How Many Clues Does a Sudoku Need?
Every Sudoku starts with some numbers already filled in - the clues, or givens. Ask any solver and the question comes up sooner or later: what's the fewest clues a puzzle can have and still be solvable, with just one answer? The answer is a clean, proven number: 17.
The magic number: 17
A proper Sudoku must have exactly one solution. Take too many clues away and the grid becomes ambiguous - two or more valid fillings - which makes it a broken puzzle, not a hard one. It turns out you cannot go below 17: there is no valid Sudoku with 16 clues. Puzzles with exactly 17 do exist (thousands of them), and 17 is the floor.
How we know
This isn't a guess or a rule of thumb - it's a mathematical result. In 2012 a team at University College Dublin - Gary McGuire, Bastian Tugemann and Gilles Civario - ran an exhaustive computer search across the space of all Sudoku grids, checking whether any 16-clue puzzle could have a unique solution. None could. The search took roughly seven million CPU-hours and was published as "There is no 16-Clue Sudoku". Since then, 17 has been settled as the true minimum.
To give a sense of the haystack they searched: there are exactly 6,670,903,752,021,072,936,960 completed 9×9 Sudoku grids (Felgenhauer & Jarvis, 2005) - about 6.7 sextillion. Proving something about all of them is no small feat.
What this means for difficulty
Fewer clues generally means a harder puzzle - but the link isn't exact. A 17-clue grid is guaranteed to be demanding, yet a cleverly built 22-clue puzzle can be nastier than a plain 18. On SudokuStreak the difficulty levels are tuned by clue count as a starting point:
- Easy - 36 givens
- Medium - 30 givens
- Hard - 26 givens
- Expert - 25 givens
- Evil - 23 givens, about as lean as a generated board gets
What never changes is uniqueness: however few the givens, every puzzle we generate has exactly one solution, reachable by logic alone - you never have to guess.
The other extreme
There's no fixed maximum, but you can keep adding clues only up to a point: the most givens a puzzle can have while every clue still matters (removing any one would create a second solution) is 40. Beyond that, some clues are redundant. Most published puzzles sit comfortably between the low 20s and high 30s - plenty of room between the 17-clue floor and the 40-clue ceiling.
None of this has to be taken on faith - the numbers are countable. Deal yourself an Evil board and count the digits it starts with; then do the same on Easy and see the gap the article is really about.