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Six-Dimensional Tic-Tac-Toe

by George F. Rice
Face it - regular tic-tac-toe is boooriiing. Only 9 starting moves are possible, and it just goes downhill from there.

Perhaps you tried 3D tic-tac-toe. It's better - 27 moves for starters, and enough strategy to keep you occupied for at least a short while.

But why stop there? Why not move to the fourth dimension? Or the fifth dimension? Or even - for those who've moved beyond Dr. Who - the sixth dimensions?

Are you ready for hypercubic mental tae kwon do?

Players: 2

Object: The object of the game is to get three marks in a row. Sounds simple, but in six dimensions simultaneously?

Equipment:

  • Printer (to create game board)
  • Gameboard (requires Adobe Acrobat Reader)

Assembly and Setup:

Simply print out the gameboard and start playing.

Well, ok, perhaps a little guided tour would be in order first...

Rules of the Game:

In normal (two-dimensional) tic-tac-toe (2D TTT), the board consists of 9 spaces in a 3x3 arrangement.

The first player to get 3 marks in a row, wins. Below are some different ways to get 3 in a row in 2D TTT.



In three-dimensional tic-tac-toe (3D TTT), the board consists of 27 spaces in a 3x3x3 arrangement. In the diagram below, imagine that each 3x3 board is stacked on top of each other.

In this way, you can see some of the different ways you can win in this game, illustrated below. Notice that you still only need 3 marks in the proper order to win - you just have more "proper orders" to choose from!



In four-dimensional tic-tac-toe (4D TTT), the board now consists of 81 spaces in a 3x3x3x3 arrangement.

This is harder to imagine (since you live in only 3 dimensions yourself!), so study the diagrams below to see some different winning arrangements.



In five=dimensional tic-tac-toe (5D TTT), the board now consists (you guessed it) of 243 spaces in a 3x3x3x3x3 arrangement (notice a pattern here?).

Some winning arrangments are shown below.



In six-dimensional tic-tac-toe (6D TTT), the board is now huge - 729 spaces in a 3x3x3x3x3x3 arrangement. Because the board takes up so much space, determining the winning positions is left for you to work out for yourself.



All of the above games, from simple 2D to the full 6D, can be played using the 6D board by using just a small section of the board. For example, a 3D game can be played on the bottom of the 6B board by using the area outlined in red below.

In fact, you can play 243 2D games, or 81 3D games, or 27 4D games or 9 5d games on each page. You may find it easier to print the gameboard using the Portable Document Format (PDF) version of the game board here.

And in case you are wondering, I didn't draw these gameboards by hand - I taught the computer to draw them for me. I used a programming language called LOGO (and a Microsoft Windows-compatible version called MSW LOGO). If you know LOGO, or are just interested in how computers are taught to draw things, here is the program. (If your browser doesn't display the text, save it to disk and open it using WordPad or your favorite editor.)

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