Sudoku Difficulty Rating (SE) Explained

Updated 23 August 2026

An SE rating is a sudoku difficulty score on the Sudoku Explainer scale — roughly 1.0 to 12.0 — that grades a puzzle by the hardest human solving technique its cheapest logical solve path requires. It is a claim about reasoning depth, not about how many cells start blank, which is why two grids with identical clue counts can sit several points apart on the same scale.

What an SE rating measures

Sudoku Explainer, the Java solver the scale is named after, solves a puzzle the way a disciplined human would: it tries the cheapest technique it knows, applies the one step that technique justifies, and starts over. Each technique carries a fixed cost, and the puzzle’s rating is the highest cost the solver had to pay anywhere along that path. A grid that never needs more than a hidden single is rated at the hidden-single cost no matter how many of them it takes. That single-worst-step rule is what makes SE a difficulty measure rather than a length measure — and it is the number behind almost every “world’s hardest sudoku” claim, including the puzzles on our hardest sudoku puzzles page, where every landmark rating is attributed to its publisher or to the wider solving community rather than measured by our own rater.

The technique-to-rating ladder

The ladder runs from the techniques every beginner uses to the ones almost nobody applies unaided. Singles occupy the bottom, with the hidden single pinned at 1.5. Intersections and subsets — pointing pairs, box-line reductions, naked and hidden pairs — sit above the singles and below the fish patterns. Basic fish carry published values: an X-Wing is 3.2 and a swordfish is 3.8. Above them sit the wings and chains — XY-Wing, X-Chain, XY-Chain, simple coloring and AIC — and above those, forcing chains and nets, which start at 7.0 and carry every puzzle in the 8.0-and-up range. Our rating package implements that table directly, and it is honest about where it stops: a board whose cheapest solve path needs something the detectors cannot price comes back as 8.5 with a ceiling flag set, never as an invented number.

What a tier guarantees

A tier here is not a blank-cell target. It is a pair of technique ladders. A candidate board is solved twice: once with the ladder of the tier below it, which must fail, and once with its own ladder, which must succeed. Miss either test and the board is thrown away and a new one is generated. That is what the “guaranteed band” column below states, and it is why two adjacent tiers can sit one clue apart and still be different puzzles. The table solves 40 fixed puzzles from each of our six tiers with the full technique registry and records what each one actually demanded.

Read the clue column and the band column against each other. Medium starts with 27 clues and Hard with 26 — a difference of one given — yet no Medium board in the sample needs a fish or a wing and every Hard board does. Nightmare removes one more clue and moves an entire band, from wings to chains. Meanwhile Newbie hands you 37 clues and Nightmare 25, 12 fewer, across a span that runs from SE 1.5 to 2.3 to SE 4.5 to 7.3. Clue count is not what separates these tiers; the technique contract is. The full argument lives in our clues versus difficulty guide.

Which techniques our tiers really require

The next table counts how many of the 40 sampled puzzles per tier required each technique at least once. Because our solver always takes the cheapest available step, a technique appears here only when nothing simpler would move the grid.

How our six tiers map today

Newbie and Easy are the two singles tiers, and they are genuinely different puzzles even though they share an SE range: a Newbie board falls to full houses and naked singles, an Easy board provably does not and needs a hidden single. They overlap on the scale only because SE prices a hidden single at 1.5, below a naked single at 2.3. Medium is the intersections-and-subsets tier at SE 2.6 to 3.4, Hard the fish-and-wings tier at SE 3.4 to 4.4, and Nightmare the chain tier at SE 4.5 to 7.3. Hell, drawn from a verified 17-clue corpus rather than generated to a band, measures SE 6.7 to 7.8 — a narrower band that starts higher than Nightmare and ends only slightly above it, with 8 of 40 boards reaching a forcing chain.

That is the honest answer to “how hard is expert sudoku, actually”: the ladder rung is the difficulty, and everything else — clue count included — is packaging. Browse the difficulty levels hub or the technique index for the patterns themselves.

Where our rating stops

Our rater prices the SE ladder up to forcing chains and nets, and no further. A board whose cheapest path needs something past that comes back as exactly 8.5 with a ceiling flag rather than a fabricated 10 or 11 — so a rating of 8.5 on this site should be read as “8.5 or above”, never as a precise score. That matters at the top of the scale: the record puzzles on our hardest sudoku puzzles page are quoted at values independent raters publish, because our own engine would report them at the ceiling. Nothing we generate comes close: no board in the sample below reached the ceiling, and the “past our detectors” column is 0 of 40 in every tier, so nothing on this page rests on a puzzle the registry could not finish. You can watch the same registry work step by step in the sudoku solver.