# Solving an Interlacing Cords puzzle inside a Truncated Octahedron

My friend got me this really interesting puzzle

Each node can be slided or docked around the Truncated Octahedron, creating knots and tangles in the middle of the puzzle. The idea is to move the nodes around until there's a bunch of knots and then unravel the knots.

To solve this puzzle, you need to following conditions

• No cords can be touching, interlacing or tangled.
• Each face must contain nodes of the same color.
• The opposite of a face must contain nodes of the same color.

This got me wondering, how would a problem like this be modelled in order have it solved by a computer?

• This is an extremely broad question. The short answer is that you store enough information to represent the current state of the puzzle and allow all the operations on that information that correspond to "moves" in the puzzle. – David Richerby Nov 19 '14 at 22:37
• @DavidRicherby I think this is fair as a modelling question: what information? How do you approach this knotty things at all? – Raphael Nov 20 '14 at 10:13
• I tried looking for similar problems (Solving Knots with a computer) but haven't found any substantial work done on the subject. Even if I were to naively solve this problem, how would you represent knots, cords and positions? – Alexandre Nov 20 '14 at 17:00
• I would represent knots and cords with polygonal chains, and I would $\hspace{1.91 in}$ represent positions with rational coordinates. $\;$ – user12859 Nov 21 '14 at 2:26