## One Million Random Twenty-Four Puzzle Instances in the STM metric

Submitted by stannic on Sun, 10/07/2012 - 07:56.I have solved sub-optimally 1,000,000 random instances of 5x5 sliding tile puzzle in STM metric (single-tile moves). The actual running time was about 18,5 hours. The minimum, maximum and average solution length were 73, 171 and 124.48 moves respectively. About 52% of 1,000,000 solutions were in range [118; 132]. There were only 32 instances with (suboptimal) solution length less than 81 (range [73; 80]). Only one instance was solved in 171 moves.

## Sliding tile puzzle suboptimal solver

Submitted by stannic on Mon, 09/24/2012 - 08:07.I wrote a program capable to solve (MxN-1) sliding tile puzzles, such as the Fifteen puzzle. The program can solve puzzles from 2x2 to 11x11.

The main thread is on Speedsolving.com:

http://www.speedsolving.com/forum/showthread.php?38689-kumi-na-tano-3-00-sliding-tile-puzzle-suboptimal-solver

- Bulat

## Policy Change for New Accounts

Submitted by cubex on Fri, 06/29/2012 - 03:50.Also the ban on gmail has been lifted. Sorry for the trouble, but deleting spam entries got tiresome.

Mark

## Megaminx needs at least 45 moves

Submitted by Herbert Kociemba on Tue, 02/28/2012 - 17:56.## A Hamiltonian circuit for Rubik's Cube!

Submitted by Bruce Norskog on Mon, 02/20/2012 - 21:30.I have found a Hamiltonian circuit for the quarter-turn metric Cayley graph of Rubik's Cube! In fact, it only uses turns of five of the six outer layers of the cube.

In more basic terms, this is a sequence of quarter moves that would (in theory) put a Rubik's cube through all of its 43,252,003,274,489,856,000 positions without repeating any of them, and then one more move restores the cube to the starting position. Note that if we have any legally scrambled Rubik's Cube position as the starting point, then applying the sequence would result in the cube being solved at some point within the sequence.

## Regularities in maximum WD values

Submitted by stannic on Sat, 01/14/2012 - 15:26.This post is about any mathematical laws inside the Walking Distance heuristic. It seems like WD is not just puzzle to be computed. Maybe the whole WD heuristic is some math structure.

## A Hamiltonian Circuit for the 2x2x2

Submitted by Bruce Norskog on Mon, 12/26/2011 - 13:33.I have found a Hamiltonian circuit for the 2x2x2 cube group (3674160 elements). I have posted the solution on the speedsolving.com forum. Link: http://www.speedsolving.com/forum/showthread.php?34318

## Number of canonical move sequences for nxnxn Rubik's cube in q-w metric

Submitted by kociemba on Mon, 12/26/2011 - 12:22.gfq[n_,x_]:=3/(6-4(x+1)^(2(n-1)))-1/2

and looks very similar to the generating function in h-w metric which is

gfh[n_,x_]:= 3/(6-4(3x+1)^(n-1))-1/2

## Number of canonical move sequences for nxnxn Rubik's cube in h-w metric

Submitted by kociemba on Sun, 11/20/2011 - 17:22.## Interchanging two faces

Submitted by brac37 on Fri, 11/11/2011 - 12:24.Just a question for fun. Suppose you have a Rubiks cube and you want to interchange two faces? How many stickers need to be moved?

Distinguish between opposite and adjacent faces and between using a screwdriver (for disassembling) or not, so you get four answers.

Next, do not read any further before adding those four answers to obtain a single answer.