pgulley / cube_solver

Set of tools and algorithms for solving an obnoxious puzzle which has been on my desk for ages.

Paige Gulley | March 2015 | Cube Solver

Tools for solving a puzzle which has been on my desk for ages

We have a sequence of 64 wooden cubes strung together. There are 44 right-angle bends at irregular positions along this string. We want to bend the string such that it forms one 4x4 cube.

Setting this up as a search problem, going depth first.

###The constraints

Accounting for symmetry, There are 4 starting positions. We can start off in any of 6 directions, and each of the 44 bends offers 4 new possible directions. The space contains around 4^45 possibilities, or 300 quadrillion states

Its too chaotic for many optimizations, but we have a few things on our side:

• Symmetry allows for some starting positions to be ignored.
• We don't check past failure, so we can throw out whole branches as we go.
• If we need to, we can start checking for cube segmentation, which would let us throw out more dead ends (not implemented yet, though)

On my machine it runs at 1 million loops every 15 seconds, or 5.7 billion loops per day.

For some reason, the script halts after about 830 million steps, around 4 hours in. Fails to find solution. Further investigation to follow