What makes a sudoku hard? We tested 500 puzzles by clue count
Printed sudoku are sold as easy, medium or hard, and the number most people reach for is the clue count: how many squares are filled in when you start. We generated 100 puzzles at each of our five levels and solved each one with only the two simplest techniques. The clue count predicts a lot, but not everything: 18 of 100 Expert puzzles, with just 24 clues, fell to those two techniques alone.
The two simplest techniques
- Only one number fits this square (a naked single): the row, column and box already use the other eight.
- This number fits only one square (a hidden single): in some row, column or box, only one empty square can still take it.
Beginners use both without knowing the names. Harder techniques start where these stop: pairs, pointing, X-wings and more.
What we measured
For each level we generated 100 sudoku with the same code that makes the puzzles on this site, puzzle numbers 1 to 100, and tried to finish each one using only those two techniques, repeated until nothing more could be placed.
| Level | Clues | Finished with singles only | Share |
|---|---|---|---|
| Gentle | 45 | 100 of 100 | 100% |
| Easy | 38 | 98 of 100 | 98% |
| Medium | 32 | 71 of 100 | 71% |
| Hard | 28 | 33 of 100 | 33% |
| Expert | 24 | 18 of 100 | 18% |
So the rough rule holds: fewer clues, harder puzzle. At 45 and 38 clues nearly everything falls to the basics. By 28 clues two thirds of puzzles need more. But inside each level the spread is wide. 29 of the 32-clue Medium puzzles need a harder technique somewhere, and 18 of the 24-clue Expert ones need none.
Why clue count is not difficulty
Difficulty depends on where the clues are, not only how many. Two puzzles with the same count can open very differently: in one, every step reveals the next single; in the other, the first useful deduction needs a pattern across three boxes.
That is why each of our levels is defined by its clue count, and nothing more. A generator that promises "difficulty" has to grade every puzzle by the techniques it needs. Ours does not, and this guide is where we say so.
One rule that does not bend: exactly one solution
A sudoku with two solutions is broken. At some point you have to guess, and the answer key may not match your correct grid. Every puzzle on this site is checked by a solver that counts solutions and stops at two; if it finds a second, the puzzle is thrown away and another is made.
The fewest clues a standard sudoku can have and still have one solution is 17. That was settled in 2012 by an exhaustive computer search showing that no 16-clue sudoku exists. Our Expert level stops at 24.
How a sudoku on this site is made
- Fill a complete, valid 9 by 9 grid at random. That grid is the answer key.
- Remove clues one pair at a time, in the mirror positions that give the grid its symmetry.
- After each removal, count the solutions. If there is still exactly one, keep going; if there are two, put the pair back and try another.
- Stop at the level's clue count: 45, 38, 32, 28 or 24. The 4 by 4 grids for children keep 6 clues and the 6 by 6 keep 15.
Nothing in those steps looks at which techniques a puzzle needs, which is exactly why the table above spreads the way it does.
Choosing a level
- New to sudoku: Gentle or Easy. In our test, every Gentle puzzle and 98 of 100 Easy ones could be finished with the two basic techniques.
- Comfortable with the basics: Medium. About seven in ten need nothing more, and the rest are where most people learn their first harder technique.
- Looking for a challenge: Hard or Expert. Expect to need more than singles in two thirds or more of them, and to meet the odd Expert that turns out gentle.
- Children: start with the 4 by 4 grids, then the 6 by 6.
Symmetry, and why the hardest ones may lose it
Printed sudoku traditionally have 180 degree rotational symmetry: turn the grid upside down and the clues sit in the same pattern. Our generator removes clues in symmetric pairs. At the lowest counts, removing a pair often breaks the one-solution rule, so for the hardest levels it finishes one square at a time and the symmetry may not survive. We chose the promised clue count over the pattern.
What this guide does not decide
- How hard a puzzle feels to you. Speed and experience matter more than any label.
- Which advanced techniques each puzzle needs. We only tested the two simplest ones.
Print them
Frequently asked questions
Does a sudoku with fewer clues mean a harder puzzle?
Usually, not always. In our test every 45-clue puzzle could be finished with the two simplest techniques, against 18 of 100 with 24 clues. Yet 29 of 100 puzzles with 32 clues needed a harder technique.
What is the minimum number of clues for a sudoku?
Seventeen. A 2012 exhaustive computer search showed that no standard sudoku with 16 clues has exactly one solution.
Can a sudoku have two solutions?
A badly made one can, and then it cannot be solved without guessing. Every sudoku on this site is checked to have exactly one.
Check these numbers yourself
- Our own test: 100 puzzles per level from the site's generator, seeds 1 to 100, solved with naked and hidden singles only, with our own script, run September 27, 2026.
- McGuire, Tugemann and Civario, "There is no 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem" (2012; published in Experimental Mathematics, 2014).