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Numbers in (red) are total solutions possible for that shape.
The checkerboard!
1 x 8 x 8 (76)
This started my quest back in the 1970's to design a puzzle to not only make the checkerboard puzzle out of wood but also to make a cube out of the same pieces – and all the other shapes that followed. It would have been nice to get all 64 permutations done but with the piece shapes I played around with I could find only 54. Perhaps CalmPlex II … Here is one solution using two 1x4x8's and a real challenge would be to form the checkerboard fully interlocking – no sub shapes.
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