3-Dimensional Tic-Tac-Toe


There are lots of Tic-Tac-Toe (Noughts and Crosses, whatever) games and strategies out there, but not many truly 3-dimensional games.  There are variations which require players to stack a piece on top of a previously played piece, which changes the game.  There are games made with a 4-by-4-by-4 array, which eliminates the problem of the first player always winning on the third move, as happens with a 3 by 3 by 3 array.  And there are virtual games and formats to play on a single sheet of paper.  But there aren’t many ways to play Tic-Tac-Toe in three dimensions the same way it’s played in two.

Here’s a solution.  This is a 3 by 3 by 3 array that allows players to play in any space in any order.  The one rule change is that the center space is not allowed on the very first move.

The first player will always win even with that rule change, however, as long as the game ends with the first “three in a row.”  So it doesn’t.

Players continue playing.  Each time a player makes a 3 in a row, he or she makes a tally mark on the appropriate line of the score sheet.  When all 27 spaces are filled, the players count up their scores.  It’s fairly common to see both players with 4 or 5 tallies in a game.  This is a good exercise in transferring 2-dimensional perception into 3-dimensional space.

For Xs, I use large Jacks and for Os, 2-centimeter cubes.

Read more about 3-D Tic-Tac-Toe

Download the rules (PDF)