meta puzzle

Arrangements, sorting, packing, partitions, critical path analysis, networks, graphs, ...
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ed_r
Posts: 1009
Joined: Sun Jul 29, 2007 10:57 am

meta puzzle

Post by ed_r »

You're hired by Wooden Puzzles R Us (WPRU) for the job of creating a new 3D jigsaw.

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.

The challenge:
  • 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?
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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.
!647 = &8FDF4C

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stijn263
Posts: 1505
Joined: Sat Sep 15, 2007 11:57 pm
Location: Netherlands

Re: meta puzzle

Post by stijn263 »

i think i've seen this question before. if i remember it right there's more than one set that optains the minimum. i'll see if i can find question and answer. before looking into it myself i want to solve problem 161 first though ;-)

again an interesting problem ed :)

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