My parents have a similar 3×3×3 puzzle, that they couldn't remember how to solve, so most times someone visited them and had a go at it, the puzzle would be left in pieces until I next visited and put it back together. One Christmas I wrote a similar solver in Python and found there were 16 solutions, only a few of which I had found (though most I had seen only once). I printed out diagrams for each solution made with Matplotlib, so now the puzzle can always be put back together. My grandmother had a different 3×3×3 one that turned out to have something like 100-200 solutions.