Message #2239

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] Re: color graphs of MagicTiles
Date: Sat, 02 Jun 2012 20:16:21 -0700

On 6/2/2012 7:26 PM, schuma wrote:
> I just got time to solve these {8,4} puzzles. I directly faced them before I looked at Ed’s drawing.
>
> Take the 9-color version for example.
>
> I first noticed that some octagons (gray, purple, orange, and cyan) have only two distinct edges, therefore the commutator of turning these two edges is not a 3-cycle. I solved these octagons first, and then avoided using these commutators. This is also what I did in the {3,5} 8C: to solve the special faces first.

Well this must be the secret that eluded me. I’ll try again using your
method and see what a difference that makes. I had the puzzle nearly
solved by move 125 and then I flailed badly until it came together.

>
> The second thing is, of course, the long long orbits, which surprised me. I haven’t found out the structure of the orbits yet. But it seems I don’t really need to know the structure to move pieces along them.

Yes, most of the orbits are 16 steps long and intersects with itself
several times in different ways, but as you can that can be largely ignored.

Thanks for taking them on and reporting back.
-Melinda