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

9 points

11 years ago

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)

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