# How is this Sudoku not correct? **URL:** \ **Category:** The Game Room\ **Created:** [August 27, 2018, 4:18pm UTC](https://boards.straightdope.com/t/how-is-this-sudoku-not-correct/820368 "2018-08-27T16:18:49Z")\ **Posts on this page:** 11\ **Page:** 2
**Author:** ![E-DUB](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/e-dub/32/403_2.png) [@E-DUB](https://boards.straightdope.com/u/E-DUB)\ **Post date:** [August 29, 2018, 1:16am UTC](https://boards.straightdope.com/t/how-is-this-sudoku-not-correct/820368/21 "2018-08-29T01:16:15Z")
> [@CookingWithGas](#): > > I was going to say this. When you solve a puzzle, for each square you determine the number it contains because it cannot logically contain any other number. Therefore if you solve a puzzle, it must necessarily have only one solution. > > If you have a puzzle with more than one solution, you reach a dead end in the chain of reasoning and you cannot solve it. In such a case you would have to go outside puzzle-solving logic to determine what the alternate solutions could be. So you’re saying you must _guess_? ---
**Author:** ![OldGuy](https://avatars.discourse-cdn.com/v4/letter/o/3bc359/32.png) [@OldGuy](https://boards.straightdope.com/u/OldGuy)\ **Post date:** [August 29, 2018, 1:35am UTC](https://boards.straightdope.com/t/how-is-this-sudoku-not-correct/820368/22 "2018-08-29T01:35:08Z")
> [@Chronos](#): > > There’s a difference between finding a solution to a Sudoku and solving it. Take the extreme example: Given a Sudoku grid with no numbers filled in, it’s really easy to find a solution, but it’s impossible to solve it. When you solve a Sudoku puzzles, you go through lines of reasoning that say that this square must be a 9, and so this square must be a 7, and so on. If you only fill in numbers (or at least, only use ink, or whatever) when you know that those numbers must be correct, then once you fill in the last number, you’ll know that there was only one solution, because it’s the one you found. I agree, but have you never made a mistake when solving one. If you have faulty reasoning you might conclude a 7 goes in a square when you really couldn’t conclude that. And that might lead to a faulty conclusion. I have at times reasoned, that a 7 must go in this square because if I put the alternative, a 5, the solution could not be unique. That reasoning is valid assuming uniqueness, but it could be that the 5 also works and the solution is not unique. ---
**Author:** ![Happy\_Fun\_Ball](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/happy_fun_ball/32/17664_2.png) [@Happy\_Fun\_Ball](https://boards.straightdope.com/u/Happy_Fun_Ball)\ **Post date:** [August 29, 2018, 2:33am UTC](https://boards.straightdope.com/t/how-is-this-sudoku-not-correct/820368/23 "2018-08-29T02:33:17Z")
> [@E-DUB](#): > > So you’re saying you must _guess_? Yes. Edited to add: When I was on a trip to Japan years ago, I had a bunch of time and programmed a Sudoku solver in Matlab. Not only did this force me to formalize my logic on Sudoku puzzles, but it ruined my enjoyment of Sudoku forever. Meh. Anyway, in my testing of the code, I found puzzles that had multiple solutions and had to add a routine where it would guess at a solution to find the answer. Was pretty disappointing really. ---
**Author:** ![Biffster](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/biffster/32/339_2.png) [@Biffster](https://boards.straightdope.com/u/Biffster)\ **Post date:** [August 29, 2018, 2:38am UTC](https://boards.straightdope.com/t/how-is-this-sudoku-not-correct/820368/24 "2018-08-29T02:38:52Z")
> [@Happy\_Fun\_Ball](#): > > Yes. > > Edited to add: When I was on a trip to Japan years ago, I had a bunch of time and programmed a Sudoku solver in Matlab. Not only did this force me to formalize my logic on Sudoku puzzles, but it ruined my enjoyment of Sudoku forever. Meh. > > Anyway, in my testing of the code, I found puzzles that had multiple solutions and had to add a routine where it would guess at a solution to find the answer. Was pretty disappointing really. I have a strategy that pretty much eliminates guess work. For any Sudoku puzzle. ---
**Author:** ![Colibri](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/colibri/32/1841_2.png) [@Colibri](https://boards.straightdope.com/u/Colibri)\ **Post date:** [August 29, 2018, 3:46am UTC](https://boards.straightdope.com/t/how-is-this-sudoku-not-correct/820368/25 "2018-08-29T03:46:46Z")
Since this has become a general discussion of Sudoku, let’s move it to the Game Room. Colibri General Questions Moderator ---
**Author:** ![Robot\_Arm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/robot_arm/32/18280_2.png) [@Robot\_Arm](https://boards.straightdope.com/u/Robot_Arm)\ **Post date:** [August 29, 2018, 4:04am UTC](https://boards.straightdope.com/t/how-is-this-sudoku-not-correct/820368/26 "2018-08-29T04:04:18Z")
> [@CookingWithGas](#): > > I was going to say this. When you solve a puzzle, for each square you determine the number it contains because it cannot logically contain any other number. Therefore if you solve a puzzle, it must necessarily have only one solution. > > If you have a puzzle with more than one solution, you reach a dead end in the chain of reasoning and you cannot solve it. In such a case you would have to go outside puzzle-solving logic to determine what the alternate solutions could be. Well, yes and no. I found an online Sudoku solver a few years ago that was very interesting. It would show, step-by-step, what deductions it was making and what rule it was using to make them. The rules that it would apply started simple (there’s only one blank square in a row, column, or box) and got progressively more complex. Some of the rules it used were more complex than I’ve ever needed, and would be hard for a person to recognize when to apply them. One of them was kind of like the situation dtilque posted; if a and b are possibilities in four cells that form a rectangle then those four cells must be a or b, and you can remove all other numbers as possibilities in those cells. I’ve almost never seen Sudokus that require rules that complex in order to solve them. If I did try to solve one, I’d probably get to the point where that rule applied and not see it. There are rules that can lead to a unique solution, but at that point I’d probably have to guess. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [August 29, 2018, 9:12pm UTC](https://boards.straightdope.com/t/how-is-this-sudoku-not-correct/820368/27 "2018-08-29T21:12:53Z")
If I’m understanding correctly what you’re trying to describe, that’s a basic technique. The true advanced techniques are much more complicated. > [@](#): > > Quoth **OldGuy** : > > I have at times reasoned, that a 7 must go in this square because if I put the alternative, a 5, the solution could not be unique. That reasoning is valid assuming uniqueness, but it could be that the 5 also works and the solution is not unique. That’s a controversial technique among solvers, for precisely that idea. My personal take is that it’s not a valid technique, but that it can be used in conjunction with other techniques which are valid in order to make them more efficient. For instance, the method of guess-and-check is valid, but it only gives validly useful results if your initial guess was wrong, so it’s helpful to know in advance which guess should be the wrong one. That is to say, if I found myself in the situation you describe, and could see no other recourse, I might pencil in the 5, and then see where that led, penciling in all subsequent steps until I (hopefully) reached a genuine contradiction. Once I got that, I would know that the 5 must not be right, not because of the multi-solution bug, but because of the contradiction. Without that bug, I might have instead guessed poorly, and accidentally made the correct guess, and followed it through to a complete solution, at which point I’d be very frustrated because I hadn’t made any progress towards solving it. ---
**Author:** ![Robot\_Arm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/robot_arm/32/18280_2.png) [@Robot\_Arm](https://boards.straightdope.com/u/Robot_Arm)\ **Post date:** [August 29, 2018, 9:40pm UTC](https://boards.straightdope.com/t/how-is-this-sudoku-not-correct/820368/28 "2018-08-29T21:40:04Z")
> [@Chronos](#): > > If I’m understanding correctly what you’re trying to describe, that’s a basic technique. The true advanced techniques are much more complicated. [This](http://hodoku.sourceforge.net/en/techniques.php) isn’t the site I was thinking of, but it’s similar. What I was trying to describe is what they refer to as an X-Wing. It’s not very far down the list of complicated solving techniques, but the sites I used to play never had a puzzle (even what they considered their most difficult) that required it. My point was that human solvers may think they’ve reached a point where they have to make a guess, but it ain’t necessarily so. There are techniques that are sufficiently complicated (both in logic, and in seeing the patterns for which they can be applied) that most solvers won’t see them. > [@](#): > > That’s a controversial technique among solvers, for precisely that idea. My personal take is that it’s not a valid technique, but that it can be used in conjunction with other techniques which are valid in order to make them more efficient. For instance, the method of guess-and-check is valid, but it only gives validly useful results if your initial guess was wrong, so it’s helpful to know in advance which guess should be the wrong one. > > That is to say, if I found myself in the situation you describe, and could see no other recourse, I might pencil in the 5, and then see where that led, penciling in all subsequent steps until I (hopefully) reached a genuine contradiction. Once I got that, I would know that the 5 must not be right, not because of the multi-solution bug, but because of the contradiction. > > Without that bug, I might have instead guessed poorly, and accidentally made the correct guess, and followed it through to a complete solution, at which point I’d be very frustrated because I hadn’t made any progress towards solving it. Guess-and-check kinda bothers me. (I don’t do Sudokus much anymore, but there are other puzzles I play where it applies.) It’s okay if you’re playing on a computer, and the software has an undo button that can take you back to where you guessed, but with actual paper and pencil it’s kind of a drag. And if I happen to guess correctly, and finish the puzzle, I always wonder if I guessed right or if the puzzle is poorly constructed and either guess could have led to a solution. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [August 29, 2018, 11:05pm UTC](https://boards.straightdope.com/t/how-is-this-sudoku-not-correct/820368/29 "2018-08-29T23:05:06Z")
Guess-and-check bothers me for the purely practical reason that it’s a dull, slow, and cumbersome method, but I don’t view it as in any way invalid. I’ll very seldom use it, for that reason. And the X-wing is properly described as an advanced technique; I just haven’t internalized it enough to recognize it as what you were trying to describe. > [@](#): > > And if I happen to guess correctly, and finish the puzzle, I always wonder if I guessed right or if the puzzle is poorly constructed and either guess could have led to a solution. Yeah, that’s the point where I erase all of that, go back and try the other guess, to verify that it’s false, and then go right back to re-do the first one. If I don’t get bored first and move on to some other time-killer. ---
**Author:** ![Atamasama](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/atamasama/32/12961_2.png) [@Atamasama](https://boards.straightdope.com/u/Atamasama)\ **Post date:** [August 29, 2018, 11:29pm UTC](https://boards.straightdope.com/t/how-is-this-sudoku-not-correct/820368/30 "2018-08-29T23:29:42Z")
> [@Chronos](#): > > And the X-wing is properly described as an advanced technique; I just haven’t internalized it enough to recognize it as what you were trying to describe. I’m good enough to recognize things like a “unique rectangle” but things like the X-wing and Swordfish are beyond me. I’m relieved to see someone acknowledge that they are difficult because honestly Sudoku sometimes makes me feel dumb. ---
**Author:** ![Biffster](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/biffster/32/339_2.png) [@Biffster](https://boards.straightdope.com/u/Biffster)\ **Post date:** [August 30, 2018, 7:55pm UTC](https://boards.straightdope.com/t/how-is-this-sudoku-not-correct/820368/31 "2018-08-30T19:55:22Z")
> [@Robot\_Arm](#): > > [This](http://hodoku.sourceforge.net/en/techniques.php) isn’t the site I was thinking of, but it’s similar. What I was trying to describe is what they refer to as an X-Wing. It’s not very far down the list of complicated solving techniques, but the sites I used to play never had a puzzle (even what they considered their most difficult) that required it. > > My point was that human solvers may think they’ve reached a point where they have to make a guess, but it ain’t necessarily so. There are techniques that are sufficiently complicated (both in logic, and in seeing the patterns for which they can be applied) that most solvers won’t see them. > > Guess-and-check kinda bothers me. (I don’t do Sudokus much anymore, but there are other puzzles I play where it applies.) It’s okay if you’re playing on a computer, and the software has an undo button that can take you back to where you guessed, but with actual paper and pencil it’s kind of a drag. And if I happen to guess correctly, and finish the puzzle, I always wonder if I guessed right or if the puzzle is poorly constructed and either guess could have led to a solution. I have a pattern that I learned to recognize that helps eliminate the need to guess and check. It involves number pairs and the odd man out. It’s a pattern that exists in every Sudoku puzzle. [Previous page](https://boards.straightdope.com/t/how-is-this-sudoku-not-correct/820368.md?page=1)