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# Difference between revisions of "Sudoku/Controversies/Uniqueness/Reddit"

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This discussion became a replay of common arguments about uniqueness, I've seen in many places. See the page supra.

from sotolf2 via /r/sudoku Jan 15 2020 15:55 GMT - quoting u/Abdlomax (Abd on this wiki) Abd's original comment is in indented italic. Responses here should be further indented, in bold italic, and signed (with ~~~~) and may be refactored for clarity. --Abd (talk) 21:50, 15 January 2020 (UTC)

This has been edited to remove comments not directly related to the sudoku issues. --Abd (talk) 15:12, 16 January 2020 (UTC)

## Definition of sudoku

Who said that uniqueness is "invalid"? Certainly not me! Rather, uniqueness is based on an assumption that was not stated when Sudoku were first formally defined and published. It was still assumed, by both authors and solvers. Some books add it as an afterthought.

So where is this authorative definition? I certainly haven't seen it anywhere, and I don't really belive one exists, if we are going to treat sudoku as a logic puzzle though it will have to have a logically deducable solution, something that is not possible if there are multiple solutions.

What is published is a picture of a puzzle with
You must place digits into the grid in such a way that every row, every column, and every 3x3 box contains each of the digits 1 through 9
This, or something very similar, is in every book on sudoku I have, which is many. As well, there are dictionary definitions. I'll link to Merriam-Webster. Given that there is no contrary definition shown, I'd call that "authoritative."
As well, the definitions claim nothing about logic or "logic puzzle". Rather, "solvable with logic" is a claim made about Sudoku, and SW Solver uses computer logic to crack any Sudoku, including multiple-solution Sodoku, reporting all solutions up to 500. --Abd (talk) 21:50, 15 January 2020 (UTC)

## Is sudoku solving logic?

Can we agree that sudoku solving is logic?

Not if a puzzle has multiple solutions, if it does it will be logically unsolveable.

Counterexample given. --Abd (talk) 21:50, 15 January 2020 (UTC)

## Any answer that satisfies the rules is "valid."

Any answer that satisfies the rules of of sudoku is "valid," so it is a solution. Claiming that guessing is required is not clear thinking.

I don't think I did, I might have though, but you can't logically deduce a solution if there are two valid solutions, unless you have some extra rules.

Underneath this appears to be an assumption that solving a sodoku is finding one answer, and that if there is more than one, one must guess which it is, when if there is more than one, any answer proven valid by checking compliance with the rules still satisfies the problem presented by the puzzle. The language of finding "a solution" assumes only one. I can find "a solution" if I find two. How do I find two? With logic from the patterns in the puzzle, each proven beyond a reasonable doubt to be valid. --Abd (talk) 21:50, 15 January 2020 (UTC)

## "unsolvable without guessing

But then difficult puzzles began to be developed, considered "unsolvable without guessing." (And the language there was way cuckoo.)

I 100% agree with you in that.

Great! Let's build on that. --Abd (talk) 21:50, 15 January 2020 (UTC)

## straw man argument

Sotolf2, you are creating a straw man argument, that someone claimed uniqueness is "invalid," when what is being said is that uniqueness is based on an additional assumption, not formally stated originally.

Again, until this "original" document of sudoku holiness is somewhere I can access it and see it I might agree with you, but I will assume that a sudoku puzzle should be logically deducible, or it is no longer a logic puzzle.

I suggest looking at any Sudoku book or any dictionary. I've pointed out that unique-answer was an unstated assumption, an intention. But in this world, we do not always realize our intentions, and a puzzle created which has more than one solution is called "improper." Not "not a Sudoku." And these are solvable, that is, on can find numbers to fill in that satisfy the constraints. "Should be" is all personal judgment, not fact. And single-solution is not a requirement for logic puzzles. Again, it is normally intended. Math is a kind of logic. A math puzzle may require finding the square root of 4. Find an answer and prove it, with logic, and then use it in the puzzle and discover that you have created a paradox. The error? It is in "the." There is more than one. --Abd (talk) 21:50, 15 January 2020 (UTC)

## An assumption of uniqueness proven invalid

What I did, among other things, was to prove that the assumption of uniqueness was invalid for this puzzle. That is most clearly accomplished by showing at least two.

This is what I personally classify as a bad puzzle, just as we would classify "10 They dog ago go buy days" as a bad English sentence even though it's kind of understandable it's still not a good sentence.

I find such puzzles interesting, and "bad" is a personal reaction, not a fact. Because "proper Sudoku" is objectively defined, we can agree that such a puzzle is improper. I happen to like some kinds of impropriety, in general. It's a personal choice; in general I recommend noticing such reactions -- which is what that is -- and digging up the roots and looking at them, because there can be found much that disempowers us. It is not therefore "bad" or "wrong," but the disempowerment can be very real. --Abd (talk) 21:50, 15 January 2020 (UTC)

## u/the_gr8_n8 is solid

u/the_gr8_n8 is solid here

How so, he's assuming some kind of "Ground rules" that he still denies to supply. Also he's using rude language for no reason at all.

Using "hate" about an inanimate object is not "rude." It's rather ordinary speech. And he has not "denied to supply." That someone does not answer immediately on an internet forum is meaningless. It was not a refusal. --Abd (talk) 21:50, 15 January 2020 (UTC)

## what does "I hate" mean?

Saying that I "hate" something is not a claim that it's wrong or bad or defective by some objective standard. It's simply how I feel

"Saying that I hate muslims is not Saying that I "hate" something is not a claim that it's wrong or bad or defective by some objective standard. It's simply how I feel"

Using an analogy like that is more evidence of attachment, setting aside the incoherence, which becomes common when we are attached. --Abd (talk) 21:50, 15 January 2020 (UTC)

Phrased like that don't you see that this doesn't really hold water?

No, I don't, the opposite. Equating "I hate [ethnic group]" is socially quite rude, even if true, and if true it is creating a social problem, because a group might decide to exclude "haters." But saying "I hate [object]" is simply an expression of a personal reaction. It was not rude, at all. It implies intensity, but is commonly used even without that. It simply means "I don't like it." As I wrote next. --Abd (talk) 21:50, 15 January 2020 (UTC)

## hatred in ordinary speech can be just a feeling, not rude

Obviously, that "hatred" is weak, just a feeling that arises. I am also eager to get the candidate lists done, making them complete, and, overall, pleasure at that dominates.

Dislike and hate is not the same.

Again, the user is assuming that he has the authority to define the meaning of language. They are the same from some points of view, and different from others, which is like just about everything. In fact, "I dislike Muslims" could be almost as rude as "I hate Muslims." Depends on context. All Muslims? And all usages of uniqueness strategies? --Abd (talk) 21:50, 15 January 2020 (UTC)

## assumption of possible solution

Yes, that a sudoku has any solution is also "up in the air," meaning unproven until the solution has been demonstrated by logic from the basics. Yet I and everyone else makes that assumption, because no-solution puzzles are even rarer than multiple-solution ones.

Yeah, so why is it okay to assume that the puzzle has any solutions but not that it has a single one?

Again we see the usage of undefined terms, not used by others, as if it what they believe. "Okay." What does that mean? And who has claimed that it is "not okay" to use the assumption of single solution? Nobody said that! --Abd (talk) 21:50, 15 January 2020 (UTC)

## speed not Abd's goal

Because speed is not my goal (at all), I prefer to use uniqueness but not to depend on it. That's a preference, not some critique of uniqueness.

Yeah, I see nothing wrong about that at all, we all have preferences likes and dislikes, what I have a problem with is to claim others make "no good" assumptions, when it's a neccessity for what we all enjoy in a puzzle, that it's logically solvable.

Again, if someone made that claim, it wasn't me. "no good" was in quotes. Okay, who said it? What is enjoyable is up to the individual, it is not a quality of the puzzle itself. All sudoku are logically solvable, so claiming the "necessity" of what is inevitable is odd. Again, the assumption underneath this is that unique-solution is necessary for enjoyment, when what we enjoy is about us, not about the puzzles. I enjoy all sudoku, except I've never tried to create them (which is more or less what the blank puzzle argument is about. I did, at one point, attempt to determine the error that made a puzzle multiple-solution. That was fun, so it stands as a counterargument to the "necessity" argument. (With a BUG puzzle, any of the BUG cells becoming a Given fixes the problem.) --Abd (talk) 21:50, 15 January 2020 (UTC)

## pointing to uniqueness as-it-is interpreted as if hatred

It has happened here a number of times that if I pointed out that using uniqueness as if proof.
A fuller quote is needed here.
It has happened here a number of times that if I pointed out that using uniqueness as if proof was relying on argument from authority, and that was assumed to be "bad," and that therefore I "hated" uniqueness, all of which was straw man. It would be totally silly to hate routine reality! It is also routine reality that people make assumptions about what others mean, that are not necessarily valid. Argument from authority is considered a logical error, and errors are bad, right? Again, notice the reactive thinking. "Trial and error" is "bad," because it is "guessing" and both "guessing" and "error" are "bad."
The user actually agrees, though we have no definition of "valid." --Abd (talk) 21:50, 15 January 2020 (UTC)

I can agree that it will be wrong to use it as a proof, as it isn't really, as a shortcut to solving, like colouring or fishes or anything I don't see how it's any less valid than anything else.

Nobody has claimed that it is not "valid." Rather it has been claimed that it is a form of argument from authority, specifically from authority that is quite reliable, but not infallible. To use it or not is a personal choice. It is only "invalid" as a logical proof, but it is totally valid (i.e, completely reasonable) as a heuristic. What I've been promoting is an awareness of the difference, and of the (very small) risk, that using a uniqueness strategy can cover up the existence of additional answers or, even more rarely, break a puzzle. --Abd (talk) 21:50, 15 January 2020 (UTC)

## meaning of argument from authority

argument from authority

An arguement from authority would be to claim that someone makes an assumption based on something like someone said, like "It's not part of the original definition of sudoku" And I'm not the one claiming that.

Authority is here being confused with verifiable reality. The "original definition" was actually examples, published puzzles with rules, and they all agree. The dictionary definitions follow that and the obvious. All that was said was that uniqueness was not part of the original definition, which it wasn't. Yes, the other user and I claimed that that it wasn't, and this is verifiable and no counter-example has been asserted. It's just fact. And it is also fact -- apparently -- that it was routinely assumed that published puzzles would have only one solution. But that was an assumption based on intention, not a fact, though supported by widespread but not universal experience that all Sudoku have only one solution. What's the reality here? I don't think there is an real disagreement about it, but only a pile of "shoulds" and "likes" and "better thans." --Abd (talk) 21:50, 15 January 2020 (UTC)

For me guessing would be to go with something before you have a convincing reason to go for it, which I don't think colouring is, colouring is not guessing, and neither is uniqueness. Not that I think guessing would not be a valid way to get to a solution, it's just not one that I like to use myself.

Agreed. Uniqueness is not guessing in itself. It is noticing a pattern that, if the solution requires it, would have more than one solution, and then using that pattern to solve the puzzle is "guessing" that the puzzle is not an exception. To be sure, it's a guess that can be expected to be "correct," almost all the time. That is not what we would ordinarily call "guessing." It is inference from what is common and normal, with exceptions being quite rare. It is simply not a proof. --Abd (talk) 21:52, 15 January 2020 (UTC)

I just get annoyed when someone claims I make assumptions that "Are not valid" and they themselves aren't able to make at least some reasoning without acting out and being rude like was the case here.

Right. And I get annoyed when someone asserts I claimed something I did not claim, or does this about someone else about what they did not claim. First question, for me, is "was this claimed?" If so, I'll write "Damn straight!" And if not, I'll object. Or not. Depends on the effect I expect. The older claims that I "hated uniqueness" I considered potentially damaging, so I confronted them. But the other user here was really just saying "I hate [to use] uniqueness," which is ordinary speech and not offensive, and I pointed out that it could be disempowering, because noticing a uniqueness strategy can be useful. Just not a proof! So if we want proof, we won't rely on it, we will use direct logic, without the assumption.
But if we just want to get the freaking answer, and don't care about proving uniqueness, we'll use it.
Neither of these approaches are "valid" or "invalid." They are choices and, as such, they are useful or not. I happen to enjoy applying logic to sudoku, and requiring proof of uniqueness requires that I do a little more of what I like. I happen to consider that fun. So I do wonder about people that avoid it, but don't question for a moment their right to make the choice. It obviously makes some people happy to use uniqueness strategies and I have never claimed it is wrong or invalid or anything like that. Just that the answer they find is then not proven to be unique.
So I ask the question here: if it is only a little more process -- or not even much more at all -- to prove uniqueness rather than assume it, what will you choose?
I do not propose that either choice is wrong or "invalid." It is like choosing a seed pair for SBN. There is no wrong choice. There are choices that require more patience than others, and patience is a fantastic thing to develop, but when and where to do that is all about personal choice (and it can involve skill), not "right" and "wrong." --Abd (talk) 21:50, 15 January 2020 (UTC)

## suggested syllogisms

So I suggest the syllogisms

### First

• A: Sudoku is a logical puzzle
That is a description of process we have developed to solve sudoku, not of sudoku themselves. Sudoku are patterns of numbers in a grid, with blanks, and a suggestion to fill in the blanks with more numbers to solve it, satisfying the rules. How we do that is not stated. We could guess, and if we find a solution that way -- pure guessing is damned inefficient! -- it would still be a solution if it satisfies the rules. --Abd (talk) 21:50, 15 January 2020 (UTC)
• B: All logical puzzle has to be solvable by logic.
That assumes the conclusion. We make that assumption, it also was not stated. A puzzle may come to us that has no solution. They are rare, but they exist. They are still puzzles, and they are still "solvable by logic" in the sense that logic can prove that there is no solution. We may, of course, depend on the authority of SW Solver and Hodoku. After all, they are always right. Or are they? How do we know this. Not by logic, but by inference from a body of experience that happens to be very wide. This distinction is quite important in science, because even universal experience is not a proof. "Absence of evidence is not evidence of absence." --Abd (talk) 21:50, 15 January 2020 (UTC)
• C: Sudoku has to be solveable by logic
The Conclusion was created by the assumptions. In fact, with a reasonable definition of "solveable," all sudoku are solvable. There might be a very large number of possible solutions. --Abd (talk) 21:50, 15 January 2020 (UTC)

### Second

• A: Sudoku has to be solveable by logic
"Has to be" is undefined. It is the language of compulsion and assumptions about what must be or else . . . or else what? Given that all sudoku are solvable by logic, this is meaningless. --Abd (talk) 21:50, 15 January 2020 (UTC)
• B: A puzzle with multiple solutions aren't solveable by logic
This assumes single solution in "solvable." But if a puzzle has two and only two solutions, logic can find both of them. Either one is a solution, satisfying the rules, and showing both completely solves the puzzle, no questions remaining. Either solution satisfies the rules of sudoku.--Abd (talk) 21:50, 15 January 2020 (UTC)
• C: Sudoku with multiple solutions are not valid
"Not valid" is undefined. The term "improper" was developed to describe Sudoku with no solution or with multiple solutions. --Abd (talk) 21:50, 15 January 2020 (UTC)

### Third

• A: A valid sudoku has one solution
This is the problem with complex chains of logic. Any defect breaks it. The term is not "valid," it is "proper." That is correct, a "proper sudoku" has one solution. By definition, not by some conclusory logic. How do we know that a Sudoku is "proper." Because the author says so? Because a computer program says so [using logic that most of us cannot follow}? Or because we use logic and prove that the puzzle has a single solution? I simply prefer the latter. But none of this make uniqueness "invalid," except I suggest avoiding confusing inference with deductive logic. In this case it's an inference based on personally accepted authority.--Abd (talk) 21:50, 15 January 2020 (UTC)
• B: A situation with multiple solutions is not something allowed in a valid sudoku
"Allowed" is again undefined. What is the authority that allows or does not allow? This special category, "valid sudoku" is used to imply that Sudoku with more than one solution are not Sudoku at all, when, by the definitions, they clearly are Sudoku, merely improper, which is a far less loaded term than "invalid." --Abd (talk) 21:50, 15 January 2020 (UTC)
• C: uniqueness is a valid technique
What does that mean? Valid for what? Not for logical proof! But it is useful for faster solution of almost all Sudoku. However, it can break a puzzle that has more than one solution -- I recall an example that was created for that purpose. So in that context it was "invalid," I'd say. Extremely rare, most users would never encounter such a puzzle. Much more commonly, it can create a solution that is not unique, but that follows the rules of Sudoku. And, again, this would be how to find a solution for a multiple solution puzzle that was allegedly unsolvable by what has been stated above. Assume there is only one and then find one, following that assumption, Which was false for that puzzle. So, then, we will think it was a proper Sudoku when it wasn't. --Abd (talk) 21:50, 15 January 2020 (UTC)

### Not arguing from authority

So I hope that makes it clear that I'm not arguing from authority, just from the assumptions that we both agreed upon.

We did not agree on those assumptions. And even if we do agree, uniqueness strategies are argument from authority -- which includes the "authority" of our personal experience. Much of the argument is is based on preference, not on fact, not on logic. --Abd (talk) 21:50, 15 January 2020 (UTC)
And I did not claim that the arguments presented were from an authority. Rather, I claimed that using uniqueness is using an argument from authority, i.e, the authority of the puzzle-maker and publisher, and perhaps the authority of a computer solver. Using those are both arguments from authority (and both are really arguments based on computer solver results). Technically, it's been done in math, an extremely complex program has been accepted as proven valid. Essentially, if we accept that review, and especially if we have verified every step of it personally, it would not be, for us, an argument from authority. It would be personal testimony.
My training in science and long experience led me to recognize that just because nearly everyone -- or "every scientist" -- believes something, that thing is not thereby proven. It does make it likely to be so, but then there are black swans, and when evidence that black swans exist is rejected because everyone knows that swans are white, we can have a strong majority stuck in an inference that is actually pseudoscientific. It looks like science but isn't,. "Absence of evidence is not evidence of absence" is well-known. Not mentioned much above is the No True Scotsman fallacy, which is often trotted out. We can assume uniqueness because if it is not unique, it is not a valid Sudoku. Yet the damn thing sure looks like a Sudoku, and it is solved like a Sudoku, and computer solvers can solve it, and SW Solver will give us the first 500 solutions, using pure logic. Computers don't guess.
As to the science I'm talking about, there are many examples, but one of them is the main subject of this wiki. I wrote a review, published in a mainstream peer-reviewed journal, on the topic. --Abd (talk) 15:11, 16 January 2020 (UTC)