3D TIC TAC TOE

In ordinary tic-tac-toe with nine squares, if both players know how to play, the game should tie, right?

This means that there is no winning strategy for either player. In tic-tac-toe 3x3x3 or even 4x4x4, this doesn't happen. There is a winning strategy for the first player.

This means that if the first player knows the strategy he will win. No matter what the second player does, he will know how to respond and will win in the end. Can you figure out how to always win on the 3x3x3 board? And on the 4x4x4 board? In fact, one of the cases is much more difficult than the other!

In the three-dimensional version of tic-tac-toe, the objective is also to make a line first, but before you start playing, see all the possibilities of forming a line!

In the next images, photographed by Rodrigo Tetsuo Argenton, we have an example of a game on the 3x3x3 board and one on the 4x4x4 board. Would you make the same moves or know a better strategy?

 

USEFUL LINKS

The most traditional of this type of game is the one-dimensional tic-tac-toe game, the 3x3 known to all. This Wikipedia page talks about it, explaining the objective of the game, its strategies and the perfect move. In addition, it analyzes how many game possibilities there are for each option, between first player to win, second player to win or tie!                                                                                    

This WikiHow page explains how to win at 3x3 tic-tac-toe, explaining in detail the possible winning strategies (if the other player doesn't play so well). The page has two distinct methods: one to win or tie being the first player to play and another to never lose being the second player. In the end, it still brings some variations of this game, so that players can try new options!

Getting into the subject of three-dimensional tic-tac-toe, this Wikipedia page explains the game in detail, analyzing the two options that Matemateca has in its collection: 3x3x3 and 4x4x4! It also brings a little about the computational implementations related to the game and mentions another game, similar to the one seen here.                                                                                    

And if you were curious and still haven't found the time to go play the three-dimensional tic-tac-toe game at some Matemateca exhibition, you can play it at Math is fun, a site that offers the possibility of playing the 4x4x4 version online, either alone (against the computer, in three different difficulties) or with a partner who is physically close.                                                                                    

There are many theoretical references about this game, which analyze it more deeply from a mathematical point of view. This Solomon W. Golomb and Alfred W. Hales's article talks about the Hypercube tic-tac-toe, which is a tic-tac-toe game played on a k-dimensional board with size n, very generic! This Alec Levine's article explores tic-tac-toe variants, explaining it in 3, 4, 5 and above 5 dimensions!

Finally, this PBS Infinite Series channel video relates the idea of the tic-tac-toe game in multiple dimensions - the Hypercube tic-tac-toe with infinite series, a concept present in mathematics, which involves a lot of analysis and demonstrations, but which the presenter of this video brings in a more playful way, with many images and comparisons.