Strategy
Why a proper Sudoku has exactly one solution
A proper Sudoku never needs guessing because it has exactly one solution. Here is why that matters and how it is checked.
A proper Sudoku has exactly one solution, so logic can always decide each digit. Setters check this with a program that searches for every solution. The fewest clues that can give a unique solution is 17, which was proved by computer in 2012.
Why uniqueness matters
If a puzzle had two solutions, no cell could ever be forced by logic, because the cell might hold different digits in different solutions. Uniqueness is what makes solving by deduction possible. It is also why you should never need to guess.
How uniqueness is checked
A solver program tries every possibility with a technique called backtracking, and counts solutions. If it finds exactly one, the puzzle is valid. Our solver does exactly this and tells you if your grid has none, one or several solutions.
Why at least 17 clues
With too few digits, there is room for several solutions. Mathematicians searched all possible puzzles with 16 clues and found none with a unique solution, so 17 is the minimum. Puzzles with 17 clues exist but are very hard to solve by logic.
How many Sudoku grids exist
There are 6,670,903,752,021,072,936,960 valid completed 9 by 9 grids. If you count grids that are the same under rotation, reflection and relabeling of digits, there are about 5.47 billion different ones. Each completed grid can produce many puzzles by removing digits.
Uniqueness is not the same as easy
A puzzle can have a unique solution and still be extremely hard. That is why our puzzles are also graded by technique, not just by uniqueness. Read about difficulty levels and how we verify every puzzle.
Frequently asked questions
Why does every Sudoku have one solution?
Because puzzle setters design it that way and check it with a program. A puzzle with several solutions is considered flawed.
What is the minimum number of clues?
17.
How many Sudoku grids are there?
About 6.67 sextillion completed grids, and about 5.47 billion if you ignore symmetries.