Message #327

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] Lower dimensional cubes
Date: Mon, 21 Aug 2006 00:05:24 -0700

I think that I’ve worked out the full state graph for the 2D puzzle. It
appears to have 8 unique states connected like this (best viewed in a
fixed width font):

0 . . 1 . . 2
\ / \ /
\ / \ /
3 . . 4
\ /
\ /
5
/ <br> / <br> 6 . . 7

State 0 is the solved state, and state 2 is the checkerboard. The
diagonal lines represent the simple click twists that you can perform
with the applet whereas the dotted lines represent the transitions
possible via middle slice moves. In a puzzle that allows middle slice
moves the diameter is 3, whereas in a puzzle without middle slices the
diameter is 4 with the checkerboard at the maximum distance from the
pristine state.

-Melinda