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Puzzle HN: Can you please help us mathematically solve a puzzle?

9 points by todayiamme ↗ HN
I encountered a very simple puzzle that has very interesting ramifications. The puzzle consists of a set of cubes grouped in 3s or 2s that are linked together in a staggered fashion with elastic. We are meant to collapse these cubes into a 3 by 3 larger cube.

Here are a few pictures: http://imgur.com/a/nxA4Y

Now we know the brute-force way to do it, but I'm wondering if there's a mathematical solution to this problem that can predict the exact sequence of folds required. Is there some way for us to derive this?

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There are 12 nodes in total and here are the pairings of these cubes:

(3,3,), (3,3), (3,2), (2,2), (2,3), (3,3), (3,2), (2,3), (3,3), (3,2), (2,2), (2,3)

10 comments

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pixl8ed
http://www.mathematische-basteleien.de/snakecube.htm

http://stackoverflow.com/questions/11622068/snake-cube-puzzl...

todayiamme
Thanks for the solution! I was hoping for a more algebraic solution as opposed to an iterative one. Is there a way to know if an algebraic solution - if any exists for this problem? And if it does, how can I find it? Because expanding upon nodes and checking every branch is still a form of brute forcing the problem. I'm wondering if there is some elegant solution to this.
317070
The green blocks have 14 possible locations. If you start at both the left and right end and look how those structures can fit, it simplifies the problem significantly.
Constantskeptik
This is very similar to a math puzzle I have. there are 12 solutions, but it appears you have them linked in a chain. This is a famous problem.
Constantskeptik
This is a quick wiki search "The puzzle was created by Franz Owen Armbruster, also known as Frank Armbruster and published by Parker Brothers in 1967. Over 12 million puzzles were sold. The puzzle is isomorphic to numerous older puzzles, among them the Katzenjammer puzzle,[3][4] patented[5] by Frederick A. Schossow in 1900, and The Great Tantalizer (circa 1940, and the most popular name prior to Instant Insanity). The puzzles use a subset of the 30 cubes devised by Percy Alexander MacMahon, but it is not known if the puzzle creators knew of MacMahon's cubes."

I have a puzzle that does indeed have 12 different possible shapes and fits together in a rectangle. You have connected the ends together as if it will be folded like oragami. Why?