9 may 2016
plus: 24 june 2016
Another story from Merv Eberhardt.
Newsletter 2015.10.08 The Normalization of SOMA solutions, by Merv Eberhardt.
And the lead story from William Kustes.
Newsletter 2003.05.18 The complete "SOMAP" is found by William Kustes.
How I Solved the SOMAP by Merv Eberhardt of Huntsville, Alabama.
This article is intended for the many readers of the SOMA newsletter that are passionate about the SOMA phenomena
and the brilliance of the SOMAP. I am dispensing with many necessary details so that I can focus on my efforts that led to my discovery of the solution to the SOMAP.
I refer the reader to the basic references at the end of this article that are critical to the background,
history, and nomenclature of the SOMA puzzle and to the SOMAP.
The key topics are: SOMA creation by Piet Hien; description of the seven SOMA pieces; makeup of the SOMA cube (i.e. faces, edges, vertices, and center); 240 SOMA cube solutions by hand by John H. Conway and Richard K. Guy; SOMAP discovery by John H. Conway; SOMATYPE (i.e., deficiency, centrality, and dexterity); and the hidden secrets of SOMA (i.e. piece #3/Green must be along an edge in FEVV orientation in every solution).
This entire effort was based on reverse engineering of the seven SOMA pieces to achieve the designated SOMAP cube codes (the SOMATYPE) as presented in the SOMAP.
My initial interest in the SOMAP focused on the "genesis" nodes. Those were the ones with the "a" sequence designation, i.e., A0a, RU4a, U2a, etc. I also noticed the 14 gy-go-oy transitions throughout the SOMAP. The sequence RU2b<gy>RU4a<go>RU2a at the bottom of the SOMAP was where I began.
So, starting with the <oy> translation between layouts RU4a and RU2a, I recognized that the RU2a layout required a dexterity of 2 to be satisfied by the Yellow (#2 / L shape) piece and that the RU4a layout would require a dexterity of 4 to be satisfied by the Orange (#4 / Z shape) piece. I determined that the following layout on the bottom layer would provide the proper transition and dexterity values.
Please note that the dexterity positions (values) are to be viewed by looking at the bottom of the bottom layer.
RU4a RU2a B Y Y Y Y Y O O Y O O<oy>Y O O T O O x Y O xThe next consideration was the <go> transition from the RU4a to RU0a. This would add the Green (#3 / T shape) piece in the two initial layouts. The piece would not influence the dexterity by itself but the transition would require the O piece to change its dexterity from 4 to 0. It was somewhat obvious that one of the ends of the G piece would occupy the remaining space in the bottom layer; but its orientation in the middle and top layers was to be determined, as well as how it would be positioned in the RU4a and RU2a layouts.
T x x x x x x x x x O x x x x x x x x x P x x O x x G x x G RU0a RU4a RU2a M x x x x x x x x x I x x O<go>x x G<oy>x x G D x x O x x G x x G B Y Y Y Y Y Y Y Y O O Y G O Y O O Y O O T G G G O O G Y O GThe <gy> transition from RU0a to RU2b was straightforward.
T x x x x x x x x x x x x O x x x x x x x x x x x x P x x O x x O x x G x x G RU2b RU0a RU4a RU2a M x x x x x x x x x x x x I x x O<gy>x x O<go>x x G<oy>x x G D x x O x x O x x G x x G B G G G Y Y Y Y Y Y Y Y O O Y G O Y G O Y O O Y O O T Y Y Y G G G O O G Y O GBe aware that the three pieces (i.e., O, Y, and G) that make up these four layouts occupy five of the eight cube corners (vertices).
T A A B A A B A A B A A B O A R R A R R A R R A R R P U R O U R O U R G U R G RU2b RU0a RU4a RU2a M A B B A B B A B B A B B I U U O<gy>U U O<go>U U G<oy>U U G D U R O U R O U R G U R G B G G G Y Y Y Y Y Y Y Y O O Y G O Y G O Y O O Y O O T Y Y Y G G G O O G Y O GWith the identification of these three swaps (gy-go-oy) of the four layouts (RU2b-RU0a-RU4a-RU2a), all of the remaining SOMAP cube codes can be revealed from the specified two and three piece swaps.
Now 2016-06-24 Merv Eberhardt wrote a commentary letter. Which I will let you read here:
Fellow SOMA Addicts,
Recently I've analyzed the SOMATYPEs of the SOMA solutions as listed in the SOMA Newsletter, 1 Feb 1999 against those of the SOMAP.
The results confirmed my most negative feelings.
Since I've successfully navigated the SOMAP, I've been interested in mapping those 240 double/triple swaps that were so brilliantly discovered and depicted in the Conway-Guy masterpiece into the incredible revelation of the 240 possible solutions of the SOMA Cube Puzzle.
It's confirmed, the majority of the 240 SOMA solutions are reflections of the SOMAP solutions.
Case 1: There are 64 RU and 1 UR SOMATYPEs on the SOMAP.
There are 34 RU and 31 UR SOMATYPEs in the 240 SOMA solutions.
The combined solutions are 61.
Case 2: There are 13 R and 38 U SOMATYPEs on the SOMAP.
There are 26 R and 25 U SOMATYPEs in the 240 SOMA solutions.
The combined solutions are 51.
There are also many differences with dexterity values that point to reflections.
I recall asking about the SOMA Newsletter solutions over a year ago.
It was stated that they were the result of some computer program.
The 240 solutions presented in the 1999-02-01 SOMA Newsletter were found using the program made by Sivy Farhi, described in the 1999-01-21 SOMA Newsletter
Well it seems that my SOMAP results are what was often stated,
"The complete list of 240 SOMA solutions was made by hand ... one particularly rainy afternoon in 1961."
Again, I'm assuming that those historical discoveries are what Conway and Guy included in the SOMAP. Their admonition that use of a computer was an "admission of defeat."
I'll now cease to try to find the SOMAP solutions amongst the SOMA Newsletter solutions.
I have found the "holy grail" of SOMAP solutions and now I can rest in peace.
Written by Merv Eberhardt. <email@example.com>
Adjusted by Thorleif Bundgaard <firstname.lastname@example.org>
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