That brings to mind a "simple" puzzle that a roommate bought in 1976 while I was attending a school in California. I think is was a 5x5 grid of tiles, each tile divided in quarters with the quarters filled with a solid color. You had to place the tiles in the grid so that all the edges matched the adjacent tiles.
Simple enough, and you could always work your way fairly quickly down to a few tiles that didn't match, so swap pieces around and keep trying.
I looked at the box and it said, as far as they know, there was only one solution.
I looked at the puzzle, then looked at the person who bought it, and said I wouldn't even bother trying to play with it. It seemed extremely pointless to me.
He wondered why, so I told him the box says there is only one solution. and since many of the tile edges easily match other tile edges, the chances of getting the solution was astronomical, and a waste of time.
I said if there is only one solution, then the first tile you pick has to the right tile (1 chance in 25) and has to be in the right orientation (1 in 4), so you have a 1 in 100 chance of placing the first tile correctly, and of course you don't know if you did. Now you have to place the second tile, and there are quite a few tiles that will match, and in possible different orientations, so you have to multiply the number of matches times your original 100 to figure out the chance of getting two tiles placed correctly, and of course you don't know if they are.
Carrying on to the third, then fourth, etc... there could be billions of combinations (or more), so you could spend the rest of your life messing with that puzzle to try to hit the solution.
Of course, now that we have computers readily available, it could be an interesting programming exercise, so writing a program to solve the puzzle could be fun, but solving the puzzle manually was not something I even wanted to try as it seemed utterly pointless.
