Learn · Difficulty
What actually makes a sudoku hard
Almost every site labels puzzles Easy / Medium / Hard / Expert. Almost none of them can tell you what the label means. We measured it instead.
The clue-count myth
The intuitive story is that fewer given digits means a harder puzzle. It is true at the extremes and false almost everywhere else. Here is the actual distribution across the 893,916 puzzles in our public source, grouped by the difficulty the source assigned:
| Source tier | Puzzles | Mean clues | Median | 10th–90th pct | Need chains |
|---|---|---|---|---|---|
| Easy | 100,000 | 30.3 | 30 | 25–36 | 0% |
| Medium | 352,643 | 27.8 | 28 | 26–30 | 0% |
| Hard | 321,592 | 27.8 | 28 | 26–30 | 37% |
| Extreme | 119,681 | 27.6 | 28 | 25–30 | 100% |
Read the median column. Medium, Hard and Extreme all sit at 28 clues. You cannot tell a hard puzzle from an extreme one by counting digits. What changes is which technique the puzzle forces you to use — and that is what we grade.
The technique ladder
Human solving techniques form a ladder. Each rung is harder to spot than the last, and — importantly — each rung can be given a cost. We use the same scale as the classic Sudoku Explainer, because it is the only one that is publicly documented and reproducible:
| Technique | Weight | What you do |
|---|---|---|
| Full House | 1.1 | the last empty cell in a unit |
| Naked Single | 2.0 | a cell with one candidate left |
| Hidden Single | 2.6 | a digit with one home in a unit |
| Locked Candidates | 3.0 | pointing / claiming eliminations |
| Naked / Hidden Pair | 3.0 / 3.4 | two digits locked into two cells |
| Naked / Hidden Triple | 3.6 / 4.0 | three digits, three cells |
| X-Wing | 4.2 | a rectangle across two lines |
| Swordfish | 4.6 | the three-line version |
| XY-Wing | 4.8 | a pivot and two pincers |
A puzzle's score is the sum of the weights of the steps needed to finish it. But the sum is not the whole story: a puzzle that needs forty singles is easier than one that needs a single XY-Wing. So the tier is set by the hardest technique required, with clue count used only as a tie-breaker.
What the tiers actually contain
We solved a random sample from each source tier with the technique solver and recorded which techniques were required at least once. This is the table nobody publishes:
| Technique | Easy | Medium | Hard | Extreme |
|---|---|---|---|---|
| Naked Single | 100% | 100% | 94% | 73% |
| Hidden Single | 51% | 85% | 100% | 98% |
| Locked Candidates | 0% | 29% | 90% | 91% |
| Naked Pair | 0% | 5% | 43% | 33% |
| Naked Triple | 0% | 1% | 25% | 21% |
| Hidden Pair | 0% | 0% | 5% | 3% |
| Hidden Triple | 0% | 0% | 2% | 2% |
| X-Wing | 0% | 0% | 10% | 7% |
| XY-Wing | 0% | 0% | 17% | 11% |
| Not solvable by these 9 | 0% | 0% | 37% | 100% |
Three results are worth staring at:
- Easy puzzles never need an elimination technique. Not once in the sample: 0% require locked candidates, pairs or anything beyond a single. That is what "easy" should mean, and it is why we grade them 100% naked-single-driven.
- Locked candidates are the real dividing line. They appear in 29% of Medium puzzles but 90% of Hard ones. If you cannot spot pointing pairs, Hard is where you will stall.
- “Extreme” is a different kind of puzzle. 100% of the hardest tier cannot be finished with any of the nine techniques — they need forcing chains or search. That is the honest definition of expert: not "fewer clues", but "no single-deduction path to the end".
How our four tiers map
| Tier | What it guarantees | What it avoids |
|---|---|---|
| Easy | solvable with full house and naked/hidden singles | any pencil-mark-only technique |
| Medium | at most locked candidates, pairs and triples | fish and wings |
| Hard | at most one fish or triple-level pattern | XY-Wings and chains |
| Expert | anything up to XY-Wings; chains allowed | — |
Every puzzle page shows the techniques it needs and its score, so you can audit the label yourself. If a puzzle's label ever looks wrong, the technique list is right there next to the board.
Reproducing this
The rating is done by the same solver that powers the hint button, so you can check any claim: open a puzzle, press H, and the hint will name the technique it is about to use. The corpus scan behind the tables above runs on every build of this site.