Imagine that you have a cube skeleton, like so:
Further imagine that you have three rubber bands that you can loop through any of the faces. However, only one rubber band may go through any particular face at any time. In addition, all 6 faces must be occupied, although any number of rubber bands may be used. I have found 16 solutions, not counting reflections and rotations.
Well...did I get all of the solutions? Also, how would I go about this analytically, preferably with graph theory?