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#1: Jan Wolter (jan) on Aug 8, 2005 [HINT]

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So when you say "By logic alone", do you mean "One line at a time"? Because I've never understood why we make a distinction between a unique solution and one that is solvable by logic alone.

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Well, my problem is that if there is a unique solution, then by definition it is solvable by logic alone. Guessing and backtracking is a form of logical reasoning. A puzzle might require me to do a lot of backtracking, but I never use anything but logic.

Of course. I should really say something like "This puzzle could be solved by someone with an ink pen and only a normal capacity for working things out in their head". Except that it's to unwieldy.

I think that's actually fairly clear what I mean because I am contrasting "logic" with "guessing". "Guessing and backtracking" is a logical procedure, but we clearly mean logic without guessing..

Well, I still object to implying that "by logic alone" means using only a certain limited form of reasoning. They sell these books in the grocery store which are titled "logic puzzles", and they're all the same kind of puzzle. I have the same objection to those - logic encompasses everything that can be deduced.

Maybe you could replace "solvable by logic alone" with "solvable without backtracking".

And also Re: #5, to me "requires guessing" means that the solution is not unique: that to solve the puzzle you have to make an arbitrary choice. Any puzzle with a unique solution does not *require* guessing - no matter how hard it is, there is some way to logically reason out the solution (in your head, if you have a big enough head), by definition.

So no, I don't think it's clear what is meant, which is why I entered #2 in the first place.

I understand your objection to the "solvable by logic alone" terminology. But I'm not happy with "solvable without backtracking". I'm not at all sure that "backtracking" is a familiar concept to the general population. "Solvable without trial-and-error" might be a bit better. Familiarity aside, I'm not sure those aren't subject to misinterpretation too. If I mentally do a proof by contradiction to figure out a square ("If that was black then blah blah blah and so it can't be black") is that "backtracking"? It all depends on how many "blahs" there are in the "blah blah blah" and how many "blahs" I can hold in my head. It's ultimately a subjective distinction.

Well, if it's subjective, what are you hoping to measure by the question?

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A puzzle from Jan that requires guessing? I thought you were a stickler for that sort of thing.

Mark, you say "to me 'requires guessing' means that the solution is not unique" but in the terminology Jan is using, the solution and the guessing are two different things. If there is only one unique solution, then there is only one way to fill in the squares to satisfy all the clues. If the puzzle is not unique, then there are multiple ways to fill in the squares that will satisfy the clues, even though the author has only deemed one of those solutions correct. A puzzle with a unique solution may or may not require guessing; a puzzle with multiple solutions will always require guessing. If the puzzle requires guessing, then I consider it not solvable by logic alone, because guessing requires little or no logic. You are solving it by trial and error. I personally (in general) hate puzzles that require guessing. When I subscribed to a logic puzzle magazine, I used to toss the puzzles that required guessing. Here, where I usually hit "random puzzle", I hit the button again when I come across a "multiple solution" or "requires much guessing" puzzle, because trial and error isn't fun to me. There's no "solving" involved in guessing.

QUESTION: How can a puzzle have a "unique solution" yet gets marked "requires some guessing"?
If it is unique then logically it must be solvable without guessing, because guessing would mean that there is more than one solution.. or maybe it just that the computer is logical & the people trying to solve it are not! who knows!

naneki... The computer isn't able to solve them either.
Try to press the Helper button. The puzzle won't be solved entirely, and that means you have to do a lot of trial and errors, and sometimes you even have to guess a lot to solve the puzzle.

If the solution is unique then there is certainly then there is certainly a "logical" procedure to find if. If nothing else, you could try every possible pattern of squares and check if each one matches the clues. Such a procedure however, is impractical for any human (and usually for any computer as well). If that was the only way to attack these puzzle, it would be completely hopeless.

Luckily there are a lot of tricks that allow us to solve puzzles step-by-step, instead of in one fell swoop. But the existence of a unique solution does not guarantee the existence of an easy step-by-step solution leading to it. That's what I'm trying to get at with the "logical solution" business.

The fuzziness in the definition comes from the question of what kind of steps we allow. Certainly we allow the traditional kind of line solving steps, where we look at one row or column at a time, compare the currently filled in pattern to the clues, and fill in a few more cells based on that.

A slightly more complex step used in multiple color puzzles involves looking simultaneously at a row clue and a column clue. The row clue might tell you that a cell has to be either black or white, and the column clue might tell you the same cell must be either red or white, so you know it must be white.

Edge solving is a bit more elaborate, typically involving looking at several cells at once, but it's still something that can be done in ones head. If someone challenged you to explain why you filled in that cell, you could explain in a couple sentences.

Occasionally other more elaborate bits of reasoning can be used, where you can show that filling in a given cell a given way would lead to a contradiction just a couple steps down the row. Finding such arguments is hard, but I consider it fair game.

What I consider over the line is when you have to go further to find a contradiction. You guess the color a cell, work from there, find a contradiction, then UNDO your way back to your guess, reverse it, and consider the reversed guess to be logically proved. Well it is, but I don't think that a well designed puzzle should require the solver to undertake brainless exhaustive searches like that. A good puzzle should be solvable by cleverness, not by a stupid trial and error procedure.

Neither of the puzzle solving programs on this site are good a measuring this. The "checker" build into the puzzle editor does line solving and color solving as far as it can, and then does exactly the trial and error procedure I described if it gets stuck. If the line and color solving solve the whole puzzle, it declares it as "logically solvable". If not, it says it doesn't know if it is logically solvable. This is because it's line solving isn't as smart as a human's and it doesn't know all the other kinds of tricks, like edge solving, that humans can apply. So many of the puzzles the "checker" can solve only be trial-and-error, a smart human can solve without resorting to that method.

The "helper" that is built into the puzzle solving environment is much dumber. It only has the half-backed line solving capability, no color-solving nor trial and error. There are many, many perfectly solvable puzzles it can't do much with.

what I mean is: lets say you create a puzzle, the computer says it has a "unique solution", so you post it...then someone tries to solve it & they mark "requires guessing" So in this case who is more logical, the one solving it or the computer? I used to avoid require guessing puzzles until I realized that just because someone marks it "requires guessing" thats not necessarily true, I have found that I can most the times solve it logically where others can't.

In theory someone eventually makes a ruling on whether or not a puzzle really "requires guessing". That someone is supposed to be me, but these days there are way more puzzles than I have time to solve. I should enable other folks to help out on that.

So this is a long-running debate here on the PBN... "brainless exhaustive searches"-- I like the way you put that, Jan. I object to that as well. But, I don't see this particular puzzle as requiring a brainless exhaustive search.

It was solvable. No guessing required. Logic is good, whereas trial-and-errror (or guessing) has no place here.

I solved it with logic alone - pretty easily, too. Don't know what all the fuss is about.

Most of this discussion is more about the general question of what "logical solvability" means than about this particular puzzle.

Also this puzzle is old enough that I wasn't all that great a solver when I first made it. So I didn't really know all the logic tricks I know today. I'd certainly call this "logically solvable" today. My standards have shifted as I've become a more sophisticated puzzle solver.

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Found to be logically solvable by jan.

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Jan ...like the puz and the conversation, learned alot..
question ...can anyone mark a check by your puzzle?

The conversation about "logical solvability" above is one of the older instances of that conversation on this site. Our collective thinking on this has evolved a lot over the years.

I don't understand your question.

Jan... i just found this forum thing... so late at re-replying
I meant can only an offical like you make a check mark?

The only check marks by puzzles that I can think of are the ones that appear on puzzle searches to mark the puzzles that you have already solved. I'm guessing that that's not what you are talking about, so I guess I still don't understand your question.

Tom - when you say "check mark", are you referring to the question mark that will show up next to puzzles sometimes?

sorry y'all.... meant ? and thanks for getting back to me
i love your site, Jan

A puzzle than can be solved with line/color logic (as checked by pbnsolve) is automatically marked as solvable by logic. A puzzle that requires more advanced techniques such as smile, edge, or two-way logic are initially set to "unknown" basically. People that play a puzzle can vote on whether they think the puzzle is solvable with logic. If the average (not sure on the mechanism of how the average works) of the votes comes out as "guessing", then the puzzle with get a "?".

Jan and I can override the votes and mark a puzzle as solvable (or requires guessing if it does).

cool, thanks for expl.

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I solved it with line logic alone until the tip of the finger, which then used smile logic.

As Jan mentions in the comments, it is really interesting to see old conversations about solve difficulty. In other threads it has been outright said how much better (more advanced) this community as a whole has gotten over the years. It has been an amazing journey!

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