N dimensional Tic Tac Toe.

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N dimensional Tic Tac Toe.

Tic Tac Toe can be played in any number of dimensions using nothing more than a pencil and paper. In order for the games to be non trivial you must add 1 square to each row for each added number of dimensions. Go ahead and make a a 3 dimensional game to familiarize yourself with the game. Draw 4 4 by 4 game boards in a row on a piece of paper. The games can be played visually but I want to introduce some notation here. This will allow 2 players to play a game in their heads. Take 1 corner and label it (1 1 1 1) Then stack them up however you like it makes no difference. ( 1 1 1 1) (2 2 2 2) (3 3 3 3) (4 4 4 4) is a winning game.(1 1 1 1) (1 2 2 2) ( 1 3 3 3) (1 4 4 4) is also a winning game. That is you now have 2 types of diagonals. Once you have mastered the 3 dimensional game make a 4 dimensional game. Draw an array of 5 by 5 5 by 5 game boards on a piece of paper. This game is the most fun You now have 3 types of diagonals. I have only played 1 5 dimensional game which I lost. You need 6 pieces of paper and making the board was too much work. Be the first to play a 6 dimensional game if you have a big enough floor for the 49 pieces of paper.
zerodish
Nullonian

Posts: 2
Joined: Tue Jan 08, 2019 1:06 pm

Re: N dimensional Tic Tac Toe.

Looks like I made a couple of mistakes. I have not played the head game since 1977. I expect this group can sort it out. Me and my friend Kenny could only play the 3 dimensional game in our heads. This allows a winning game of say (1 1 1) (2 2 2) (3 3 3) (4 4 4). Still it would be interesting to see what the world record head game would be.
zerodish
Nullonian

Posts: 2
Joined: Tue Jan 08, 2019 1:06 pm