This brings up something you said in the article. You wrote:

“Since I know the puzzle has already been found to have one, and only one solution, I know that if making a particular decision (such as marking a particular edge in Slitherlink) will result in two equally valid solutions that don’t affect the rest of the puzzle, I can assume that candidate decision is invalid. When the computer is testing puzzles for validity, it can’t use this “meta” technique.”

While I have used that method on particularly tough puzzles, I have always felt like it is cheating a little. I prefer to do the puzzles as if I am confirming that there is one and only one solution. (I would not have caught the problem above if I had used this meta technique because the new path generates TWO new solutions!)

But even beyond this meta technique, I hate to guess when I get near the end. While I can often figure out a path that will work just by looking at the puzzle, I prefer to only use logic so that I know that it is the ONLY path that will work.

That’s just me though. It probably comes from my background doing mathematical proofs.

-David

The third slitherlink puzzle on that site (and perhaps the second also) do not have unique solutions though! I’m very surprised by this, but I have checked my work many times now. I could send you a pdf of two alternate solutions if you’re interested.

The solutions differ at the very top of the puzzle. There are two 1’s at the top in the center. My two alternate solutions have the line passing the left 1 along its southeast side, rather than its northeast side. This then forces a small change around the 2 to that 1’s southwest….and then allows for the line to continue in two different ways to the 2 to its left. When you include the solution that you gave, this makes three solutions in total.

I’m very curious how this could happen. …and if there is a problem with your program, why wouldn’t this be more common? (I’ve done at least 50 of your slitherlink puzzles).

Thanks for the puzzles.

-David