The "jigsaw" is to consist of eight pieces arranged into a 4x4x4 cube. Each piece is a polycube made of eight 1x1x1 cubes glued together in some way (up to you how you do this). The eight pieces must all be different and WPRU has told you that you must make a puzzle with as few solutions as possible.
- Is it possible to make a 4x4x4 jigsaw out of eight distinct pieces?
- If so, what's the minimum number of solutions (ignoring rotations)?
- And how many sets of eight pieces achieve that minimum number?
PS: to PE dev team: I've not even thought this one through myself so am not seriously proposing it as a problem candidate; but you'd be welcome to grab it if you can see any potential. Probably much too hard/fiddly for PE.