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.<p>Here are a few pictures: http://imgur.com/a/nxA4Y<p>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?<p>---<p>There are 12 nodes in total and here are the pairings of these cubes:<p>(3,3,), (3,3), (3,2), (2,2), (2,3), (3,3), (3,2), (2,3), (3,3), (3,2), (2,2), (2,3)