The program took 2 hours 44 minutes to run on a 2.2GHz Core 2 Duo processor (using one core) and uses about 1.4GB of RAM while running.

Here's a list of how many positions are at each number of moves away from a solution. I've included an example of one position at each level.

total positions = 2940537600

 0          1 ..---..12.....34ba
 1          4 .1.--..32b.-...4a.
 2         12 13b.-...2a.-...4.-
 3         36 3.ab.1..2..-...4--
 4        104 3..b.2..4.a.1-..--
 5        303 3.b..a4.....21-.--
 6        884 3....b.2....a41---
 7       2579 ....3a2....b.41---
 8       7521 ...42a......b31---
 9      21937 4..2...3.b..a.1---
10      63923 ..a.3b4......21---
11     186196 .....a43.b...21---
12     542124 ..4.b......3a21---
13    1577700 ......4.3a.b.21---
14    4585298 b.......4a..321---
15   13282991 .ab.......4.321---
16   38149858 ...b.a...4..321---
17  107133350 .....a....b4321---
18  283555419 ........a.b4321---
19  644626804 .......a..b4321---
20 1014637237 .........ab4321---
21  719688345 .........ba4321---
22  111515380 .a....b...4.321---
23     959587 ..4...ab..32..1---
24          7 ...b4.--.3..1a-.2.

Update:

Here are the seven positions that are 24 moves from solved:

-b2..4-...1...-a.3
-..42.-...1a..-b3.
-.2.....-3.ba..-14
b-2....-a.1..-..43
.-24.13.-....b-a..
..3..a---.4..b..21
...b4.--.3..1a-.2.

21.90 21.51 19.39 21.50 19.03 18.72 23.63 (16.58) 16.84 (23.70) 18.67 21.18

Average is 20.24.

I've got a new version of these pages available now. This version uses a different style of diagrams, and it also allows you to select last layer cases in a different order. For example, you can select piece orientation before permutation or vice versa.

This is also useful if you want to know, for example, what is the shortest algorithm for swapping two corners without flipping any edges. To do this, you would click on the first diagram on the first page. This will give you only algorithms that don't flip edges. Then you click on the "PC" link. This gives a list of all of the corner permutation algorithms.

However, I noticed that something weird is going on with the tab widgets in the program. Due to the way the 3d borders are drawn, the tabs seem to be connected to the edge of the window rather than the GUI element that they are controlling.

Also, my finger continues to bother me. I went to my doctor at the end of February, and she put it in a splint and told me to keep it there for a couple weeks. I left it in the splint for three weeks, but it didn't help much. So, this week I went to the National Hand Center in Baltimore. The doctor there told me I need to stop doing things that irritate the finger for six weeks. They gave me some different types of splints and protective gear that I can try out to see what works best for me. If my finger isn't better at the end of six weeks, they will try giving me a steroid injection in the joint, which is supposed to be kind of painful.

If you're interested in helping with this program, let me know. There's lots of stuff to do: adding additional puzzles, improving the speed of the program, improving the user interface, improving the web site, cleaning up the source code, etc.

I haven't picked out a license for the program yet. I'm leaning toward BSD, since that is what all of the Tcl3d stuff is licensed under.

The puzzles included are the NxNxN cubes, two dodecahedra, an octahedron, a cuboctahedron, and an icosahedron.

The program was built using Tcl3d by Paul Obermeier.

Downloads:

twisted-1.4.exe (a windows executable)

twisted-1.4.zip (the source code)