Eternity Puzzle, Part 5

This puzzle has about a gazillion combinations, only one of which is the correct solution, so unless you get really lucky, you are not going to solve it. The odds are worse than the lottery.

To avoid spending a bunch of money, I generated a random puzzle, and used the tiles from that as input for my solver. I figure if I can come up with a scheme to solve a random puzzle, then I might have a chance with the real puzzle. I changed the reporting scheme so now it only issues a report every 10 million tiles, which is about every three seconds.

Anyway, it's one thing to say there are a gazillion combinations, it's another thing to sit and watch this program try a billion combinations a minute and not make any progress. It's been running for a couple of days now and it hasn't gotten past the 16th tile, and there are 256 tiles in the puzzle. And it's not like it's going to suddenly start making progress. It was up to 16 tiles in the first minute. That's how far it can get before it can't find another matching tile, and it starts backing off and retrying, again and again and again ...

There are a thousand edges (256 tiles times 4 sides). There are ten colors. Ten is just an arbitrary number I picked. Each time we place a tile we have two known edges we have to match against. (We start in the corner with two known edges and then work our way up the side, over the top, then down, spiralling ever closer to the center.) One known edge cuts the number of possible tiles to 100 (1/10th of 1000), two edges cuts it down to about 10 (divide by ten again). So for each spot on the board, there are ten possible tiles. Ten million is 10^7 (ten to the seventh power). Every three seconds (ten million trials) we see the most recent seven tile id numbers change. Hmmph. Imagine that.

I should put it away now and move on to other things. We'll see how that works. There are a couple of other tricks I could try ...