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If I’ve found all the different ways to cut the cube, and calculated the number of even-sided and odd-sided faces correctly, this code should give the answer. Ideally I’d like the program to calculate the different slices and enumerate the faces, but that will be more work. On the plus side, it only takes 34ms to run.

Solution:You started with 4 cubes.If I have counted the correct number (not guaranteed) of even and odd faces from these diagrams: