Icebox maze

And the Icebox maze was amazingly complex for such a small puzzle.
I wrote a program to solve it. There are 99264 physically possible 
states (nothing hanging off the board or overlapping), and 96480 of 
them are connected. Compare to 100 or so for the tromino maze.

The shortest solution (probably one of many) was in 27 moves.
0s 0s 1w 2n 0e 1s 2w 2w 0n 1n 2s 0e 2e 2e 2n 1s 2w 0w 0s 2e 1n 0w 0n 2s 1e 0n 2e
where 0 means move block 0 (IC), 1 means move EB, 2 means move OX.

11 states were farthest from the starting position, 43 moves away, including:
####
CI##
XOBE

The handful of states unreachable from the starting position include such 
impossibilities as two blocks upright on the center two spaces.

Joseph DeVincentis


A sequence of 53 moves to solve the maze is:
IC-EES
EB-NE
OX-WNNE
IC-WSE
EB-SWN
OX-SSW
IC-NN
OX-ESW
EB-SES
IC-SWW
EB-NNNW
IC-EES
OX-NEN
IC-WNE
OX-SWSE
EB-ESWS
IC-NWW

---------------------------
Ed Pegg: Since you have a program, what happens if only one face of each block
has lettering?  Is the puzzle still solvable?
    
Joe: I modified the program in this way, now checking 64 times as many states. It reached 771840 of 6352896 states, did not reach the goal, and the hardest 3 states were reached in 56 moves.
These hardest states are 00ED 03WS 13SE, 01WS 03WS 12SU, and 01WS 22NW 02EU.
Read these states as row and column number for the I, E, and O, followed by the direction in which the other end of each block faces, and the direction that the letters face. So the first one has each block back in its starting position, with the EB turned around, the OX turned the right way, but the letters on IC face down, EB south, and OX east.
Here are the paths to reach these states: 0s0s1w2n0e0n1s1w0w0s2w2w0e0n0n0w1e1e0s1e1n0e0e2e2s2s1w1s2w2n1s1w0w0w0n0e2e1n2s0w2e2n2n0s0e1e1s2w0n1e1n2s0w1n2e2e
0s0s1w2n0e1s1w1n2w2s2w0n0e0s0w0n0e1e1e2e2s2w2n2e2s0w0n1s0w0s1w1n1w2e2n2n0e0e1s1s2w0e1e1n2s2w1w1s0w0n0w1e1n1n2e2e
0s0s1w2n0e1s1w1n2w2s2w0n0e0s0w0w1e1s1s1e1n1w1s2e0n1w2e0e0e1n1n0s0w0n1e0n1s1w0e1n2w2s2w2n0s1e2e2s1w0n2e2n1s0w2n1e

The biggest growth in states occurs at move 39 when 50350 new states are reached.

Joseph DeVincentis