SOMA News 5 january 2016 E-Mail.

# Ed's Continued Quest for all solutions.

As you know from Newsletter N150728.HTM Edward Vogel is on a Quest for finding all the 240 solutions of SOMA

 Previous stories from Edward Vogel. Newsletter 2015.07.28   Ed's Quest for all solutions, by Ed Vogel. Newsletter 2014.11.26   Graph Theoretic Methods for SOMA, by Ed Vogel. Newsletter 2002.06.21   World's Largest cardbox SOMA by Ed Vogel.

In 2015-10-14 Ed stumbled upon an article: "All solutions of the Soma cube puzzle by Christoph Peter-Orth". Maybe you find it interesting.
The original article is here     www.sciencedirect.com/science/article/pii/0012365X85901608     Or here on my mirror site.

This Quest now continues at an impressive rate.
But first let us take a look at how these puzzles are used:

This quest has led Ed to an immense number of puzzle combinations.
All these are documented in a huge spreadsheet - that you can get here:

Now let us look at a few of the branch spreadsheets. Then let Ed explain his ideas, and finally you may scroll through a huge number of photos showing SOMA.

So what went on with all these colored squares.? - I will let Ed explain the immense work.

2016-01-03 Topic: SOMA Cube Solutions Arranged from 42 Starting Positions

Hi Thorleif
I have successfully (I believe) found and documented the solutions to the cube puzzle by:
1. Locking the Tee in on position
2. Creating 42 starting positions from the combinations of the Tee and one of Helix pieces

Unfortunately I appear to have found 250.
I have checked for duplicate solutions three times and do not find any.> Does "unique solution" mean something more than I am understanding?> There are 58 solutions that share a rotation of the "L" and "Z" for instance. . . >

2016-01-03
Hi Ed
Thank you for the link to all your pictures, that is an impressive work you have done.

I would have expected that the pieces T+A would be a mirror of T+B though.

A unique solution is understood like this.
1. It cannot be a rotation of a known solution.
2. It cannot be a mirror image of a known solution.
Because mirrors can be done by exchanging pieces A & B
All other pieces are their own mirrorimage.

Remaining is of course the big task of compiling and describing it all in a manner that can be understood by others.
I imagine you could reduce the imageges, by taking representative selections

Fortunately for me Merv's work Newsletter 2015-10-08 translates easily into my color scheme.
This will ease my comparing the current accepted solution set of 240 to what I have come up with using a tree categorization method.

I am guessing my final format will be about twenty tabloid pages showing on or more tree graphs.
A single tree graph with 42 branches using a "readable" font size looks to be about 8 feet in diameter . . .

have the comparison done early next week. / Thanks for you interest and encouragement.

Hi Thorleif
Discovered that I am missing some of the combinations of the Tee and HelixBlue in my scheme.
I think then the reason I got 250 is that if I have all of the starting combinations of the Tee and HelixBlue I will find 480 solutions. . .

Not as simple a way to discover the solutions as I had hoped but it is I think a valid approach.
This is going to take a couple more weeks.

Hi Thorleif
I am continuing my quest to find all of the Soma cube solutions.

You may have noticed I have made many sets of Soma puzzles.
I discovered that if one has access to a table saw that rip cutting 1 inch x 12 inch x 4 ft boards into strips
and then cross cutting into 3 cube, 2 cube and 1 cube length pieces is pretty doable.

The pieces are then glued into the pieces and colored using food coloring.
I made 150 or so sets.
I was hoping to get 240 done for a "Gathering for Gardner" event in October 2015 but didn't quite make it.
They are fun to play with like building blocks.

Some of the cubes are shown in this video made for a local film festival:
Thorleif's note: This is the video shown in top of this Newsletter

Also in the video is a demonstration of encoding solutions using music.

Best regards
Edward Vogel

Now let us look at Edwards impressive number of photos of SOMA
Thank you Ed for all this work.

Now it is 2016-06-25 and Ed Vogel wrote some thoughts to me, regarding: "Analysis of SOMA/SOMAP".

 Mirror Case 2 Auburn and Blue have changed orientation but retained half of their original positions " Mirror Case 1 Auburn and Blue very obviously have swapped

Perhaps a new Super Somap is needed that sorts and displays the relations ship between all 480 solutions.
The attached pic shows (I think) three interesting properties of mirror solutions:
1. The distance between two helical pieces
2. The number of touching faces of the two helical pieces
3. Change in position of the the two helical pieces

I am thinking Group Theory may provide some insights into representing these relationships that could then be used to organize a new Somap of all 480 solutions.

Nathan Carter's text (suitable for students with only high school math) "Visual Group Theory":
This text refer to "Visual Group Theory (MAA Classroom Resource Materials) (MAA Problem Book Series) by Nathan Carter"

Great videos from a class using this text start here: