On fiddling with things and getting in knots - Christmas Puzzles 3

This is the third of three posts on work-related thoughts I had whilst puzzling at Christmas time.

I was given this puzzle over Christmas. The object is to disentangle both steel rings. It's the hardest one of its type I have come across. It took me about three hours to work out the right sequence of (as it turned out, 18 separate) passings of one thing through another to solve it. As I did it, I thought about the parallels with puzzles at work.

I started by picking up the puzzle and fiddling with it. No analysis. I tried lots of things. I quickly learned the basic constraints of what would fit through what, but ended up in hundreds of blind and knotted alleys. As I experimented, I became more familiar with the puzzle and the consequences of the various moves. After lots more knots (but not at all by chance) I ended up with one of the rings in my hand.

It took me quite a bit more time to repeat the feat. Not wasted effort though: documenting what I was doing as I went along would have been far too hard, far too time consuming and er… daft.

Given a photograph of the puzzle, I imagine it would be possible for a mathematician to reduce the puzzle to its fundamental topology then use some sort of algorithm to work out what moves were necessary to solve it. But that also would have been daft: this is a trial and error job if ever there was.

I couldn't help thinking how much time and money has been wasted by organisations not letting their people fiddle with things and get in knots.

And, for the avoidance of doubt...