SOMA News 4 september 2020 ✉ E-Mail Ps: This page hold 3 hidden links ⊂ ⫓ ☯

SOMA in Red, White and Blue.

The findings of Bob Nungester.

"Is it possible to form a cube, Paint the outside of the cube, and then reassemble the cube, to have no paint visible?"
Well, it is not. but another question was posed on the front page 2019-12-22 by Paul Habere.

"Is it possible to assemble a cube of all white pieces, color two opposing faces, and then reassemble the cube, to have no paint visible?"
I assued this question would wait a long time, but already 2 days later, Bob nungester responded with a pretty answer
"Yes, it is possible There are 3 possible ways to color the SOMA cube, and and then hide the colors."

The question about painting two opposing sides of a SOMA cube and then hiding the painted squares in another cube solution at first seems too difficult to solve.
After some analysis it turns out there are several very restrictive rules that eliminate most of the 240 solutions to the cube.

Can you solve one of those two color cubes. ?

Now this could have been the end of that question, were it not for the persistance of Bob. Who continued the quest with a further question.

As Bob Nungester wrote on 2020-04-23

I finished analyzing Painted SOMA, including painting three faces. And making an updated spreadsheet showing all two-face and three-face solutions that can be painted and hidden.
I wasn't going to send an email until I had written the draft of a Newsletter, but the analysis of three painted faces brought up a truly unique puzzle.

It turns out one of the painted three-face solutions can be hidden in another painted 3-face solution. The two solutions are hidden in each other!
What this means is that the cube can be painted so it's possible to put it together with three painted faces of one color (such as Blue) or with three painted faces of another color (such as Red).
Other faces are the unpainted original color (such as White).

This is the only coloring pattern that works in this way, and there is only one solution that shows three painted faces of Blue and only one that shows three painted faces of Red!
This is a very difficult problem to solve and would make a good puzzle to actually produce.

Bob continued: I'm going to paint a wooden SOMA cube I have, but today I created a prototype to make sure it works.
Starting with a red cube, I used blue tape to simulate one painted color and blue tape with a black X on it to simulate the other painted color.

 One thing though - Bob initially uses a red SOMA set, with strips of blue tape and a black marker. But more logical, as Bob live in USA the colors should be a White cube with Red and Blue faces on its pieces. Which is what Bob finally did. (I have changed the initial text to reflect this.) By the way that color combination is also used in flags of other countries like France, United Kingdom, Russia, Norway, Faroe Islands, Iceland ... Well actually 121 countries. https://en.wikipedia.org/wiki/List_of_flags_by_color_combination#White,_red,_blue

Now I will leave the words to Bob, as he tell us more about this intriguing puzzle.

Thorleif did ask if the colors could be hidden in an all white cube.?
"No. The painted pieces can't be hidden in an all-white cube. I was thinking how to prove that and I remembered there were some statistics in Spotted SOMA related to how many squares can be visible. I looked up the newsletter and it notes there are 90 squares on the seven pieces that can possibly be visible in any solution. With six painted faces (three blue and three red), that's a total of 54 painted squares. That leaves 90 - 57 = 33 possibly visible squares left to be white, which isn't enough to make an all-white cube with 54 white squares.

It's interesting that this problem didn't require any computer programming to find all the solutions. Programs were used to solve Spotted SOMA, Balancing SOMA, detailing all transitions in the SOMAP, etc. Just inspecting each of the potential solutions can solve this problem.

It turns out two of the solutions with three painted sides can be hidden in each other. This means it's possible to assemble a cube that has three painted faces of one color, and then rearrange it to have three painted faces of another color. The figures below show how to paint the pieces and the two ways the cube can be assembled. The two solutions are the only ones possible, so this is a difficult puzzle if you don't have the table.

Thorleif:
Further explanation is available, in this Newsletter, but just writing it below would be disclosing the solutions, don't you think?
A hidden key will reveal the rest.

Can you find the solution to this puzzle     Now, that we know it IS possible to solve

Thorleif:
By the way. Everything has two sides.
The great discovery in this letter, is that two completely different solutions could hide each other, just like the Yin and Yang
Sometimes I refer to such a situation as "Hidden in plain sight".
That is, everyone can see it all but never really discover the whole truth.
Just like the old method of hiding money notes within the pages of an uninteresting book on a bookshelf. Everyone can see the book, but no one opens it.
Actually - this newsletter hold three hidden keys that will expand the information.