Puzzling Addiction

I've run an analysis of all of the positions in the Triple Cross puzzle. I count the number of positions with the horizontal slider centered and the left slider in the down position. There are four sequences that change the tiles and return to this position: LUCD, ULDC, RUCD and URDC. All puzzle positions can be solved within 24 moves. There are only 7 positions (out of 2.9 trillion total) that take 24 moves to solve.

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.

I'm trying to do another blog upgrade...

I've found a new job in Seattle, so I'll be moving from Maryland to the Seattle area in a few weeks.

I'm in the process of moving the site to a new host. Please let me know if you see any problems.

• Profilactic.com - david3x3x3's mashup
  This is my "mashup" on profilactic. It should aggregate content that I create on various sites.
  (tags: imported firefox:toolbar)

I post to this blog infrequently enough that I'm thinking about getting rid of MT and putting up static pages. Anyway, I thought that I'd try out Ligit on my Blog to see how it works.

I'm trying for a sub-20 second average on the Rubik's cube. I got pretty close tonight:

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.

About a year ago I made a page that let you find any last layer position and it would show the most efficient algorithm for solving that position. The algoritm data came from Bernard Helmstetter.

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.