# Ought puzzles (like sudoku) have only 1 solution? **URL:** \ **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:** 2
**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:** [March 25, 2025, 12:23am UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/21 "2025-03-25T00:23:04Z")
> [@Richard\_Pearse](#): > > I’m discounting pure brute force guess-check as a valid technique here. Why? And if that’s not valid, what is? Ultimately, all sudoku techniques can be thought of as just special cases of guess-and-check. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [March 25, 2025, 12:43am UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/22 "2025-03-25T00:43:26Z")
One could probably design a Sudoku that requires some extremely large number of operations (10^20, say) to solve by guess-and-check, but where a uniqueness assumption bypasses all that. Sudokus are generally supposed to be solvable by _human_-level deduction, which might include shallow guess-and-check but nothing that requires more than dozens of operations. ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [March 25, 2025, 12:43am UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/23 "2025-03-25T00:43:29Z")
I think you should be able to see the logic ahead of time. Guessing a number and carrying on to see what happens without having any idea of what the result will be is both uninteresting and distinctly different from seeing a pattern of candidates and knowing that the pattern allows you to rule out candidates from certain cells _without_ having to follow a process of trial and error. My 7 year old daughter could brute force _any_ sudoku given enough time and motivation. ---
**Author:** ![Andy\_L](https://avatars.discourse-cdn.com/v4/letter/a/c67d28/32.png) [@Andy\_L](https://boards.straightdope.com/u/Andy_L)\ **Post date:** [March 25, 2025, 1:10am UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/24 "2025-03-25T01:10:23Z")
In KenKen (a Sudoku variant) I have used the fact that solutions must be unique to eliminate possibilities. ---
**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:** [March 25, 2025, 3:05am UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/25 "2025-03-25T03:05:48Z")
But “carrying on to see what happens” is exactly what “seeing a pattern of candidates” is. Heck, even trivial techniques like “when 8 of the numbers in a row are filled in, fill in the last one” are based on guess-and-check: “Is this a 1? Check… No, that means two 1s in the row. Is this a 2? Check… No, that means two 2s in the row”, etc. One can certainly say that it should be possible to do all of the work in one’s head… but then we have to ask whose head. It’s possible to do guess-and-check in one’s head, if one has a good memory and it’s not too many steps. On the other hand, for many “logical” techniques, most solvers find they can’t do all of the work for the technique in their head. ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [March 25, 2025, 4:12am UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/26 "2025-03-25T04:12:18Z")
> [@Chronos](#): > > Heck, even trivial techniques like “when 8 of the numbers in a row are filled in, fill in the last one” are based on guess-and-check: “Is this a 1? Check… No, that means two 1s in the row. Is this a 2? Check… No, that means two 2s in the row”, etc. But that’s not what you do is it? You look at it and see a 1 is missing, you don’t literally go through each number and mentally fill it in. Look at a naked pair of a 3 and 5. If I see a 35 naked pair, I know I can remove those two candidates from all other cells in the region without having to literally put a 3 in one of the cells, see that a 5 is forced to be in the other cell and then see that there is no way for 3 and 5 to go in the regions that see the pair, even though that is the underlying logic. This is totally different from not knowing about naked pairs, guessing a 3 in one of the other cells then eventually finding there’s nowhere to put 3 in the naked pair cells. In one case you’re using a generalised technique that has been proven to work, in the other you are blindly trying stuff until it doesn’t work and then trying something else. Same with an X-wing. I know the X-wing pattern eliminates all candidates in the same row/column as the X-wing, I’m not thinking about what happens if I put a particular number in a cell, I don’t even need to know the number, I could just colour the applicable cells blue. I want to use techniques that can be generalised, I don’t want to be in a position where I’m literally putting a number in a cell without knowing what will happen. > [@Chronos](#): > > On the other hand, for many “logical” techniques, most solvers find they can’t do all of the work for the technique in their head. This paragraph suggests you know very well the difference between guessing and using “logical” techniques. ---
**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:** [March 25, 2025, 4:12am UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/27 "2025-03-25T04:12:22Z")
> [@RitterSport](#): > > 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. I like that style, but but the English cultural references usually stump me. Have they ever done puzzles by Cox and Rathvon? Those are my favorite constructors; they recently reitred and put their whole archive online. I’m working my way through it, although I’ve probably done most of them before. ---
**Author:** ![RitterSport](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rittersport/32/6326_2.png) [@RitterSport](https://boards.straightdope.com/u/RitterSport)\ **Post date:** [March 25, 2025, 10:29am UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/28 "2025-03-25T10:29:35Z")
No idea on that front. I’ve only ever occasionally done puns and anagrams in Games magazine, and in the NY Times, when they used to post their extra puzzle on the website. ---
**Author:** ![Dinsdale](https://avatars.discourse-cdn.com/v4/letter/d/97f17d/32.png) [@Dinsdale](https://boards.straightdope.com/u/Dinsdale)\ **Post date:** [March 25, 2025, 11:37am UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/29 "2025-03-25T11:37:17Z")
Thanks, all. Wife claims the Sudokus she does (in the Chicago Trib) have had such multiple answers in the past. She has discussed it with her friend - a more involved puzzler, who agrees. I personally am not interested in the puzzles (or my wife’s interpretation of them) enough to take this further. Sorry I missed the previous thread. ---
**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:** [March 25, 2025, 12:07pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/30 "2025-03-25T12:07:26Z")
> [@Richard\_Pearse](#): > > This paragraph suggests you know very well the difference between guessing and using “logical” techniques. No, it suggests that I know that others think there’s a difference, and sort some techniques into the category they call “logical” and others into the category they call “non-logical”, even though they all work the same way. ---
**Author:** ![RitterSport](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rittersport/32/6326_2.png) [@RitterSport](https://boards.straightdope.com/u/RitterSport)\ **Post date:** [March 25, 2025, 12:51pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/31 "2025-03-25T12:51:20Z")
Well, if you can share just one of the ambiguous puzzles here, I bet we can figure it out for sure. ---
**Author:** ![Dinsdale](https://avatars.discourse-cdn.com/v4/letter/d/97f17d/32.png) [@Dinsdale](https://boards.straightdope.com/u/Dinsdale)\ **Post date:** [March 25, 2025, 1:24pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/32 "2025-03-25T13:24:09Z")
Thanks. I’ll see if I can easily pull up a link to the Sudoku in yesterday’s Chicago Trib, but I doubt it is publicly accessible. I appreciate that you guys enjoy these so much, and I intend no disrespect, but I’ve surpassed my very limited interest in Sudoku, so I won’t be putting in much effort to share them. Nor am I interested in proving my wife right or wrong. I’m happy she enjoys doing them. And Wordle - another puzzle I do not do. ---
**Author:** ![colinfred](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/colinfred/32/21338_2.png) [@colinfred](https://boards.straightdope.com/u/colinfred)\ **Post date:** [March 25, 2025, 1:34pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/33 "2025-03-25T13:34:27Z")
No disrespect to your wife but if it’s happening to her regularly, especially with a large paper like the Chicago Tribune, I’m pretty certain that the error is on her end, the “selective blindness” I mentioned earlier. ---
**Author:** ![colinfred](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/colinfred/32/21338_2.png) [@colinfred](https://boards.straightdope.com/u/colinfred)\ **Post date:** [March 25, 2025, 1:47pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/34 "2025-03-25T13:47:54Z")
[![](https://images4.imagebam.com/65/91/2b/ME10KUZP_o.jpg) ](https://images4.imagebam.com/65/91/2b/ME10KUZP_o.jpg) I don’t know if this is the puzzle but it’s the one for 24 March on the Tribune’s website. It is fully solvable with only 1 unique solution. ---
**Author:** ![Dinsdale](https://avatars.discourse-cdn.com/v4/letter/d/97f17d/32.png) [@Dinsdale](https://boards.straightdope.com/u/Dinsdale)\ **Post date:** [March 25, 2025, 2:02pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/35 "2025-03-25T14:02:42Z")
> [@colinfred](#): > > No disrespect to your wife but if it’s happening to her regularly, especially with a large paper like the Chicago Tribune, I’m pretty certain that the error is on her end, the “selective blindness” I mentioned earlier. That is entirely cool. As you might imagine, since Sudoku is not something that is at all important to me, I’m not terribly interesting in proving her (and her friend) right or wrong. 😉 Maybe later I’ll see if the puzzle in question is still readily accessible in our recycling bin… But other than checking to see if it is the same puzzle you linked, I’m not going to “check her math.” After 39 years of marriage, we have no difficulty finding plenty of other things to fight about! 😃 ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [March 25, 2025, 7:13pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/36 "2025-03-25T19:13:00Z")
> [@Andy\_L](#): > > In KenKen (a Sudoku variant) I have used the fact that solutions must be unique to eliminate possibilities. Other considerations notwithstanding, perhaps a puzzle designer might exploit the existence of multiple solutions to make things more challenging. ---
**Author:** ![Dinsdale](https://avatars.discourse-cdn.com/v4/letter/d/97f17d/32.png) [@Dinsdale](https://boards.straightdope.com/u/Dinsdale)\ **Post date:** [March 25, 2025, 7:39pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/37 "2025-03-25T19:39:06Z")
> [@colinfred](#): > > I don’t know if this is the puzzle but it’s the one for 24 March on the Tribune’s website. It is fully solvable with only 1 unique solution. Pulled it out of the recycling - it was a different puzzle. In fact, the Business section has a “bonus puzzle page” that had a different Sudoku than the one you found on line. Curious - they seem to be skimping on all aspects of news reporting, yet they appear to be Sudoku RICH! 😃 ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [March 25, 2025, 7:54pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/38 "2025-03-25T19:54:37Z")
> [@Chronos](#): > > No, it suggests that I know that others think there’s a difference, and sort some techniques into the category they call “logical” and others into the category they call “non-logical”, even though they all work the same way Do you think there’s such a thing as fun Sudokus and less fun Sudokus? ---
**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:** [March 25, 2025, 8:03pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/39 "2025-03-25T20:03:28Z")
A fun sudoku is one that’s easy enough that I’m able to finish it, but difficult enough that I’m not able to finish it too quickly or easily. Of course, by this definition, different sudokus will be fun to different people. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [March 25, 2025, 8:07pm UTC](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037/40 "2025-03-25T20:07:48Z")
But easy and hard isn’t a 1-dimensional spectrum. Pure guess-and-check is easy–it just takes a while. And you can solve any Sudoku that way. At least for me, the satisfaction comes from seeing a pattern that logically constrains the solution. And also discovering the general form of these patterns. A Sudoku that didn’t have any of these patterns would not be fun for me. [Previous page](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037.md?page=1) [Next page](https://boards.straightdope.com/t/ought-puzzles-like-sudoku-have-only-1-solution/1016037.md?page=3)