3D Math Puzzle
May. 5th, 2011 11:38 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
mathhobbitI want to play with different ways of arranging 27 colored cubes into a larger cube. Can anyone suggest a better tool for this than transparent colored dice? Dice are tricky to swap in and out, and the central die will be hard to see.
The puzzle is to fill in a 3x3x3 cube in such a way that there are no "3 in a row" matching cubes. In other words, to make as many plays in a 3D tic-tac-toe game as possible without winning.
To make it trickier, I'm assuming opposite faces of the cube are identified to make a sort of 3-torus.
If you're still reading at this point, you might be interested to know that for really high dimensional cubes, this problem is somehow related to the question of how prime numbers are distributed among natural numbers. Here's a preprint that improves the bounds on the maximum number of plays you can make in this high dimensional tic-tac-toe game without losing:
http://arxiv.org/abs/1101.5851
The puzzle is to fill in a 3x3x3 cube in such a way that there are no "3 in a row" matching cubes. In other words, to make as many plays in a 3D tic-tac-toe game as possible without winning.
To make it trickier, I'm assuming opposite faces of the cube are identified to make a sort of 3-torus.
If you're still reading at this point, you might be interested to know that for really high dimensional cubes, this problem is somehow related to the question of how prime numbers are distributed among natural numbers. Here's a preprint that improves the bounds on the maximum number of plays you can make in this high dimensional tic-tac-toe game without losing:
http://arxiv.org/abs/1101.5851
