Comments on: Tic Tac Toe in Four Dimensions http://www.thebigquestions.com/2010/04/07/tic-tac-toe-in-four-dimensions/ The Big Questions | Tackling the Problems of Philosophy with Ideas from Mathematics, Economics, and Physics Fri, 10 Feb 2012 08:35:58 -0700 http://wordpress.org/?v=2.8.5 hourly 1 By: Kristal Cantwell http://www.thebigquestions.com/2010/04/07/tic-tac-toe-in-four-dimensions/comment-page-1/#comment-5111 Kristal Cantwell Fri, 09 Apr 2010 18:46:05 +0000 http://www.thebigquestions.com/?p=3090#comment-5111 I think this game is known to be a win for the first player. See the following article: "Qubic: 4 × 4 × 4 Tic-Tac-Toe" Oren Patashnik Mathematics Magazine, Vol. 53, No. 4 (Sep., 1980), pp. 202-21 I think this game is known to be a win for the first player.

See the following article:

“Qubic: 4 × 4 × 4 Tic-Tac-Toe”
Oren Patashnik
Mathematics Magazine, Vol. 53, No. 4 (Sep., 1980), pp. 202-21

]]> By: Martin http://www.thebigquestions.com/2010/04/07/tic-tac-toe-in-four-dimensions/comment-page-1/#comment-5102 Martin Fri, 09 Apr 2010 16:03:08 +0000 http://www.thebigquestions.com/?p=3090#comment-5102 In the science museum La Villette in Paris, they have this 3D tic tac toe, composed of a very big a 4x4x4 (or 5x5x5 cant remember) structure with nodes that can light up in the colors of each player. You play by typing in the coordinates of a node on a control panel in front of the 3D structure causing the node to light up. Remeber playing this as teenager , was great fun. But then the whole structure just reset in the middle of a game - guess they wanted other ppl than me and my friend to use it. In the science museum La Villette in Paris, they have this 3D tic tac toe, composed of a very big a 4×4x4 (or 5×5x5 cant remember) structure with nodes that can light up in the colors of each player. You play by typing in the coordinates of a node on a control panel in front of the 3D structure causing the node to light up.

Remeber playing this as teenager , was great fun. But then the whole structure just reset in the middle of a game – guess they wanted other ppl than me and my friend to use it.

]]> By: Blogging, Tic Tac Toe and the Future of Math at Steven Landsburg | The Big Questions: Tackling the Problems of Philosophy with Ideas from Mathematics, Economics, and Physics http://www.thebigquestions.com/2010/04/07/tic-tac-toe-in-four-dimensions/comment-page-1/#comment-5021 Blogging, Tic Tac Toe and the Future of Math at Steven Landsburg | The Big Questions: Tackling the Problems of Philosophy with Ideas from Mathematics, Economics, and Physics Thu, 08 Apr 2010 07:02:51 +0000 http://www.thebigquestions.com/?p=3090#comment-5021 [...] Buy « Tic Tac Toe in Four Dimensions [...] [...] Buy « Tic Tac Toe in Four Dimensions [...]

]]> By: Scott F http://www.thebigquestions.com/2010/04/07/tic-tac-toe-in-four-dimensions/comment-page-1/#comment-4998 Scott F Wed, 07 Apr 2010 22:08:29 +0000 http://www.thebigquestions.com/?p=3090#comment-4998 If you have been playing 4D tic tac toe against a friend (who happens to be a physicist who studies string theory) you may want to buff up your understanding of higher dimensions. I really like this video and I think it breaks it down into to sufficiently easy to understand ideas: http://www.youtube.com/watch?v=8Q_GQqUg6Ts You may still lose to your friend but at least I think you'll enjoy the video. If you have been playing 4D tic tac toe against a friend (who happens to be a physicist who studies string theory) you may want to buff up your understanding of higher dimensions. I really like this video and I think it breaks it down into to sufficiently easy to understand ideas:

http://www.youtube.com/watch?v=8Q_GQqUg6Ts

You may still lose to your friend but at least I think you’ll enjoy the video.

]]> By: Al V. http://www.thebigquestions.com/2010/04/07/tic-tac-toe-in-four-dimensions/comment-page-1/#comment-4990 Al V. Wed, 07 Apr 2010 20:43:50 +0000 http://www.thebigquestions.com/?p=3090#comment-4990 What's the algorithm for the number of winning lines? In a 3x3 square, there are 8 lines. In a 4x4 square, there are 10. In a 3x3x3 cube there are 76? 8 in each of 9 faces, plus 4 diagonals. Obviously, the algorithm needs to include the side length and the number of dimensions, but I don't see it. What’s the algorithm for the number of winning lines? In a 3×3 square, there are 8 lines. In a 4×4 square, there are 10. In a 3×3x3 cube there are 76? 8 in each of 9 faces, plus 4 diagonals. Obviously, the algorithm needs to include the side length and the number of dimensions, but I don’t see it.

]]> By: Fenn http://www.thebigquestions.com/2010/04/07/tic-tac-toe-in-four-dimensions/comment-page-1/#comment-4989 Fenn Wed, 07 Apr 2010 20:42:07 +0000 http://www.thebigquestions.com/?p=3090#comment-4989 when you ladies are done playing tic-tac-toe, give the 4-d Rubik's cube a try ;) http://www.superliminal.com/cube/cube.htm when you ladies are done playing tic-tac-toe, give the 4-d Rubik’s cube a try

;)

http://www.superliminal.com/cube/cube.htm

]]> By: Al V. http://www.thebigquestions.com/2010/04/07/tic-tac-toe-in-four-dimensions/comment-page-1/#comment-4987 Al V. Wed, 07 Apr 2010 20:13:47 +0000 http://www.thebigquestions.com/?p=3090#comment-4987 My guess is that it has something to do with the relationship between the number of ways of winning and the number of blocking opportunities. On a 2D 3x3 board, the best opening move is in the middle, and there are 4 ways of winning through the middle square. The second player has 4 moves, so he or she can, if playing correctly, always place the O to block a win. In a 4D 3x3x3x3, I think there are (if I counted right) 40 ways of winning through the middle square. If X takes the middle square, he or she should not only always be able to win, but always win by the 5th move. I haven't extended to 4x4x4x4 yet, but it seems likely that the ratio of winning paths to blocking moves is less than for 3x3x3x3, since the number of winning paths should be the same (40). My guess is that it has something to do with the relationship between the number of ways of winning and the number of blocking opportunities. On a 2D 3×3 board, the best opening move is in the middle, and there are 4 ways of winning through the middle square. The second player has 4 moves, so he or she can, if playing correctly, always place the O to block a win.

In a 4D 3×3x3×3, I think there are (if I counted right) 40 ways of winning through the middle square. If X takes the middle square, he or she should not only always be able to win, but always win by the 5th move.

I haven’t extended to 4×4x4×4 yet, but it seems likely that the ratio of winning paths to blocking moves is less than for 3×3x3×3, since the number of winning paths should be the same (40).

]]> By: David http://www.thebigquestions.com/2010/04/07/tic-tac-toe-in-four-dimensions/comment-page-1/#comment-4977 David Wed, 07 Apr 2010 15:28:39 +0000 http://www.thebigquestions.com/?p=3090#comment-4977 You can play against another person or a computer program (that is quite good) here: http://www.ugcs.caltech.edu/~willsmit/4d/index.html Pretty fun! You can play against another person or a computer program (that is quite good) here: http://www.ugcs.caltech.edu/~willsmit/4d/index.html

Pretty fun!

]]> By: Jonathan Kariv http://www.thebigquestions.com/2010/04/07/tic-tac-toe-in-four-dimensions/comment-page-1/#comment-4976 Jonathan Kariv Wed, 07 Apr 2010 14:05:25 +0000 http://www.thebigquestions.com/?p=3090#comment-4976 I remember a old computer game that was 3-d tic-tac-toe game on a 4x4x4 board. I thought about this at some point in college and managed to convince myself that 5x5x5x5, 6x6x6x6x6 etc boards (side length n+1 in dimension n), where interesting games in the some sense. If I remember right I think it (my conjecture) was that the 1st player can always win on other kind of board (I assumed it was regular in the sense that 3x4 boards didn't count, but what is a diagonal there anyway). I remember a old computer game that was 3-d tic-tac-toe game on a 4×4x4 board. I thought about this at some point in college and managed to convince myself that 5×5x5×5, 6×6x6×6x6 etc boards (side length n+1 in dimension n), where interesting games in the some sense. If I remember right I think it (my conjecture) was that the 1st player can always win on other kind of board (I assumed it was regular in the sense that 3×4 boards didn’t count, but what is a diagonal there anyway).

]]> By: SB7 http://www.thebigquestions.com/2010/04/07/tic-tac-toe-in-four-dimensions/comment-page-1/#comment-4972 SB7 Wed, 07 Apr 2010 11:53:33 +0000 http://www.thebigquestions.com/?p=3090#comment-4972 I'm going to guess that it's something like the first player to move always winning. If I remember correctly, that was the case with 3x3x3 games. I found that out the hard way when the A* algorithm I coded up for my undergrad AI class would essentially panic whenever asked to go second. I mention that because I have a feeling the sea change you're talking about is using computerized search and proof mechanisms. (Actually now that I think about it may not have been A*, but it was something like that.) I’m going to guess that it’s something like the first player to move always winning. If I remember correctly, that was the case with 3×3x3 games. I found that out the hard way when the A* algorithm I coded up for my undergrad AI class would essentially panic whenever asked to go second. I mention that because I have a feeling the sea change you’re talking about is using computerized search and proof mechanisms.

(Actually now that I think about it may not have been A*, but it was something like that.)

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