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SOMA News 27 April 2008 + april 2015 + august 2016 + july 2017
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A Spotted SOMA.

Now it is 20160827 We (Theo Geerinck and I) figured the position of all the spots.
This makes it possible for anyone to make a copy of this puzzle - See the drawing almost at the end of this text.

A Question: We assume that "when" these pieces are assembled correctly,
then the spots will form a specific pattern on the sides. maybe checkered or maybe something else.
If YOU find such a solution, then please take a set of photos so that we can see how it is assembled
and eMail them to me = Thorleif (my eMail is at the bottom of this Newsletter).


We are writing 20170701 After several months of hard work by Bob Nungester. We conclude that there is no "Very pretty" solution to the "Spotted SOMA".
However through a lot of programming and mathematical reasoning we can show that this pussle Do have one specific (and nice looking) solution.
We believe that this probably is the right one. Featuring sides of |◥| + | X | T | · |  .|
Mike Beeler found thet there is a very specific solution that will produce 6 sides of the cube, so that each side has exactly "6 white and 3 red spots".
Though this is unlikely to be the original solution because it is virtually impossible to reach that solution without a computer program.
Now follow this Newsletter to hear the story that led us to the intriguing solution.
Either scroll down, or jump direct to the new text by pressing [HERE]


HOWEVER If "ANYONE should know more about the Spotted SOMA.
Then PLEASE write to me about it. It would be fasinating to find out more.
This puzzle is Industrial grade. So there MUST be more of them out there,
and if we are extremely lucky, Someone know more about its history and its use.




   The story of a Spotted SOMA.   

April 2008 A week ago I received a mail from Theo Geerinck.
"In a sale I bought a SOMA like puzzle in the sense that the seven pieces have the shape of the standard soma pieces but they are spotted with red and white dots on all sides of the unit-cubes of which they are build. It is made from black plastic and there are 67 red, and 55 white spots."
Apparently he had a SOMA with colored dots on the cubes. At first I imagined something like pieces made from dice, or spot colors alternating, like the twocolored wood SOMA's we know. But a pair of fotos soon revealed that this was indeed something special.


Soma One side

Soma Other side

The thing is - None of us have ever seen this version before. And we dont know the challenge involved.

BUT - the way the dots are placed, makes me feel that it should be possible to assemble the SOMA 3x3x3 cube having it all red, or with sides of same colors. So I imagine that this is the purpose of these dots.

Why then.?

Lets see. http://www.fam-bundgaard.dk/SOMA/NEWS/N990201.HTM
Scroll it down to the color drawing in the middle.
There you see some pieces, and their position in the box.
This diagram shows the ONLY possible positions that each piece can have.
(No other positions are possible, if you want to assemble the cube)(( Except mirror versions !!!!))

Now, look at the 'L' shaped piece, you see that it will always show its left side to the public.
Looking at the spotted cube I see that the 'L' piece show the 'right' side as 'ALL RED'
Not the same side as my drawing - but remember, mirror versions also exist.
OK so the 'L' is not 'same color' on its back, so this would mean that the ONLY position for the 'L' is the diagrams position "Y=2 Deficient"

Then look at the 'T' piece, according to the diagram, this can "Only" be a "G=3 Normal" requiring it to be the same color on one of its sides, AND, same color at the ends and its back.
Alas, I cannot see its end colors, nor its 'back' color - But - If it is red, then all sides assembles to red.
However - IF the ends are white, then I would assume the finished cube to have some sides all red and the rest to be all white.
[by the way I just noticed that the 'L' has a white top, so this speaks for a cube with alternating side colors.]

I use the figure diagram to establish that piece 'T' have only ONE possible position, and that 'L' and 'Z' is limited to one of two places, this is helpfull when assembling, because the number of triels are reduced this way.

If YOU have any experience with this, or own a SOMA like this, then please let me know.

It is now april 2015.
And Theo wrote to me again. This time with one more foto, so now we have 'almost' all the sides of this interesting puzzle version.
Can anyone out there help us with a solution or explanation.
Soma
Third side

Theo wrote: "I tried in vein to find a special pattern, while forming a 3x3x3.
So I wonder about the objective of the puzzle. Can anyone help me out?
The reason I returned to this problem was that I got the design of a Soma cube with dotted pieces so that the die pattern gave an unique solution. The designer is unknown to me.
I have tried the free Burrtools program that allows you to try patterns on the outside, so I know that two all white dotted sides are impossible."

Can we make a copy ?

I tried to combine all Theo's pictures, to find out where the spots appear.
On the left of each little drawing field, you see a piece slightly from above,
and on the right you see the same piece then turned 180 deg, and the view is now slightly from below.
This should make all sides visible and making it possible for you to create a copy.
Now in this image I have (Red side = Red spots) (White side = White spots).

Will anyone help us finding a solution to this enigma ?.
Soma
The color distribution


Another spotted SOMA

Let us divert for a moment, while seing spots. ;-)
Then have a look some another of theo's spotted cubes. A dice and its pieces :o)
Soma Soma

"Hi Thorleif;
This is another example of how a prescribed pattern can force an unique solution
to the Soma Cube (240 solutions). The design is by Ken Johnson and the pattern
is my first name in capitals on four sides (top and bottom are blank)."
Soma
TH side
Soma
EO side


Forward to spring 2017

9 years have passed since the spots appeared, and this could be just another story with no end, if it were not for one of our mathematical and programming puzzlers Bob Nungester (Newsletters from 1992-11 and 1992-12)

A LONG sequence of mails is the result.

The following is the mail account that led us to find a "plausible" solution to the Spotted SOMA
The mails have been 'slightly' edited, and some of the chit/chat among us has been omitted.
However, the mail sequence illustrates the many thoughts that goes into solving problems of unknown substances, and as such, it may be inspiring to some.

However, if you want, you can skip the mails, and go straight to the real "Spotted" solution. by pressing [HERE]. - Or go back here [TO THE TOP].


2017-04-12
Bob Nungester wrote the starting mail:
I looked up your SOMA page to see what was new and noticed the spotted SOMA. ...
... Anyway, I saw this problem and got interested. The main thing I noticed in reading your analysis is that the back and one side of the T piece are always visible. Either side has all squares the same color, but the back is one red square and two white ones. This means that one side of the cube can't be all one color, and it also can't be a checkerboard pattern (red/white/red or white/red/white).
Given that, I'm not sure what we're looking for. Imagining the assembled cube I tried forming letters in a red pattern to spell out S,O,M,A on four sides, but with only nine "pixels" it's impossible to make an M or A (or they look the same anyway). The side with the back of the T piece represents something, but with no idea what that is. It's going to be almost impossible to find the solution.

I'm thinking of writing a program to analyze the 240 cube solutions with all possible reflections and also piece-in-place differences. Rotations don't matter because they just interchange the various faces.

The piece-in-place differences are pretty easy to see. I believe the pieces 1-7 have a number of possible orientations of 2,1,2,2,2,2,3. Multiplying these out gives 96 combinations of piece orientations for any given cube configuration.

Therefore, a program would need to analyze 240 cubes x 6 faces x 96 piece-in-place symmetries x 25 reflections (24 actual reflections plus the initial identity matrix), which gives 3,456,000 faces to be analyzed.
That's not a huge number for a computer, but we've got to know what we're looking for.
It's easy to use parity to check for all one color (parity = 9) or checkerboard (parity = 4 or 5 and then do further checking for the correct pattern), but for anything else we'd need to know what we're looking for.
I'm not sure there aren't duplicates in the 24 reflections since some of them are double or triple reflections, but I'm not too concerned about that. I can think of 9 that definitely apply, so the maximum reduction would be less than a factor of 3. Processors are fast now.

Writing the program would be in two parts.
The generation of 3.4 million faces is one part, and once it's done it won't change. The hard part is how to analyze the faces and get them down to a reasonable amount of "interesting" combinations that a person can then look at.
Other than solid color and checkerboard, can you think of other likely patterns that may exist? There's something different included because of that visible white/white/red pattern on the back of the T piece. It couldn't be a dice pattern either because the solid color of both sides of the T piece doesn't fit any of the 1-6 patterns on a die.
Since there are only 9 pixels on a side there are only 512 possible patterns (2^9) so maybe I'll look at them to see how many form readable letters.
Somehow we need to narrow it down and generate a score for patterns that look interesting so the program will just show six face patterns that are a really interesting combination.

It's a lot of work to code in the piece configurations and then cycle through the various combinations and reflections. If we knew what we were looking for it'd be worth doing, but without some "solution" to search for it's basically impossible to know when it's right.

Let me know if you have any ideas to narrow down the possibilities of what may be represented on the faces.


Thorleif Bundgaard: I'd say that the spotted SOMA is an actual challenge.
I also figured that sides of a single color would not be right, neither the Dice. (Which actually had been my favorite until I got the piece colorations right). Then I thought of letters like X, O, H, -, = Or something like a dot on the side opposing O, and X opposing an X of opposite color.
I dont think we are looking for letters to form text, although I have seen an alfabet with very few dots, then it would still not be readable enough.
So I believe we are looking for patterns. Maybe like triangles of 1,2,3 dots. Or maybe a red box with white lines around like string around a gift - maybe with an x on top of the "wrapping".


Bob:
I like your thoughts that X, O, a central dot or bands of red/white may be involved. My thought is to have the program generate a score for each of the 576,000 sets of six sides and output the highest scores.
The first X, O, band or single center point would get a few points. A second one in the same set would add those same points again, plus a bonus for two in one set. A third one would get a bigger bonus and each additional one would get even more.
In this way it's not just the face patterns that score, but the combination of several recognizable patterns. Each high score can be output so we can look at them to see how the faces match up. Hopefully that will find the target pattern.
If not, it'll take more manipulation of different pattern scores to get to the final result.


After some information exchange with Merv Eberhardt, as to the correctness of the 240 normalized solutions table, Bob continues:
I had not read the interesting newsletter on Mirroring and SOMA before,
Referring to the SOMA Newsletter:
"A whole graphical SOMA presentation (incl all 240 cube solutions), by Jan de Groot."
https://www.fam-bundgaard.dk/SOMA/NEWS/N160806.HTM
but I was aware of the 240 mirror solutions with swapped pieces 5 and 6 that need to be added to the standard 240 solution list.
With Spotted SOMA each piece can be placed in a given cube solution in two orientations (except only one for #2 and three for #7), so there are 96 unique piece combinations for each of the 480 cubes. This gives 46,080 cubes to be analyzed for surface dot patterns.
The program won't take long to run, but writing it is going to be a challenge, especially coming up with a good scoring system to automate the review of all those dot patterns and getting it to a reasonable number for Thorleif and me to look at manually.

I saw the newsletter about your work with the SOMAP.
I followed a couple of paths to see how it works, but for now I'm going to concentrate on that pesky Spotted SOMA problem.
Ps: Merv Eberhardt has done a lot more work on the SOMAP problem.
This can be read in the Newsletter:
https://www.fam-bundgaard.dk/SOMA/NEWS/N170711.HTM


Thorleif:
When a program emerges, I think it would be super if it had the option of (also) generating all 46080 solutions in some sort of text file.
Maybe something like this: (The 6 faces, and the piece positions that make the cube)

147
  o-o  -o-  ---  ooo  ---  o-o   |153|752|772|
  -o-  o-o  -o-  o-o  ooo  ooo   |113|553|762|
  o-o  -o-  ---  ooo  ---  o-o   |443|644|662|
148
  ooo ..... next solution ......
This "might" enable a leasurely 'reading' and one could tick off the appearences that looked interesting.

Of course the "finding" algorithm would also output "it's" preferred solutions, but such a list might allow us to spot some subtle unforeseen combination.

What about some way of entering the piece coloration. Maybe in some text file. ?
That way, if some other pattern should appear, we may [sort of] quickly discover if it generates a pattern.


Bob:
Yes, I'm planning to generate a text file with that format. There will actually be two programs. The first one will cycle through all the cube solutions and piece placements to generate the huge text file. That program only needs to run once. The second program will then read from the file and score all the solutions.
It'll then sort them by score and output to another file for viewing.
If a good solution doesn't pop out we'll need to make changes to the scoring to try and find a good one. Once the solution file is available, anybody is welcome to get it for viewing or writing their own scoring program (if we don't find the correct one).

I have finished figuring out how to program the solver. There are 120 cube solutions and 120 reflected solutions with pieces 5 and 6 interchanged. You may have already known that, but it took me a while to figure out that only one (any) reflection plane produces all possible reflected solutions. I was thinking it would take one in each axis, plus diagonals, etc.
I've got all 120 normalized solutions now, so I'll create the other 120 with a short program that just exchanges the right and left numbers from each solution (with 5-6 swapped).
That file will be input to the solution generation program.
The program cycles though the seven pieces, determining which of the 24 possible orientations (six directions to point times four 90-degree rotations). That will automatically find all the ways (1, 2, or 3) that each piece can be rotated to fit. That'll also be a check in the program to make sure it finds the correct amount or throw an error. Each piece will also have six normal unit vectors for each small cube, including the color of that surface. Rotating these vectors with the same matrix used to orient the piece makes it possible to pick the correct normal for each visible surface. That'll serve as another error check since a normal pointing to another connected small cube in the same piece should never appear on a face.

The 24 orientation matrices are the same as the 48 symmetries of SOMA.
All of the matrices with a positive determinate are rotations and all with negative determinates are reflections (not needed). I know I'm talking to a Mathematics professor, so I apologize for explaining things you already know. It was interesting to me to figure all this out.
[ Thorleif: Yes I do teach math, but this I didn't know. Its very interesting. ]

For entering piece colors. I will use a text file to input the six face colors for each of the three or four small cubes in each SOMA piece.
I've worked out all the coordinates and normal directions and colors for all the pieces, so I'll just convert that to a text file instead of hard-coding them in the program. I think it'll just have one line for each piece with a digit for each normal (six times the number of small cubes).
White will be 0, red will be 1 and all normals pointing to another connected small cube will be 9.


Bob continue:
That file was easy to make so here it is "NormalColors.txt".
091009901101111190
090119900101010199111190
091099901011101009011090
091109901091111109010190
099111901101010919101090
199001911009111190110911
199009910101100901010191
The file has the color number for each face of each of the small cubes.
0=White, 1=Red and 9=Shared Face between adjacent small cubes.
Each line represents one of the 7 pieces.
Numbers are in groups of six, representing the colors of the -X, +X, -Y, +Y, -Z, and +Z faces of each small cube. Looking at your illustration in this newsletter. (just the left picture of each piece)
The X axis is coming out of the screen to the right.
The Y axis goes right and back, and the Z axis is up.
The small cubes are listed in the following order:

Piece 1 - The first cube is the middle one, second is in the -X direction and third is in +Z
Piece 2 - Same as 1 with the addition of the fourth piece on top.
Piece 3 - First is the middle one, second in +X, third in -Z and fourth is +Z.
Piece 4 - First is the second one from the top. Second is +X, third is +X and -Z, fourth is +Z.
Piece 5 - First is the one in the back, second is +X, third is -Y, and fourth is -Y and +Z.
Piece 6 - First is in the back, second is +X, third is +X and +Z, and fourth is -Y.
Piece 7 - First is the middle one, second is +X, third is -Y, and fourth is +Z.

Ps: That table is included in the final compilation, and not available to the normal user.
At this point Bob had the horrifying thought that "What if the cubes could rotate relative to each other.
So we contacted Theo (Owner of the Spotted SOMA)


?? Are there any additional information you have about your spotted version.
?? Did it come with anything, like papers or a box ??
?? How and where did you get it ??

Theo Geerinck answered:
I cannot add much. All connections are rigid.
I collected the puzzle in 2008 at the fifth German Cube Day in Gütersloh. Just the pieces, no box, no description.
I cannot guarantee that there was never tampered with the pieces, on close inspection there seem to be a different glue- connection on one of the pieces.
All the best and keep up the good work.


So work could continue.
Bob:
OK, I was just checking all information available to find any possible errors in the text file. I'm going to start writing the easy parts of the program such as inputting the 240 cube solutions, 24 orientations of each piece, colors of each small cube face, etc. and then I'll move on to the more complex parts like cycling through the piece orientations and extracting the patterns on each of the six faces.

Now we examined the point in the photo's that looks like a glue joint on piece #5 on the end cube.
Whoever repaired the piece probably did it correctly, but if not it's still easy to correct in the program.

Bob now has the 240 normalized solutions from Merv:
As the first step I've converted all of Merv's solutions to Thorleif's standard format, and also generated the 240 reflected solutions that are needed since Spotted SOMA pieces show different faces in mirror solutions. The attached file has all 480 solutions, numbered 001-240 followed by 001R-240R. Now comes the hard part of placing pieces in every orientation in each cube and figuring out the dot patterns on the faces.

I'm now at the difficult part of writing the recursive subroutine that cycles through each piece placement and outputs all the spotted face solutions.


Bob some days after:
It was a lot of work, and some very complicated debugging, but I think the program to generate solutions is done! The file is with all 46,080 solutions (4MB of text).

Each solution has a cube number (001-240 and 001R-240R) followed by 01-96 representing the 96 combinations of piece orientations in the cube.
This has to be used with the file of 480 cubes, to visualize each solution. (with some fiddling to get each piece in the correct orientation).

The faces are ordered Left, Front, Right, Back, Top, Bottom where the top and bottom would attach to the front at its top or bottom edge. I'm pretty sure it's correct.

At this point Thorleif had a copy of the software, and were able to do parallel search for patterns.

Let's start talking about scoring strategy. A simple text file with 3x3 faces and an associated score for each one can be used as input to a scoring program. I'll start writing that much simpler program next.

Note that our approach assume that each cube face is an entity in itself
Thus NOT searching for concatenated patterns.


Bob continues:
Yes Thorleif, in looking at the file it's apparent there's no simple way to find good solutions. I'll write the scoring program that will score each face against a list of patterns and output the list in sorted order (highest to lowest scores). If we don't find anything we can just change the scoring file and run it again. It should only take a few seconds to execute each run. I optimized the code for generating solutions and it only took 15 seconds to run all the combinations of pieces and extract the face values for all 46,000+ solutions.

The first Scoring file was defined.
A score is entered, followed by the pattern of X and O values. There's no need to enter the inverse since the program will automatically check for that as well. In other words "Scores.txt"
50        This number is the score points of this pattern
XXX
XOX
XXX

will also check for this pattern.
OOO
OXO
OOO

I'll have the program written in a few days and we can start looking at promising solutions and maybe generate other search patterns.
When the program is written it will be very easy to try other patterns or even change the scoring logic to look for certain combinations of faces.
It's also trivial to use other characters other than X and O if that helps.

A few days later - Bob:
The scoring program is ready, and the first result (top 100 scores, can be checked). It doesn't look good for finding a solution to Spotted Soma.
The good news is that we have all 46,080 solutions and can sort them based on any face scoring system.
The first scoring with the obvious patterns of solid colors and straight lines didn't find anything better than four faces with good scores.

Maybe fame is harder to come by than I thought ??.
Let's try some other patterns and see if anything pops up.

Let me know if you have any ideas on ways to score the solutions.

Thorleif:
That was a fast result. And a fine list.
My immediate favorite is (almost) this one.

045-22 Score = 95
OOO XXX OXO OOO XOO OOO
OOX XXO XXX OOO OXO OOO
XXO OOX OXO XXX OOX OOO

So I was eagerly looking for a pattern like this below - though with no succes.
OOX XOX OXO OOO XOO OOO
OOX OXO XXX OOO OXO OOO
XXO XOX OXO XXX OOX OOO

But for now we must think differently in patterns.

From your files I think we can be sure that it is NOT letters in some form, unless its a gift from some compagny named "CUTO" - which is unlikely.
So I imagine our search should be for sequence patterns.
This could be eyes on a dice - but that didn't seem to be available.
My next thought is that it might be a geometric representations.
So looking at your "scores.txt" I thought of these.

XXX   OOO
OOO   XXX
OOO   OOO
Or maybe these are checked by rotation the 3 patterns of a vertical line ?

XOX   XOX
OXO   XXX
XOX   XOX
I couldnt see these "2 lines" - "3 lines" in your list

Maybe its a pattern representing geometry, 0 lines, 1 line / or |, 2 lines X or +, 3 lines U or H, Square O, All dots on, triangle ◥ .
Or the + might also represent a circle figure.

So how about something like this?
OOO    OOO    XOX    XOX    XXX    XXX
OOO    XXX    OXO    XOX    XOX    XXO
OOO    OOO    XOX    XXX    XXX    XOO 
Not showing "all on" because thats the opposite of "all off"
The "U" might be a "H", and the "-" might be "/"

Now its june 2017 - Bob:
Yes, we're going to need to look at different patterns. Since we can't do a text search for any face pattern in the file (three partial text lines), the only way to check for a pattern is to give it a score and then run the scoring program.
I added the face you suggested, but the results didn't show any meaningful combination of faces.
I'll look at the 3x3 fonts you sent and see if any of those look promising.



We're to the point now where we're looking for any meaningful patterns that might be in there.

I made a Spotted Soma set by putting white electrical tape on my classic red Soma set. It checked out with all three photos on your web page.
I assembled one of the solutions and it worked fine, so I'm pretty sure the program is bug-free at this point. When playing with the pieces I noted that piece 6 is self-similar in rotation so both placements of that piece generate identical spot patterns. That means all scored solutions will be duplicated. It's not a big deal, but an interesting fact.

Let me know if you have any suggestions of patterns to search for. It's best to generate a scoring file and I'll give it a run.
OBS: I've found it's a bit of a pain to enter rotations of each pattern, so if we end up generating a lot of patterns I may change the program to automatically rotate any pattern while scoring.

Note: The final program handles rotations of patterns.

Bob:
The scoring program now is operational.
The newest version can be found at the end of this web page. by pressing [HERE].


Now its 2017-06-05 Bob summarises what he has found:
Well, I spent a few hours today playing with patterns and even putting a 3x3 font set into the scoring file and nothing turned up. I think I'm about done with this problem. Since I had a couple of errors in my dice Soma colors I even tested the Spotted Soma dot color file to make sure it's correct. I assembled a cube (Spotted Soma cube) the usual way I do and looked up that it's orientation 105R in the cube list.
I set up a scoring file with the six faces as they appeared on the cube, and sure enough the program found an exact match of all six patterns in solution 105R-31. That verified 54 of the relevant color dots, and given that the file has the correct number of red and white dots, the others are probably correct too.

Here are some things I noticed while trying to find a solution:

Many of the dots are irrelevant. Any dot on an internal corner face of a piece cannot appear on the cube. If it did, another cubelet or two would be sticking out of the cube.
There are 31 of these cubelet faces, plus the one on the end of the T in piece #3 that is always internal to the cube.
The 27 cubelets have 6 x 27 = 162 faces.
40 of these are glued to each other to form the 20 connections between cubelets in the pieces.
162 – 40 – 32 = 90 relevant cubelet faces that can possibly be displayed.
Of these, 43 are red and 47 are white.

With 240 cube solutions and their mirror images (since the spotted pieces are different in reflection) there are 480 possible cube solutions. Each piece can be oriented either of two ways, except piece #2 (1 way) and piece #7 (3 ways). Multiplying these together gives 96 combinations of piece orientations for each cube.
That means there are 480 x 96 = 46,080 ways to assemble a cube with the Spotted Soma pieces.
Later, I noticed that piece #6 has the same spot pattern in either orientation, so there are actually no more than 23,040 unique solutions with these spotted pieces. There are almost certainly more duplicates since only 54 of the 90 relevant dots are visible in any solution.

Looking at the pieces there are some combinations of patterns that are impossible. For example, to make a side with all dots the same color you can see the maximum number of dots each piece can provide. For a side with all white dots the maximum dots each of the seven pieces can provide is 2 + 1 + 4 +2 + 1 +1 +3 = 14.
For red, 3 + 4 + 4 + 0 + 2 + 2 + 1 = 16.
That means at most one face (9 dots) of each color is the maximum possible.
When the program scored all the solutions it found many with one red or white face, but none with both red and white faces.

Once the program generated all the solutions the task was to search for patterns of dots and output the highest scoring solutions.

The program searched for patterns of solid color, an X, a +, one dot in the center with the rest opposite color, one or two straight lines of three dots, a diagonal line of dots, one or three dots in a corner, a U, a T, an H and a few other patterns. It automatically generated the four rotations of each pattern as well as their inverse (swap red and white dots).


These are the shapes we have testet until 2017.07.01


It found some of each one, and many combinations of two, but always with random patterns in three or four faces. With that little correlation between face patterns I'm almost sure there is no solution to this as a cube.
Possibly it's a different figure, but that could be anything.

The best patterns found were combinations of only two faces with random patterns on the other four. These included a solid white face with a white X face, a solid red and a red dot, a solid white and a red diagonal, and one white line face and one red dot face.

One of the few with three pattern faces is #90-03 which has a red T on top, white T on bottom and a red dot on the right side.
That's one of the best combinations of patterns, but the three faces together don't mean anything.

Oh well, maybe the next Soma problem will be easier to solve.


Bob thinks about dublications:
There's a CondensedSolutions.txt file that's ½ the size of the original one.
If anyone wants to write a scoring program to sort through the solutions they can use this one.

It was very easy to eliminate the duplicate solutions. Since piece #6 has identical spots in either of its placements, every group of six solutions has the first three duplicated as the next three.
This is because the cycling of piece orientations (A, B for most pieces and A, B, C for piece #7) is ordered like this:

... 5A, 6A, 7A
... 5A, 6A, 7B
... 5A, 6A, 7C
... 5A, 6B, 7A
... 5A, 6B, 7B
... 5A, 6B, 7C

Then piece #5 cycles to B, and so on up the tree until all 96 placements are done. The only change to the program was the addition of an IF statement that only prints to the file if (SolutionNum – 1) Mod 6 < 3. SolutionNum goes from 1-96 so this eliminates solutions 4-6 in each group of 6.

Thorleif summarize:
It works fine. so I tried a few things, Nothing great.
But one seem to be interesting. 066-57 = 066-60




I dont have a Spotted SOMA, and I'm on vacation in my caravan while writing this. But I have a "DBOX" set of 40 cubes,
So I built myself a SOMA set, and placed cuts of "Pose-it's" as white spots.
Read about DBOX here:
Newsletter 2011.10.06 DBOX a fun way to SOMA by Thorleif Bundgaard

Here we see the 6 sides as (X=red, O=White)

OXO XXX XXX XXX OOO OOO
XXX OXX OXO OOO OXO OOO
OXO OOX OXO OOO OOO OOX

Showing: | + |◥| T | ▔ | · |  .|

Or as a 3D drawing.



Thorleif:
By the way. How do the faces in our table connect to each other ?
Well: The faces are ordered Left, Front, Right, Back, Top, Bottom"
So, let's see how they are connected. (For the solution nr. 066-57)
OXO XXX XXX XXX OOO OOO
XXX OXX OXO OOO OXO OOO
OXO OOX OXO OOO OOO OOX
Lef Fro Rig Bac Top Bot

Will join sides like this (Top and Bottom attach to Front, to form the figure shown in 3D above.)

    OOO
    OXO
    OOO
OXO XXX XXX XXX
XXX OXX OXO OOO
OXO OOX OXO OOO
    OOO
    OOO
    OOX

If we now look in the Solving programs, file "[Solutions to 480 figures].txt" we find the solution 066.
/SOMA066
/772/762/422
/755/466/436
/115/415/333
Remember that THIS representation, is our standard way of showing the Top layer first, and the Bottom layer last. The solution Top is the same as the side named Top, in the 6 side list.
Now, lets see (In general) which piece contributes to the 6 visible sides of the cube.
This solution.
/ABC/JKL/STU
/DEF/MNO/VWX
/GHI/PQR/YZ-

Will give these sides

ADG GHI IFC CBA ABC YZ-
JMP PQR ROL LKJ DEF VWX
SVY YZ- -XU UTS GHI STU

For our figure that means:

/SOMA066 (Solution)         Show these 6 sides.
/772/762/422             771 115 552 277 772 333
/755/466/436             744 415 562 267 755 436
/115/415/333             443 333 362 224 115 422
Top Mid Bot              Lef Fro Rig Bac Top Bot

Now, that was Not complicated, was it? .. No I did'nt think so. ;-)

Bob's method:
I built a few figures and found the easiest way for me is to just put the pieces in any way to make the figure from the SOMA format, (top, middle and bottom slices) and then look at the faces to see where there are errors.
These are corrected by just carefully removing the piece giving the error and rotating it to it's other orientation (or 3 orientations for piece #7).


Mike Beeler enter the scene:
Bob, I wrote to Thorleif Bundgaard about some Soma work I am doing, and he suggested that I might contact you because you are also working on the Spotted Soma that Theo Geerinck has.


Thorleif - A question came up, if we are sure about the 'P' pieces rotation:
Great to hear your thoughts about the solutions.
Regarding the "P" piece you are quite correct about the ambiguity.
Back in 2016 I wrote to Theo. Part of that mail is here:
Date 2016-08-25 21:25
Hi Theo
.............
But by a strance chance, all your photos of piece "P" are either showing the inner colors or the outer colors.
So, I know both the outside and the inside. But I do not know which of the three possible rotations we have.

Take a look at my attached drawing.
Piece P
Which P is correct.

Showing the known inside, and then rotating it in two steps to show the outside (in gray)
As I know the outside constellation, it boils down to the question.
IF all upward faces are red dotted, do we then see figure K, L or M ?
----------------------------------------------------------------
Hi Thorleif,
No doubt we see K!
ALL the best,
Theo

----------------------------------------------------------------

So - The answer resulted in the spot positions shown on the web.

Theo comments on the findings:
Although these are nice patterns on the sides it seems very unlikely this is the goal intended by the designer, because it is hard to describe (other than through a picture) and does not feel "satisfactory".
But I admire you for all the work done and the determination shown.
It is strange that a "mass"-produced puzzle is so little known.
All the best,

Thorleif:
Yes you are right.
We are not "quite" happy about it, but it is the only one that seem pleasing on all sides.

The method we use is that:
We have a total of about 46000 possible solutions of the SOMA cube, taking into respect the various rotations of all pieces.

These solutions are then sendt through a graphical search program, that scan the 6 sides of the cube for a series of patterns that we describe.
Including their rotations, and including that search patterns may be "red on white" or "white on red" (Remember that with only 3x3 dots. The H looks like : or like I )
The patterns we have scanned for can be seen in a "Scores" file.

Generally we don't believe in letters, the only real visible ones being "T, I H, U C, X, |". But they are tried of course.
This points towards inclusion of a graphical solution of maybe '+', '-', '_', '/', 'triangle', 'whole side white or red', 'a single dot in center' OR something like that.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Bob Nungester writes to us all, Thorleif Bundgaard, Theo Geerinck, Mike Beeler
I agree with Mike that there is no "good" solution with the spotted Soma pieces making a cube.
With the 480 cube solutions (including reflections) and 48 combinations of piece rotations (piece #6 is identical in both its placements) there are 23,040 sets of faces to search through. We now have those in a file, but every type of pattern we search for only comes up with a few faces showing anything meaningful, and never in combination with each other.

I'm wondering if it was intended to make a different figure, such as a company's logo on one of the relatively flat figures (like 006, 007, 011 on Thorleif's site), or one that looks somewhat like a building (008, 021, etc.). Most of those only have a few solutions, other than rotating the spotted pieces, so I tried some of them manually and couldn't come up with any good solutions there either.

Spotted Soma must have some figure/solution that makes sense, but with the thousands of possible figures I don't think we'll ever be able to find it without more information.

I think I'm going to give up on it at this point, but I hope someone eventually solves it.


An alternative ?

Mike Beeler finds "An Optional Solution":
Like Bob, I am done looking for solutions that the maker of Spotted Soma might have intended.
However, I found one that, to me, looks a little more likely than others. It is shown below.

In favor of this one is that the goal is simple to state:Every face shows six white spots.
Also in favor is that it is easy to see whether a solution meets this goal. And the solution is unique.

But against this being the goal, is that the faces do not all show any interesting pattern, such as symmetry.

Thorleif comments: This will be an extremely difficult solution to seek, as there will be no clues in the sides telling if at least one side is ok.
Unless the puzzler is "really hardcore", I doubt that finding this pattern is possible without a computer.


This solution has the maximum number of white spots, 36, but 226 other solutions also have that.
The diagrams of the faces are shown here:
Solution # 9908 of 23040 in Mike's test-
     Top
Left Front Right Back
     Bottom

    OOX                LVV
    OXO                LVP
    XOO                LPP            Top Mid Bot
OOX OXX OXO OOX    LLL LPP PPV VVL    LVV LBB AAB
OOO OOO XOO OXO    LAZ ZZP PZB BBL    LVP AZZ ATB
XXO OOX OXO OXO    AAT TTT TBB BAA    LPP ZZP TTT
    OOO                TTT             f r o n t
    OOX                ATB
    OXX                AAB
Here's the data from Bob's solution files.
CondensedSolutions.txt           [Solutions to 480 figures].txt
086-69                           /SOMA086
OOX OXX OXO OOX OOX OOO          /211/266/556
OOO OOO XOO OXO OXO OOX          /217/544/536
XXO OOX OXO OXO XOO OXX          /277/447/333

Mike's 6+3 solution



Here are Theos photo's, of Mike's 6+3 solution, for the "Spotted SOMA"





   Some Conclusion   

So: 2½ month after Bob started the search.
Our suggestion for a solution to the 'Spotted' SOMA is:
Back to the mail text [HERE].

Do note that there is also a special (Non gaphical) "6+3 solution", found by Mike Beeler. [Check it HERE].

Bob's program.
We found the solutions using this program from Bob Nungester
The scoring program will run without an install program since it runs OK on Bob's Windows 10 computer which doesn't have VB6 installed on it.
Download here: N080427SpotTool.zip

The scoring program can be put in any directory and it needs the Solutions.txt file (the 46,080 solutions) and Scores.txt (any number of scoring face descriptions and their scores) in the same directory.
ScoreSolutions.exe The program scanning for solutions.
CondensedSolutions.txt file of cube solutions that's ½ the size (23040 solutions) of the table.
Scores.txt Text file with the patterns we are searching for. You may change this file to your own patterns.
SortedScores.txt The resulting solutions, sorted. Generated as UNICODE txt

[A visual list of Scores].png An image showing the scores we have searched (red) and some possible ideas (Orange)
[Solutions to 480 figures].txt A list of how to build each solution.
The user interface is very simple. It just has a Run button and only takes a few seconds to run.
It generates a file named SortedScores.txt (The text in this file is in UNICODE) that contains the first 100 solutions with the highest scores.

The Spotted SOMA Solution.
The final 'Spotted' solution, we think consist of | + |◥| T | ▔ | · |  .|
The trick is to make each of the figure sides, to hold one of the 6 shapes.


Soma
| + | · |◥|
Soma
| T |  .| ▔ |



If it still gives you trouble, then here is a complete "How To" description.

/SOMA 066-57 from the "480 output.htm"
/772/762/422
/755/466/436
/115/415/333

Step by step
Spotted solution

Start by arranging the 7 pieces as in the top left, Then assemble one by one.




Ps. I just got this idea.
From Bob I know that it can not be a line requiring that all visible parts of a cube are the same color.
But what if the solution is some "Meandering line", that folds around the cube.?
I haven't tested it, but take a look at the following (Note. It's Pure fantasy)
    OXO
    OXX
    OOX
OXX XXX OOO OXO
OXO OXO OXX XXO
OXO OXX XXO OXO
    OXO
    XXX
    OXO
Just an idea - NOT Tested

It probably won't give anything, but then again you never know ?


Lines:
Oh yes, now we are at the subject of a Meandering line.
On the web back in 2015, I once stumbled across this different version of SOMA.
Giving you another way of having a line around the assembled cube.

The picture is from puzzlewillbeplayed.com/333/SomaLine/
Design and Copyright: Naoyuki Iwase
A line on SOMA

Note that this Japanese version use a letter notation that differs from this Website.




Submitted by Theo Geerinck
Processed by Bob Nungester
Comments by Mike Beeler
Edited by Thorleif Bundgaard <thorleif@fam-bundgaard.dk>

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