3 field, in which it is necessary to make two rows to win, while the opposing algorithm only needs one.<ref>[https://videogamegeek.com/videogame/368786/twice-crosses-circles Twice crosses-circles]</ref>
* [[Quantum tic-tac-toe]] allows players to place a quantum superposition of numbers on the board, i.e. the players' moves are "superpositions" of plays in the original classical game. This variation was invented by Allan Goff of Novatia Labs.<ref>{{Cite journal|last=Goff|first=Allan|date=November 2006|title=Quantum tic-tac-toe: A teaching metaphor for superposition in quantum mechanics|journal=American Journal of Physics|location=College Park, MD|publisher=American Association of Physics Teachers|volume=74|issue=11|pages=962–973|doi=10.1119/1.2213635|issn=0002-9505|bibcode=2006AmJPh..74..962G}}</ref>