Is that really the theoretically smallest?
I think you can prove that some states representable by your proposal are unreachable. E.g. a board with 16 2s. So there might be another bit to spare.
I think you can prove that some states representable by your proposal are unreachable. E.g. a board with 16 2s. So there might be another bit to spare.
But whether that is practical is a different matter. It does allow you to unambiguously define state #5546335 with the lowest number of bits