Have you ever thought about what the ultimate jigsaw puzzle would look like? At a certain level of complexity, puzzles based on static images all seem to become indistinguishably different. Whether it’s a closeup of a plate of baked beans or an image of the cut lines on the back of a jigsaw, recut into a different jigsaw…or whatever.
I hate solving jigsaws only slightly less than watching someone else work on one, but designing the ultimate puzzle is still something I’m thinking about.
Anyway, on a related theme, Rubik’s cube is both mechanically ingenious and a challenging puzzle…two things I greatly admire. I lost interest in it when they started having robots undertake the solution algorithm and it became just a wrist exercise.
There are now versions of the original cube which contain some lights, but today’s invention is to improve on these by fitting each of the square facets with an LED (and no sticky coloured squares). The lighting behaviour would be programmable, so that it would be possible to challenge your smartest friends with a cube algorithm whose target end state was, for example, that in which the lights on the cube faces mirror the colours on the conventional cube.
The difference with this design would be, though, that the lights would be free to switch colours, depending eg on the colours of their neighbours. This could be made fiendishly difficult and keep any computer scientists you know completely absorbed and thus out of trouble when away from their workstations.
Imagine believing that you were one move away from completion, only to have the colours then change, under algorithmic control, on a far-side facet ; )