Sudoku FlowCan 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
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:
| 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.
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.
Practice
Every Find the Mistake puzzle on this site has exactly one wrong digit, and you can play each board right on its page.
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