Taking an Artistic Approach to MathWorking to sort through the 240 unique solutions of the SOMA puzzle. My theory is an elaboration of work by others that is is summarized nicely in the last paragraph here:
My method is to treat the problem as "not a problem." The SOMA cube pieces are beautiful objects so why not make many of them and treat them as a the medium for math based sculpture. I discovered that 1" x 12" x 48" pine board rips and cross cuts into lots of 3/4" cubes. The cubes are glue into the seven SOMA pieces and then colored with food coloring.
With lots of cubes visualizing the variety of solutions that can grow.
I worked through the 42 seedlings and discovered that I was coming up with more than 240 solutions. Reviewing previous work on sorted solutions:
I discovered that 42 is not (this time) the answer to the life the universe . . . everything
Interesting patterns emerge nonetheless showing the similarities of many solutions.
I think this one is particularly beautiful growing from what I originally considered to be Branch 4.
I call it "Triplets Two Twins and Twisted Sister."