Sudoku · graded by the logic it takes

A thousand puzzles,
each graded by its hardest step.

Every puzzle here was generated offline, proved to have exactly one solution, and then solved the way a person solves one — the easiest step that makes progress, every time. Its grade is the hardest step it could not do without: singles, then pairs and triples, then pointing and claiming, then fish and wings. A puzzle that needed anything harder than that was thrown away, and the count of those is printed below.

Play today’s puzzle in any of the four grades, or any of the thousand. Pencil marks, undo, a check, and a hint that names the technique that applies next — the same solver that graded the puzzle, reading your board. Nothing is fetched while you play, and nothing you enter leaves this browser.

1,000 puzzles · four grades of 250 · one solution each · thirteen named techniques · nothing fetched

Play

Today’s puzzle, or any in the bank.

A grade opens that grade’s puzzle for today — the same one for everyone on your date. Type or tap digits; switch to notes for pencil marks. The hint names the technique first, shows the cells on a second press, and takes the step on a third.

Sudoku

Time on this puzzle: 0:00

The board appears here once the page’s script has run.

Sudoku runs in your browser. If this line stays, the page’s script did not load — reload the page.

What this puzzle takes — a mild spoiler

Open it to see every rung the grading solver used.

Keys: arrows move · 1–9 enter · Shift+1–9 or N for notes · Backspace erases · Ctrl+Z / Ctrl+Y undo and redo · H hint. On a touchscreen, tap a square, then a digit. The small figure under each digit on the pad is how many of it are still to place.

The four grades

Graded by the hardest step, not the count.

A grade is not a number of givens or of moves. It is the highest rung of the ladder the puzzle forced the solver onto — a moment when nothing easier anywhere on the board would do. Every puzzle in a grade needed that rung at least once. Your record beside each is kept in this browser and nowhere else.

1 Gentle

Singles only — a full house, a hidden single, a naked single. Clues were added back after thinning, so the first grade is also the friendliest.

2 Moderate

A naked or hidden pair or triple, at least once: two or three cells in a house that own two or three digits between them.

3 Tough

Pointing or claiming, at least once, at a moment when no single, pair or triple anywhere on the board would do.

4 Fiendish

An X-wing, a swordfish, an XY-wing or an XYZ-wing, at least once. Nothing beyond those: no chains, no colouring, no guessing.

Your record appears here once you solve a puzzle.

Method

How the bank was made, and how it is graded.

Made offline, proved twice

A script in this page’s own folder made the bank before the page was published; nothing is generated in your browser and nothing is fetched. For each seed it fills a blank grid at random, then empties it in pairs of squares a half-turn apart — which is why every puzzle looks the same upside down — keeping a pair whenever taking it out would let the puzzle have a second solution. What is left has exactly one. No puzzle was copied from a book, a newspaper or another site: the bank is this site’s own, and so are the grades.

That is proved twice, by two solvers that share no code: the page’s own depth-first search, and Knuth’s Algorithm X over the 324 exact-cover constraints of the grid, written separately in Python. Each stops at a second solution; both must find one, and the same one, or the build fails.

The ladder

Then a logical solver works each puzzle from the givens, always taking the first rung below that makes progress anywhere on the board — a placement or a struck candidate — and starting again from the top. The puzzle’s grade is the highest tier it had to use. The order of the rungs is this site’s choice and it is published here: pairs and triples are tried before pointing and claiming, so a Tough puzzle is one where, at some moment, no subset anywhere would do.

What the hint does

It runs the same ladder on your board: your digits, and your pencil marks wherever you have made some. First it checks that nothing you have entered is wrong and that no pencil mark rules out the digit that belongs there, because logic cannot go on from a wrong board. Then it names the first rung that applies; a second press shows the cells, a third takes the step. A step that strikes candidates pencils in the cells it touches first, so the strike has somewhere to land.

The daily puzzle

Today’s puzzle in each grade is picked from your local date by a fixed stride through that grade’s 250, so everyone on the same date gets the same four, and no puzzle comes round again for 250 days.

What stays in your browser

Your board, pencil marks, time, hints and checks, and the list of puzzles you have solved, are kept in this browser’s local storage under one key, labs.sudoku.v1, and never sent anywhere; “Forget my record” deletes it. The site’s usual analytics count the visit and that the tool was used — never a digit. The clock runs only while the board is on screen and the tab is in front.

Seeds 1 to 11,011 were tried, in order, until every grade held 250. Of those 11,011 puzzles, 7,424 (67.4%) finished on singles alone, 830 (7.5%) needed a pair or triple at most, 250 (2.3%) needed pointing or claiming, 472 (4.3%) needed a fish or a wing, and 2,035 (18.5%) needed more than the ladder has and were discarded. The bank keeps the first 250 of each grade: 1,000 puzzles.

The four grades, as shipped

GradeHardest rung allowedPuzzlesGivensMean givensMean steps
1 · GentleSingles25030–3632.948.1
2 · ModeratePairs and triples25024–3227.255.7
3 · ToughPointing and claiming25023–3227.157.3
4 · FiendishFish and wings25024–3227.757.8

The ladder, top to bottom, and how many puzzles in each grade used each rung

TierRungWhat it doesGentleModerateToughFiendish
1Full houseA house with one empty cell takes the one digit it is missing.250250250250
1Hidden singleA digit that fits in only one cell of a row, column or box goes there.250250250250
1Naked singleA cell with only one candidate left takes it.2174175165
2Naked pairTwo cells of a house that can only hold the same two digits own them; strike those digits from the rest of the house.—221151153
2Hidden pairTwo digits that fit only in the same two cells of a house own those cells; strike every other candidate there.—618271
2Naked tripleThree cells whose candidates, together, are only three digits own those digits.—152025
2Hidden tripleThree digits confined to the same three cells of a house own those cells.—275
3PointingA digit whose places in a box all lie on one row or column is struck from the rest of that line.——235146
3ClaimingA digit whose places in a row or column all lie in one box is struck from the rest of that box.——5454
4X-wingA digit confined to the same two columns in two rows (or the reverse) is struck from the rest of those columns.———70
4SwordfishThe X-wing over three rows and three columns.———12
4XY-wingA two-candidate pivot and two pincers: whichever way the pivot goes, one pincer holds z, so no cell seeing both can.———213
4XYZ-wingThe same with a three-candidate pivot: z is struck from cells that see the pivot and both pincers.———28

The limits

The ladder has thirteen rungs and stops at fish and wings: no chains, no colouring, no uniqueness arguments, no forcing. So Fiendish here is the hardest grade this solver can finish, not the hardest sudoku there is. A grade measures the hardest single step, not the length of the work — a Gentle puzzle can still take a while. The order of the rungs is one judgement among several; other graders rank pointing below pairs. The hints name a square by its row and column: r4c7 is row 4, column 7, counted from the top left. Questions and corrections: labs@labs.llc.