I apologize if this question is too elementary for your group. My sister is a math teacher & is trying to find the answer for her class. Has an algorithm been discovered that will solve any configuration of the cube in smallest possible number of moves? What is the smallest number of moves that will solve any configuration? Thanx much for any help.

Recently I was asked about some of the older cube programs written about here. Some of the programs are missing in action, including a couple of my own. It seems worthwhile to try to preserve the older software so if anyone can locate them please send me an email.

If you have written a cube program yourself or know of some forgotten old program feel free to tell people about it in this forum.

The router for the server was acting up and I had to reflash it. Please let me know if there are any other problems. admin mail

As a thought experiment consider the case of the familar 4x4x4 cube with a 2x2x2 cube embedded inside it, instead of the usual mechanism. I'll call this the "Interdimensional 4x4x4 cube" for lack of a better name. Now clearly if we turn the slices of the 4x4x4 cube it would have an effect on the internal 2x2x2 cube. Now moving the slice adjacent to the U face and moving the slice adjacent to the R face this would be the equivalent of turning the internal 2x2x2's U face and R face.

My question is: Is it possible to reach all the positions of the internal 2x2x2 without having any constraints on the 4x4x4 cube? How many positions are there?

We all know that commutators can be used to generate half of the Cube group G. My first question is: Can all elements of the commutator subgroup themselves be written as commutators? i.e., the problem is to determine whether the set of commutators is closed under multiplication; it need not be in general, but is it true here?

If it is closed in this case, then a natural question to ask is How do we write a given element of the commutator subgroup as a single commutator?

On the other hand, if the set of commutators is NOT closed under multiplication, then how many elements of G can be written in commutator form?

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I was wondering if anyone has ever build a bi-directional tree search for solving specific cube positions.
Let me explain.

Suppose one starts with a solved cube (3x3x3) and find all the configurations after one rotation, and so on say until 10 or 11 rotations. The resulting tree will contain a large number of nodes, but not completely unreasonable.

Now suppose you wish to find the shortest solution for a specific configuration. You may start building another tree similar to the above and look for collisions between nodes of the two trees. After exploring say 10 or 11 levels of the tree it is very likely that the two trees will connect and the shortest path can be obtained.

Service is back up, fixed ip address is 216.138.229.145, enjoy :)

I'm changing to a better ISP with a fixed IP address. The current service will go down sometime on July 5th, 2004 and should be back up by the 6th.

www.olympicube.com


new cube family are ready to born