Boolean Tumble Solution: Is there a way to calculate a board layout for a given input and output with some kind of math?
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There’s only so many boards, so a program can run through every possible board and see if any of them work.
But I don’t think what you’re asking is possible if you don’t limit the size of the board or the number of balls. I don’t know how to explain it, but I know how the Halting Problem, something closely related works. Perhaps you should look it up.
https://en.wikipedia.org/wiki/Halting_problem
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You could figure out how to make gates and then use boolean algebra to simplify a given truth table.
https://www.youtube.com/watch?v=kh1jlQD252Y
You could then use the Turing Tumble gates you made to assemble the given equation with TT