
SOMA News 
20 Dec 2020
EMail. 
The 7 SOMAPieces
can be combined to the cube
in over 100 Ways.
If you switch a Piece
in one SOMApuzzle with one
in another, ie. Nr.4 with Nr.7,
just not Nr1, you may still
always build the Cube.SOMA can be played by
two or more. You start
simultaneously building the same
Figure with separate SOMA
Games, or exchange a Piece
and build the Cube.
The one, finishing
first, has won
The TradeGame.xls file analyzes the SOMA game of two players trading a single piece to form two nonstandard sets.
Using the Double Solver program and the Unique Solutions program
I analyzed each of the 30 possible nonstandard sets to see how many cube solutions are possible with each set.
The number of solutions varies greatly from only 13 (no piece 2, extra piece 4) E5:
up to 849 (no piece 5 or 6, extra piece 2) C8 or C9:.
In any game the two sets are complementary, so the second table in the spreadsheet shows the ratio of
solutions for these two sets.
For example, the set with no piece 7 and an extra piece 2 C10: has 635/18 = 35.28 times as many solutions
as the set with no piece 2 and an extra piece 7 H5:.
These tables show the best piece for the first player to give up is piece 7 since more solutions are
available than the other player's set regardless of which piece they trade back.
Piece 2 should never be given up since the other player will have from 935 times more solutions available.
Swapping piece 5 for piece 6 is interesting since the two sets are mirror images of each other.
That means they both have an identical number of solutions.
The cell formulas in the lower part are the divisions. D17=D5/C6 C18=C6/D5 and E17=E5/C7 C19=C7/E5 etc.
The file, WinningWays.xls shows the number of solutions where each piece is in each of its possible positions.
These numbers can be derived from the solver program, or directly from an analysis of the SOMATYPE of each solution on the SOMAP.
A lot more about examining the SOMAP is found Here.
The cell formulas of row 10 are "Total =SUM(B5:B8) =SUM(C5:C8) etc.
In column F [5,6*] the pieces 5 and 6 are reflections of each other instead of reflections of themselves,
so occurrences of each can't be separated from the total of both.