--- title: "Can a Sudoku Have Two Solutions? | Sudoku Flow" description: "A proper Sudoku has exactly one solution, but a badly made one can have two. A real example made by removing one given, and why one answer matters." url: https://sudokuflow.com/guides/can-sudoku-have-two-solutions/ language: en last_modified: 2026-11-06 --- [Sudoku guides](https://sudokuflow.com/guides/) # Can a Sudoku Have Two Solutions? A proper Sudoku has exactly one solution, but a badly made one can have two. A real example made by removing one given, and why one answer matters. Updated 2026-11-06 ## Quick answer A proper Sudoku has exactly one solution, and that is what makes it fair: every digit can be found by logic. A badly made puzzle can have two or more, and then at some point you can only guess. Taking a single given out of a real puzzle is sometimes enough, as the example below shows. - A well-made Sudoku has exactly one solution. - With two solutions, some squares can only be guessed. - Taking out one given can be enough to allow a second answer. - With fewer than 17 givens, a puzzle never has exactly one answer. - Experienced solvers even use the one-answer rule as a technique. ## The short answer Yes, if it is badly made. A proper Sudoku has exactly one solution, and careful puzzle makers check that before they publish. When a puzzle has two, the logic runs out: some squares could go either way, and nothing on the board decides which. ## One given makes the difference This is puzzle 3 on Medium sheet 1 from our printable Sudoku, with one given taken out: the 8 in row 4, column 9. The original has exactly one answer. Without that 8, it has exactly two. They agree everywhere except the 4 marked squares, where the same two digits swap places: ```text 5 7 . | . 2 . | . . . 6 2 3 | 4 . 1 | . . 9 . . 1 | 5 . 9 | . . . ------+-------+------ . . 6 | . 3 . | . . . . . 8 | . 9 5 | 3 . . . 3 4 | . . . | 7 9 5 ------+-------+------ . . 7 | . 5 . | 1 . . 8 4 . | . . . | 9 5 . . 6 5 | 9 . 2 | 8 . . ``` *Medium, sheet 1, puzzle 3, with one given taken out: the two answers differ only in the marked squares.* | Square | Answer 1 | Answer 2 | |---|---|---| | Row 1, column 8 | 8 | 1 | | Row 1, column 9 | 1 | 8 | | Row 4, column 8 | 1 | 8 | | Row 4, column 9 | 8 | 1 | ## Why two answers is a problem Solving is ruling out. With two answers, no amount of ruling out can settle the marked squares, because each digit there is right in one answer and wrong in the other. You have to guess, and either guess finishes the grid. That is why a puzzle with more than one answer is not considered a proper Sudoku. ## How few givens is too few A Sudoku with exactly one answer needs at least 17 givens: Gary McGuire, Bastian Tugemann and Gilles Civario announced in 2012, after an exhaustive computer search, that no 16-given puzzle has only one. But 17 or more is no guarantee. What matters is where the givens are, as the example above shows with 35 of them. [The mathematics of Sudoku →](https://sudokuflow.com/encyclopedia/math/) ## A technique built on it Experienced solvers turn the rule into a move. The Unique Rectangle looks for four squares in two rows, two columns and two boxes that could swap the same two digits, the pattern in the example above. If none of the four is a given, a proper puzzle cannot leave that choice open, so one of them must hold another digit. In the original puzzle, the given 8 is what stops the swap. 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We also make a Sudoku app for iPhone, iPad, Mac and Android. There are no ads in it at all, it works offline, and when you ask for a hint it shows you the technique instead of just filling in a number. [App Store iPhone, iPad, Mac](https://apps.apple.com/app/apple-store/id6502922368?pt=125379530&ct=sudokuflow_web&mt=8) [Google Play Android](https://play.google.com/store/apps/details?id=com.rubigogames.sudoku&referrer=utm_source%3Dsudokuflow%26utm_medium%3Dweb%26utm_campaign%3Dsite) Sudoku Flow is made by Rubigo Games, the developer of the Sudoku app recommended on this site.