# Thread: Lower bound for Megaminx in htm and qtm

1. ## Lower bound for Megaminx in htm and qtm

I analyzed the number of generic move sequences to get lower bounds for God's number of Megaminx, taking into account the commutativity of moves. There are a lot of commutating moves because of the many disjoint faces of Megaminx. In htm, I found a lower bound of 45 moves and in qtm a lower bound of 55 moves.

I posted the details here:

http://cubezzz.dyndns.org/drupal/?q=node/view/328

2. I made a somewhat similar recursion a while back and ended up with, I think, 43 moves for the Megaminx. I'm not sure exactly where our techniques differ, but I do like this technique in general, as you can get some pretty nice results without a huge amount of work.

3. Originally Posted by qqwref
I made a somewhat similar recursion a while back and ended up with, I think, 43 moves for the Megaminx. I'm not sure exactly where our techniques differ, but I do like this technique in general, as you can get some pretty nice results without a huge amount of work.
I assume, the techniques differ somehow, because the difference between 43 und 45 means that you have more than 1000 times the number of move sequences with 45 moves.
I would be really pleased, if
1. Someone could double check, that there are 25 unordered pairs of faces (X,Y), which have no pieces in common and either X or Y (or both) have pieces in common with some arbitrary different fixed face,e.g. U.
2. The same for 15 unordered triples (X,Y,Z), which have no pieces in common and either X or Y or Z have pieces in common with another different face, for example the U face.
3. Compute the true number of positions of Megaminx out to some depth in htm and qtm to check if the numbers are the same for the first ??? depths. This depends on the length of the shortest nontrivial identity. Btw, What is the shortest nontrivial identity on Megaminx?

4. Originally Posted by Herbert Kociemba
What is the shortest nontrivial identity on Megaminx?
At most 10 moves. FRU'R'U2F'L'ULU2' works on Megaminx.

5. The niklas done the wrong way (L' U R U' L U R' U') is a 8-move identity.

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