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i think i figured it out. I am gonna use a 2D array implementation of a graph making it 36 by 36 since there are 36 total sides. Then fill out a 0 if those 2 sides match and a 1 if those 2 sides dont match. Then traverse the graph finding all combinations with a 0 as the value and those are the sides that have to be matched up. Also, i am switching to C++ because i have some graph comparisons in C++ before.
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