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Topic: 3D Tic-Tac-Toe (Read 541 times) |
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BNC
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3D Tic-Tac-Toe
« on: Aug 8th, 2006, 6:41am » |
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Here
I think it's worse than the 2D version, as I believe a win may be assured for one player.
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How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]
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Aravis
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Re: 3D Tic-Tac-Toe
« Reply #1 on: Aug 8th, 2006, 8:01am » |
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Yeah, a win is guaranteed forr the person who goes first. As far as I can tell (no real mathematical proof for this) if you are playing on a ND board, you need a grid with N+1 squares on each side ie 3x3 for 2D, 4x4x4 for 3-d (trying to get 4 in a row). However, I think that this will always leads to a draw. Perhaps ith a time limit for play, the larger N will become tough, because you can't keep trackof it all in your head.
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Duct tape is like the force. It has a light side, a dark side, and it holds the universe together. -Carl Zwanzig
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SMQ
wu::riddles Moderator
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Re: 3D Tic-Tac-Toe
« Reply #2 on: Aug 8th, 2006, 9:15am » |
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Hmm, I'm not sure your hypothesis generalizes to higher dimensions. I agree that 3x3x3 is always a win for player 1, but I played a lot of 4x4x4x4 back in school and if there's a winning strategy for either player it's certainly not obvious...
--SMQ
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--SMQ
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rmsgrey
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Re: 3D Tic-Tac-Toe
« Reply #3 on: Aug 8th, 2006, 9:45am » |
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The hypothesis doesn't even get into 3D - 4*4*4 is a first player win (according to Wikipedia)
It's obvious that such games can never be a second player win - the first player's extra move can never be a liability.
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| « Last Edit: Aug 8th, 2006, 9:47am by rmsgrey » |
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