# Ought puzzles (like sudoku) have only 1 solution?
**URL:** https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037
**Category:** The Game Room
**Created:** [March 24, 2025, 3:21pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037 "2025-03-24T15:21:56Z")
**Posts on this page:** 20
**Page:** 1
### Author:  [@Dinsdale](https://boards.straightdope.com/u/Dinsdale)
#### Post date: [March 24, 2025, 3:21pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/1 "2025-03-24T15:21:56Z")
My wife does sudoku - I don’t. Today was supposed to be an easy puzzle. She was mildly displeased that the answer was ambiguous - it would have worked equally well if you had placed a 6 and a 7 in one place, and reversed them in a different place (or something like that.) Suffice it to say there was not one single correct answer. I guess she disliked that, because it caused some ambiguity in the way she solved it. And, she thought if that WERE how it was constructed, it was not appropriate for an ostensibly easy puzzle.
I’m sure opinions and conventions vary on this, but I was wondering what you all think. Ought a word/number puzzle like Sudoku have only one “correct” answer, or are multiple possible solutions just fine?
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### Author:  [@colinfred](https://boards.straightdope.com/u/colinfred)
#### Post date: [March 24, 2025, 3:24pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/2 "2025-03-24T15:24:12Z")
Either your wife made a mistake or the puzzle creator did. A Sudoku has to have only 1 valid solution.
I wouldn’t be so quick to assume it’s the puzzle creator though, it’s easy to get selective blindness where you cannot spot your own mistake in a “solved” section.
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### Author:  [@Dinsdale](https://boards.straightdope.com/u/Dinsdale)
#### Post date: [March 24, 2025, 4:01pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/3 "2025-03-24T16:01:58Z")
My wife is not home right now. As I understood it, she said it would have worked if the positions of the 6 and 7 were switched in 1 or 2 of the subsections of 9. My impression was that if you switched the 6 and 7 in both subsections, the overall puzzle would work. But I did not press her on it or “check her work.”
Are you saying that the way the math works, there can only be one solution? Or is that the “rule” set by Sudoku’s creator/publisher?
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### Author:  [@RitterSport](https://boards.straightdope.com/u/RitterSport)
#### Post date: [March 24, 2025, 4:05pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/4 "2025-03-24T16:05:30Z")
> [@Dinsdale](#):
>
> Are you saying that the way the math works, there can only be one solution?
Certainly, poorly formed boxes of 9 boxes can have more than one solution. It’s not a math puzzle. But, a sudoku with two solutions wouldn’t really qualify as a valid sudoku puzzle. Valid puzzles have to have one unique solution.
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### Author:  [@The\_Other\_Waldo\_Pepper](https://boards.straightdope.com/u/The_Other_Waldo_Pepper)
#### Post date: [March 24, 2025, 4:25pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/5 "2025-03-24T16:25:39Z")
> [@Dinsdale](#):
>
> I’m sure opinions and conventions vary on this, but I was wondering what you all think. Ought a word/number puzzle like Sudoku have only one “correct” answer, or are multiple possible solutions just fine?
I’m reminded of the NYT Election Day crossword puzzle where one clue was their lead story for tomorrow — and they rigged it to fit either ‘Clinton Elected’ or ‘Bob Dole Elected.’
(So, one clue was Black Halloween Animal: you could make it work with _Bat_ if you’d wound up needing the first letter of _Bob,_ but it of course also works just fine with _Cat_…)
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### Author:  [@thorny\_locust](https://boards.straightdope.com/u/thorny_locust)
#### Post date: [March 24, 2025, 6:20pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/6 "2025-03-24T18:20:19Z")
> [@colinfred](#):
>
> I wouldn’t be so quick to assume it’s the puzzle creator though, it’s easy to get selective blindness where you cannot spot your own mistake in a “solved” section
Published sudokus are sometimes wrong. I’ve got one in a book of them that has the same number filled in twice – by the puzzlemaker – on the same line; making the puzzle impossible to solve correctly. So I have no doubt that an occasional two-solution sudoku sneaks through the process, as the format apparently can theoretically have two solutions.
However IMO that doesn’t produce a valid sudoku, because the point of the structure of a sudoku is that there’s one and only one correct place to place each number. While you certainly can guess if you feel like it, you’re not supposed to have to guess – the needed information is supposed to be contained in the puzzle; and, for a puzzle with two possible solutions, some of it isn’t.
There may well be other puzzles in existence that can properly have two solutions; I don’t know. But a standard sudoku isn’t one of them.
> [@The\_Other\_Waldo\_Pepper](#):
>
> I’m reminded of the NYT Election Day crossword puzzle where one clue was their lead story for tomorrow — and they rigged it to fit either ‘Clinton Elected’ or ‘Bob Dole Elected.’
>
> (So, one clue was Black Halloween Animal: you could make it work with _Bat_ if you’d wound up needing the first letter of _Bob,_ but it of course also works just fine with _Cat_…)
That must have been fun to write! – and, yeah, I think that’s a valid crossword. Once you figured out what was going on you could fill in both alternatives; and it’s fair to say that it would have been possible to figure out what was going on. But a crossword puzzle filled in two valid ways is finished. A sudoku filled in two ways isn’t finished; that “6/7” or whatever stuck into a square is an intermediary technique to be used in solving the puzzle, not an end point.
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### Author:  [@RitterSport](https://boards.straightdope.com/u/RitterSport)
#### Post date: [March 24, 2025, 6:41pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/7 "2025-03-24T18:41:24Z")
Heck, the NY Times had a puzzle last week that had multiple clues with two answers. I didn’t even notice until I finished and couldn’t figure out the theme.
But, a sudoku? No way, unless it’s some complicated rule set variant sudoku. Even then, there would only be one solution, even if some cells might contain two numbers. Yes, I spend too much time watching Cracking the Cryptic videos. Why do you ask?
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### Author:  [@Chronos](https://boards.straightdope.com/u/Chronos)
#### Post date: [March 24, 2025, 7:04pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/8 "2025-03-24T19:04:39Z")
Put it this way: Imagine a sudoku grid that’s entirely blank, with no numbers filled in at all. It’s certainly possible for the puzzle’s player to complete it in a valid way, as any sudoku solution at all will work in a blank grid. Does that count as a “valid sudoku”?
A sudoku with two valid solutions is just as invalid as one with six sextillion valid solutions.
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### Author:  [@Sage\_Rat](https://boards.straightdope.com/u/Sage_Rat)
#### Post date: [March 24, 2025, 7:35pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/9 "2025-03-24T19:35:07Z")
> [@RitterSport](#):
>
> Yes, I spend too much time watching Cracking the Cryptic videos. Why do you ask?
I just happened to be watching the following episode:
[ ](https://www.youtube.com/watch?v=iiQ9MXrfb7A)
In it, he is discussing how he generally avoids a technique for solving, called Gurth’s Symmetrical Placement theorem, because it makes the assumption that there’s a single, unique solution for the puzzle and he doesn’t usually make that assumption.
> **[Gurths Theorem - SudokuWiki.org](https://www.sudokuwiki.org/Gurths_Theorem)**
>
> Gurth's Symmetrical Placement Theory is discussed
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### Author:  [@RitterSport](https://boards.straightdope.com/u/RitterSport)
#### Post date: [March 24, 2025, 7:43pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/10 "2025-03-24T19:43:39Z")
Right. Also, if they come across something that would be what they call a Deadly Pattern, they don’t use that impossibility as a logic move either.
So, let’s say in columns 4 and 8, in rows 5 and 6, you have four numbers. If column 4 row 5 were a 1 or 2 and row 6 were a 1 or 2, column 8 couldn’t have 1 or 2 in those rows, because they would be reversible and you would have two solutions. So, if you have three of those in place and 1 or 2 is a possible answer in the fourth, but would create a deadly pattern, you could assume that 1 or 2 can’t go there because it would result in a non-unique solution. However, they never make that assumption, and instead use logic elsewhere to eliminate the ambiguity.
I’m sure that’s clear as mud.
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### Author:  [@Chronos](https://boards.straightdope.com/u/Chronos)
#### Post date: [March 24, 2025, 7:47pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/11 "2025-03-24T19:47:53Z")
On the other hand, with the logical method of guess-and-check (and yes, that is a perfectly valid logical method), you want to start by making the wrong guess, so that you can eventually confirm that that guess is wrong. If you’re using guess-and-check, and you spot a potential Deadly Pattern, then that’s the one you guess.
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### Author:  [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)
#### Post date: [March 24, 2025, 8:57pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/12 "2025-03-24T20:57:30Z")
A properly constructed sudoku should have just one solution but you will sometimes find poorly constructed ones that have multiple solutions in lower quality books and apps.
I would say that 99% of the time I see a “This puzzle is broken!” post on the sudoku subreddit it’s a case of the poster making an error rather than a problem with the puzzle.
You can enter sudokus at [Sudoku Coach](https://sudoku.coach/en/play/000000000000000000000000000000000000000000000000000000000000000000000000000000000) and it will tell you how hard it is and how many solutions it has.
Personally I’m not a fan of using the assumed uniqueness of a sudoku to help solve it. It feels like using information from outside the game itself. By the same token I don’t think a sudoku should be created that _relies_ on that technique to solve. There should be some other pathway to solve it. That’s just my personal preference as a solver though and I’m aware that I’m essentially placing my own restrictions on my solving techniques.
As for guess-and-check, I would prefer to be able to see the logic in the chain without having to enter a number first to see where it leads.
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### Author:  [@Robot\_Arm](https://boards.straightdope.com/u/Robot_Arm)
#### Post date: [March 24, 2025, 9:07pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/13 "2025-03-24T21:07:17Z")
> [@RitterSport](#):
>
> Yes, I spend too much time watching Cracking the Cryptic videos. Why do you ask?
I haven’t heard of this. Is it only for sudokus, or do they cover other types of puzzles, too?
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### Author:  [@Robot\_Arm](https://boards.straightdope.com/u/Robot_Arm)
#### Post date: [March 24, 2025, 9:13pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/14 "2025-03-24T21:13:26Z")
> [@Richard\_Pearse](#):
>
> As for guess-and-check, I would prefer to be able to see the logic in the chain without having to enter a number first to see where it leads.
I would prefer that, too. Plus, I started doing sudokus with pencil and paper. It’s hard to do guess-and-check without a “back” button to return to the point where you made the guess.
I think part of the reason I stopped doing sudokus is because some of the solving techniques got so esoteric that they were somewhat beyond my ability to recognize. I’ve done them on planes the last few times I’ve flown anywhere, and the or expert level puzzles either require those difficult techniques, or have more than one solution.
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### Author:  [@Chronos](https://boards.straightdope.com/u/Chronos)
#### Post date: [March 24, 2025, 9:16pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/15 "2025-03-24T21:16:23Z")
> [@Richard\_Pearse](#):
>
> By the same token I don’t think a sudoku should be created that _relies_ on that technique to solve.
Any sudoku that relies on a unique-solution method to solve it, itself does not have a unique solution.
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### Author:  [@RitterSport](https://boards.straightdope.com/u/RitterSport)
#### Post date: [March 24, 2025, 9:48pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/16 "2025-03-24T21:48:19Z")
> [@Robot\_Arm](#):
>
> Is it only for sudokus
It’s mostly “variant sudoku”, which are sudokus with all kinds of interesting and complicated rules. Rarely do they do a straight up sudoku anymore.
One of the two vloggers does the Sunday Times (of London) crossword, which is a puns-and-anagrams type of crossword. The other one does Heardle in a Minute.
Sometimes, they will solve other puzzles, like nurikabe, but it’s 90% variant sudoku.
I learned about the channel on this Board, in this thread:
> [@The Miracle Sudoku: 'the most riveting video I’ve seen all year'](https://boards.straightdope.com/t/the-miracle-sudoku-the-most-riveting-video-i-ve-seen-all-year/854306):
>
> I never thought I could ever watch a full 25 minute video of a guy solving a sudoku puzzle… but I watched the whole thing right through without my attention wandering for a moment, and it seemed like 5 min. Article: [Puzzled man solving ‘miracle’ sudoku becomes YouTube sensation](https://www.theguardian.com/lifeandstyle/2020/may/22/cracking-the-cryptic-puzzled-uk-men-become-internet-sensation-with-sudoku-channel) Video: [The Miracle Sudoku](https://youtu.be/yKf9aUIxdb4)
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### Author:  [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)
#### Post date: [March 24, 2025, 9:52pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/17 "2025-03-24T21:52:19Z")
Is that true?
I’m thinking of puzzles where you have four squares spread over just two rows and columns with say 2, 3 candidates in three of them and 2, 3, 5 in the other. If we know the puzzle has a unique solution then we know the fourth square must be a 5, otherwise the solution would not be unique. I’m discounting pure brute force guess-check as a valid technique here.
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### Author:  [@Pleonast](https://boards.straightdope.com/u/Pleonast)
#### Post date: [March 24, 2025, 9:54pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/18 "2025-03-24T21:54:37Z")
> [@Dinsdale](#):
>
> Or is that the “rule” set by Sudoku’s creator/publisher?
It’s a convention of terminology. It’s certainly possible to have a puzzle with multiple solutions. And it’s certainly possible to have a puzzle with exactly one solution.
In the case of Sudoku:
> However, the puzzle type only began to gain widespread popularity in 1986 when it was published by the Japanese puzzle company [Nikoli](https://en.wikipedia.org/wiki/Nikoli_(publisher)) under the name Sudoku, meaning “single number”.[[6]](https://en.wikipedia.org/wiki/Sudoku#cite_note-6)
So, by definition, a Sudoku puzzle has exactly one solution, and if a puzzle has more than one solution, it is not a Sudoku puzzle.
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### Author:  [@RitterSport](https://boards.straightdope.com/u/RitterSport)
#### Post date: [March 24, 2025, 10:04pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/19 "2025-03-24T22:04:52Z")
Man, you explained that so much better than I did. Anyway, assuming the answer is 5 because of uniqueness is exactly what the Cracking the Cryptic guys won’t do.
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### Author:  [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)
#### Post date: [March 24, 2025, 10:16pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/20 "2025-03-24T22:16:39Z")
Recent thread on the same topic:
> [@Sudokus don't always have unique solutions](https://boards.straightdope.com/t/sudokus-dont-always-have-unique-solutions/1010447):
>
> Yes, I may be a few decades late to this realisation. I was doing a sudoku on a flight and got horribly stuck towards the end. All of the remaining cells only had one of two values that they could be, but there didn’t seem to be any logical basis to rule out either value for any cell. After staring at it for about half an hour, I eventually realised that both sets of values made complete and correct sudoku grids. I had always assumed sudokus were always solvable to one unique solution.
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