About Triliza
Originally called noughts and crosses (and still known as this in Britain and Australia), Xs and Os (in Ireland) and X and 0 (in India) is a pencil-and-paper game for two players, X and O, who take turns marking the...
Originally called noughts and crosses (and still known as this in Britain and Australia), Xs and Os (in Ireland) and X and 0 (in India) is a pencil-and-paper game for two players, X and O, who take turns marking the spaces in a 3×3 grid. The player who succeeds in placing three respective marks in a horizontal, vertical, or diagonal row wins the game.
Despite its apparent simplicity, Tic-tac-toe requires detailed analysis to determine even some elementary combinatory facts, the most interesting of which are the number of possible games and the number of possible positions. A position is merely a state of the board, while a game usually refers to the way a terminal position is obtained.
Naive counting leads to 19,683 possible board layouts (39 since each of the nine spaces can be X, O or blank), and 362,880 (i.e. 9!) possible games (different sequences for placing the Xs and Os on the board). However, two matters much reduce these numbers:
The game ends when three-in-a-row is obtained.
The number of Xs is always either equal to or exactly 1 more than the number of Os (if X starts).
The complete analysis is further complicated by the definitions used when setting the conditions, like board symmetries.
Previous Versions
Here you can find the changelog of Triliza since it was posted on our website on 2013-08-22 13:20:26.
The latest version is 1.1 and it was updated on 2024-04-23 09:37:13. See below the changes in each version.
Triliza version 1.1
Updated At: 2013-03-20
Triliza version 1.1
Updated At: 2013-03-20
Changes: Several fixes and updates
Disclaimer
External Download
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