Puzzling Addiction

Here are a few moves for solving Rubik's Slide (in hard mode). If you number the squares from 1 to 9, each sequence swaps square #9 with another square.

8: D + R + U + L + D + R + U -
7: U + U L + R + L + D + U + U -
4: R - R + L + D + U + U + R + U
1: U L + R + L + D + U + U + R -

I'm working on a more efficient solution, but using these sequences, you can solve the center square first, and then use these moves to swap any two squares on the outer ring. For example, to swap 3 and 9, you can do a "++", followed by the sequence to swap 7 and 9, followed by a "--".

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.