#1: MrsThing (MrsThing) on Jul 11, 2009

I have trouble rating a puzzle's solvability. Where does one draw the line between guessing and testing? One could argue that any test starts with a guess. Someone else could argue that any puzzle, no matter how illogical the solution may be, can be solved by testing. This is a gray area for me.

Unfortunately, you are not alone. This topic has been discussed to death in previous forums, and in the comments section of a few puzzles. That is why there are options for you to choose from. If you feel you had to guess, then mark it as guessing required (either a little or a lot). Jan has the final say, though, and will often override the vote of many solvers.

This question causes a lot of people trouble, because "logical" isn't really exactly the right word for it, and because the line isn't 100% crisp. Yet I think the distinction is vitally important, and makes the difference between a good puzzle and a bad one.

So here's a couple different explanations for what I mean by "logically solvable" on this site:

(1) A "logically solvable" puzzle is one that you could do in ink.

(2) A "logically solvable" puzzle is one that could be solved by techniques described in the "Advanced Puzzle Solving Techniques" page and similar techniques.

(3) A "logically solvable" puzzle is one where you could verbally explain why every cell you mark MUST be that color by an explanation that is not more than a sentence or three long.

(4) All puzzle solving requires some "proof by contradiction " things, where you say "if this cell was marked black, then this would happen and that would be impossible, so it must be white", and this is in a sense guessing. This kind of guessing that we don't want in a "logically solvable" puzzle is the sort where the chain of consequences between the guess and the contradiction is so long that the only way a normal human could work it out would be by marking it on the puzzle, and then undoing back to the guess point. Guesses whose consequences you can work out in your head are fine. Guesses that need to be worked out on the puzzle grid are not.

Adam and Jon, Thanks for the feedback.

Jan, your explanation is one that feels comfortable to me, a mathematician and software tester. I find that long strings of layers of guesses lead to trouble when the UNDOs get confused and (out of sequence) start changing parts of the puzzle that I already had solved. (I suspect this has to do with embedding some UNDOs within the test sequence.)

I have resorted to keeping a text window open and recording each of my nested hypotheses. When I reach an absurdity, I back out through my nest, ruling out each hypothesis after I have tried all logical branches. This works ok in an obsessive-compulsive way. If I'm not in the right mood, I can get crabby.

I prefer the pristine beauty of the logically solvable puzzles.

Thanks for the website. Your efforts are appreciated by so many people.

In terms a mathematician would understand, I think the distinction we're trying to make with this is more like "an elegant proof" than "a logical proof". There are theorems that have only been proven by having a computer exhaustively analyze thousands of cases, but nobody loves those proofs. So I've considered calling this "elegantly solvable" instead of "logically solvable" but I don't think that would cause much less confusion.

Well said.

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