Unfilled boxes, but puzzle already solved?

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Unfilled boxes, but puzzle already solved?

Postby flycaster » Tue Apr 26, 2022 4:28 pm

I'm a newbie and have made this observation: I am finding, let's say for example, that when I've almost completely solved the puzzle and have maybe have 4-8 boxes with each box having only possible two numbers in it, that choosing any one of those two numbers will allow me to completely solve the puzzle without any further thought...it's been an "automatic" finish. In other words, if one is left with several boxes, each box having only two numbers, one can consider the puzzle to be already solved???
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Re: Unfilled boxes, but puzzle already solved?

Postby eleven » Thu Apr 28, 2022 5:28 pm

Strange question.
If you choose the correct one of the 2 digits, and made no mistake before, and the puzzle has only one solution, it will be solved with easy singles.
Personally i consider a puzzle to be solved, when the last number is solved (i.e. you have the complete solution).
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Re: Unfilled boxes, but puzzle already solved?

Postby flycaster » Thu Apr 28, 2022 6:48 pm

eleven wrote:Strange question.
If you choose the correct one of the 2 digits, and made no mistake before, and the puzzle has only one solution, it will be solved with easy singles.
Personally i consider a puzzle to be solved, when the last number is solved (i.e. you have the complete solution).


I may not have made myself clear. I was trying to find out if one is left with a few boxes, each of which have only two possible correct answers (and all other boxes have been correctly filled with a single number,) then it doesn't matter which of the two possible numbers you pick from one of those remaining boxes as once chosen, then all other remaining boxes will be filled in correctly. This has been my experience as I often wind up this situation and I find that the puzzle will be solved by choosing one number and then going one tot he rest. But now as I think about Sudoku having only one solution, this observation appears to say that Sudoku may have two possible solutions. Of course, it could be that I'm not really paying enough attention to the "solved" puzzle. therefore, next time this situation arises, I will submit photos of just what I saying.
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Re: Unfilled boxes, but puzzle already solved?

Postby Mathimagics » Fri Apr 29, 2022 8:00 am

If the puzzle has a unique solution, and you have only bi-values (cells with 2 possible values) remaining, then ...

Pick any one of those cells - selecting one choice should lead to a solution, while the other choice should lead to a contradiction.

If both lead to a solution, then you have made some sort of mistake (or the solution is not unique).
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Re: Unfilled boxes, but puzzle already solved?

Postby eleven » Fri Apr 29, 2022 1:06 pm

Two ways, a puzzle with only 2 candidates in unsolved cells can look like:
Code: Select all
+-------------+-------------+-------------+
| 29  7   29  | 3   5   1   | 4   8   6   |
| 3   4   1   | 8   6   9   | 5   7   2   |
| 8   6   5   | 2   4   7   | 1   3   9   |
+-------------+-------------+-------------+
| 1   3   4   | 9   2   8   | 7   6   5   |
| 29  8   29  | 5   7   6   | 3   1   4   |
| 7   5   6   | 4   1   3   | 9   2   8   |
+-------------+-------------+-------------+
| 5   2   8   | 7   3   4   | 6   9   1   |
| 4   1   7   | 6   9   2   | 8   5   3   |
| 6   9   3   | 1   8   5   | 2   4   7   |
+-------------+-------------+-------------+

by dukuso:
Code: Select all
+-------------+-------------+-------------+
| 1   37  24  | 46  36  9   | 5   8   27  |
| 8   57  24  | 37  45  1   | 39  29  6   |
| 39  6   59  | 78  2   58  | 14  34  17  |
+-------------+-------------+-------------+
| 47  24  16  | 5   9   68  | 23  37  18  |
| 25  8   16  | 14  7   3   | 29  46  59  |
| 57  9   3   | 18  46  2   | 14  67  58  |
+-------------+-------------+-------------+
| 29  1   7   | 36  35  56  | 8   29  4   |
| 34  24  8   | 9   1   7   | 6   5   23  |
| 6   35  59  | 2   8   4   | 7   1   39  |
+-------------+-------------+-------------+

(you need some chains to bring it there)
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Re: Unfilled boxes, but puzzle already solved?

Postby flycaster » Fri Apr 29, 2022 2:08 pm

Mathimagics wrote:If the puzzle has a unique solution, and you have only bi-values (cells with 2 possible values) remaining, then ...

Pick any one of those cells - selecting one choice should lead to a solution, while the other choice should lead to a contradiction.

If both lead to a solution, then you have made some sort of mistake (or the solution is not unique).


Ah, so you are confirming my observation about having a solution when a few of the last cells contain 2 possible values. Obviously, by my having made no prior mistakes, I will then assume that I've been doing puzzles that do not have unique solutions. I thought that all these Sudoku puzzles were unique...guess not...at least not the easy ones.
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Re: Unfilled boxes, but puzzle already solved?

Postby dobrichev » Fri Apr 29, 2022 6:45 pm

Finding several solutions usually is a sign that the original puzzle isn't a classic sudoku but has some additional constraints. For example, that both diagonals must contain 1 to 9.
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Re: Unfilled boxes, but puzzle already solved?

Postby flycaster » Fri Apr 29, 2022 7:04 pm

I'm just a "casual" Sudoku doer, so please excuse what might be my naive questioning. But, out of curiosity, here's ( https://soduko-online.com/) where I've been getting (I copy onto paper) the puzzles (Medium) and would like to know if they are/aren't classic Sudoku with some constraints? Thanks.
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Re: Unfilled boxes, but puzzle already solved?

Postby SteveG48 » Fri Apr 29, 2022 7:59 pm

The first two puzzles that I tried in the medium category were classic Sudoku.

If I might suggest, download the program Hodoku. Copy the puzzles into that program and it will immediately warn you if the puzzle is not a valid puzzle with a unique solution.
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Re: Unfilled boxes, but puzzle already solved?

Postby flycaster » Fri Apr 29, 2022 8:10 pm

SteveG48 wrote:The first two puzzles that I tried in the medium category were classic Sudoku.

If I might suggest, download the program Hodoku. Copy the puzzles into that program and it will immediately warn you if the puzzle is not a valid puzzle with a unique solution.


Thanks. They probably are all classic. Which, now leads me to question myself about "no mistakes." I will have to pay more attention in looking for mistakes the next time I come across a solution has two variables in a few of the uncompleted boxes.
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Re: Unfilled boxes, but puzzle already solved?

Postby SteveG48 » Fri Apr 29, 2022 9:34 pm

Indeed. Sudoku is incredibly unforgiving. Working with pen and paper, I screw up more puzzles with simple blunders than by inability to find a path forward. :D
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Re: Unfilled boxes, but puzzle already solved?

Postby flycaster » Fri Apr 29, 2022 10:50 pm

SteveG48 wrote:Indeed. Sudoku is incredibly unforgiving. Working with pen and paper, I screw up more puzzles with simple blunders than by inability to find a path forward. :D


Ain't that the truth...happens all the time.
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