Message #2417

From: Eduard Baumann <baumann@mcnet.ch>
Subject: Re: [MC4D] MagicTile Solving
Date: Wed, 17 Oct 2012 11:55:47 +0200

Here are some elements of the story.

MT hyp {5,4} 12 F 1:0:0 V 1:0:0 —– || 10/08/2012 || 13’004 twists

The 12 colors are not at all topologically equivalent. There are two disting colors (for me withe and marin).You have 3 types of elements. 2 colored edges, 1 colored corners and 1 colored faces. Without macros you can arrange the edges and corners in about 1000 twists. For the faces I constructed a single 3-cycle (macro). You need very tricky setups to reach all faces in this color topology.


MT hyp {5,5} 6noB V 1.33:0:0 —– || 10/16/2012 || 1096 twists

All the 6 colors are equivalent. All simple commutators have two elements in the intersection. Hence you have a double 3-cycles. A double 3-cycle has 6 elements. You have only 15 different elements in the puzzle. To get a single 3-cycle you must ‘dislocate’ 5 of the 6 elements in the complement. Once you have such a single 3-cycle (macro) you see that he works only in 50% of the pentagons with the right color in which you have defined the macro (reference). To construct a two element flipper you can not go around the pentagon to return flipped on the starting position because this tour involves allmost all 15 elements.

Kind regards
Ed

—– Original Message —–
From: Melinda Green
To: 4D_Cubing@yahoogroups.com
Sent: Wednesday, October 17, 2012 1:34 AM
Subject: Re: [MC4D] MagicTile Solving

What was the story about the hard ones?
-Melinda

On 10/16/2012 2:38 PM, Eduard wrote:
> Solving of MT irp {3,9} b24 V 0:0:1 —– || 10/11/2012 || 450
> Solving of MT irp {3,9} a36 V 0:0:1 —– || 10/11/2012 || 503
> Solving of MT irp {3,7} 56 V 0:0:1 —– || 10/13/2012 || 909
> Solving of MT hyp {5,4} 12 F 1:0:0 V 1:0:0 —– || 10/08/2012 || 13’004 twists
> This was definitly not a « low hanging fruit ».
> The logfile was to big for wiki.
> I have put it in the yahoo group « 4D-Cubing »
> Solving of MT hyp {8,3} 6 V 1.5:0:0 —– || 10/16/2012 || 101
> Solving of MT hyp {5,5} 6noB V 1.33:0:0 —– || 10/16/2012 || 1096
> Difficult.
>
> New ranking
> 1. Ed 196
> 2. Nan 146
> 3. Andrey 53
> 4. Melinda 17
> 5. Zhao 9
> 6. Roice 2
>
> Still 4 to get my 200 solvings.