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Originally Posted by imcalledtyler05
Does the puzzle usually include repeated shapes on the higher difficulties, because if they do, you might be able to reduce the time needed to find a solution by removing a pair and the running the algorithm(s) to see if the puzzle can be solved and just place the repeated shapes on top of eachother. In your example, it could reduce the possibilites to a twelve-thousanth of the number of possibilities you would get if you ran your original algorithm. Though I suppose that would only be for a special case.
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I did think of that. While it's not exactly common, it's far from uncommon...
However, you'll notice that, in the puzzle, there are three states and not just two. So, you would need
three similar shapes for your suggestion to make sense. Furthermore, if you think about the likely implementation of the puzzle generator, you'll see that it's exceedingly unlikely that the similar shapes are placed over each other in the final solution...