Why does my sudoku have more than one solution?
The four real causes, the rectangle pattern that guarantees a second solution, why 17 is the famous number, and what a solver actually checks.
A sudoku is only a puzzle if it has exactly one solution. That is not a stylistic preference — it is what makes reasoning possible. If two different completed grids both fit the clues, then at some point no amount of logic can tell you which way to go, and the only way forward is to pick one and see.
If you have hit that, there are four realistic causes.
1. You made a mistake earlier
This is by far the most common, and it disguises itself well. A wrong digit placed twenty moves ago does not usually produce an immediate contradiction. It produces a position where two cells look interchangeable, because the constraint that would have separated them was destroyed by the bad entry.
The test is quick: check every digit you entered yourself against the row, column and box rule. If any digit appears twice in a unit, that is your answer and nothing about the puzzle is wrong. An app that highlights mistakes will show this immediately; on paper you have to check by hand.
2. The deadly rectangle
This is the one that genuinely guarantees two solutions, and it is worth being able to recognise.
Suppose four cells sit at the corners of a rectangle: two rows, two columns, and — this part matters — only two boxes. Suppose all four of those cells are empty and each can only be one of the same two digits, say 2 and 5.
Then whatever solution you find, you can swap all four: turn every 2 into a 5 and every 5 into a 2 around the rectangle. Every row still has one of each. Every column still has one of each. Both boxes still have one of each, because each box holds one full side of the rectangle. Nothing else on the grid is touched. So a second, equally valid solution always exists.
The two-box requirement is what makes it work. If the four corners fall across four different boxes, the swap breaks the box constraint and the pattern is harmless.
Experienced solvers use this in reverse: in a puzzle they trust to be proper, they know the deadly pattern cannot occur, so they can eliminate the candidate that would create it. That inference is only sound if the puzzle really was verified unique — which is why it is a shortcut and not a technique.
3. Too many clues were removed
If you built the puzzle yourself, or removed digits from a finished grid, uniqueness is not automatic. Every cell you empty is a constraint you delete, and there is no warning at the moment you cross the line.
The known lower bound is 17. In 2012 an exhaustive computer search by McGuire, Tugemann and Civario established that no sudoku with 16 clues has a unique solution, and 17-clue puzzles do exist. Note what that does and does not say: 17 is a floor, not a guarantee. Most 17-clue arrangements have many solutions, and plenty of 25-clue arrangements have several too. The count tells you almost nothing; only checking tells you.
4. The generator never checked
Some puzzle sources — free grid printers, older apps, puzzles scraped from elsewhere — dig holes until they hit a clue count and ship the result. Uniqueness testing costs real work, and skipping it is invisible until a player runs into an ambiguous position and assumes they made a mistake.
What a real check looks like
Verifying uniqueness means counting solutions, not finding one. A solver runs its normal search but does not stop at the first complete grid; it keeps going. The trick that makes it cheap is an early exit: you never need the total, only whether it is one or more than one, so the count is capped at two and the search abandons the moment it finds a second.
Sudoku - Calm Number Puzzle applies this after every single dig. Cells are removed in symmetric pairs, and after each removal the solver counts with a limit of two. If the answer is not exactly one, that pair is put straight back and the generator continues elsewhere. A puzzle that fails the check never reaches you, so an ambiguous position in this app always means cause number one.
A short checklist
- Two cells look interchangeable → check for a duplicate digit you entered, first.
- Four empty corners, two rows, two columns, two boxes, two shared candidates → deadly rectangle, the puzzle genuinely has two solutions.
- You removed the clues yourself → assume nothing; count the solutions.
- A printed or scraped grid you cannot verify → the source may never have checked.
Frequently asked questions
What is the minimum number of clues for a unique sudoku?
Seventeen. A 2012 exhaustive search by McGuire, Tugemann and Civario proved no 16-clue sudoku has a unique solution, and valid 17-clue puzzles are known. It is a floor for the whole space of puzzles, not a property any particular 17-clue arrangement has.
If a puzzle has two solutions, is it still solvable?
You can complete it, but not deduce it. At some point you have to choose between two consistent options with no logical reason to prefer either. Most solvers would say that stops being sudoku at that point.
How can I tell if a puzzle has a unique solution?
You have to count solutions with a solver — there is no visual test. The one exception is the deadly rectangle: four empty corner cells spanning two rows, two columns and two boxes, each with the same two candidates, guarantees at least two solutions without any further checking.
Does this app ever produce a puzzle with two solutions?
No. Uniqueness is checked after every cell removal during generation, and any removal that breaks it is reverted immediately. A puzzle that is not unique is never finished, let alone shown.
Try it on a real puzzle
Sudoku - Calm Number Puzzle grades every puzzle by the hardest technique it actually needs, verifies a single solution before you ever see the grid, and its hints name the technique instead of just filling in a digit. Free, offline, no ads and no account.