Sudoku Made and maintained by Brian Hamilton and Karan Hamilton.
Brian builds the playable puzzle tools, while Karan helps test clarity, difficulty feel, and the player experience.
Playable puzzles and controls are tested in the browser for rule accuracy, usability, and a clear solving experience. See how we make and test puzzles, our editorial standards, or report a problem.
What is Greater Than Sudoku?
Greater Than Sudoku is ordinary sudoku with signs between some pairs of neighbouring squares. Fill the grid so that:
- every row, column and 3×3 box holds 1 to 9 exactly once;
- and wherever a sign sits between two squares, it opens toward the larger digit and points at the smaller, like > and < in arithmetic.
Signs run both ways: across a row they read as > and <, and down a column the same shape is turned on its side. A sign only compares its two squares; it says nothing about how far apart they are.
A 9×9 grid has 144 borders between neighbouring squares, and every one of them separates a larger digit from a smaller one. This page shows a share of those signs — 100 on Easy, 72 on Medium, 44 on Hard and 32 on Expert — and a border without a sign is simply not a clue. That is not true of every variant: on Battenburg Sudoku every marker is shown, so a missing one is a clue.
How do you read a sign?
A sign turns a digit into a range. Next to a given digit it cuts the empty square to the digits on the right side of that given; write that into your pencil marks straight away:
Signs between two empty squares work too, and they work in chains. If A > B > C, then A is at least 3 and C at most 7 before anything else is known, and every mark you strike at one end can move the next square along:
Across 40 boards per level, reading the signs this way strikes a median of 54 pencil marks on Easy and 43 on Expert before any digit is placed. On Easy that settles 18 squares outright and takes an empty square from 2.9 candidates to 1.7; on Expert, with far fewer signs, it settles 2 and takes a square from 4.7 to 3.9.
Do the signs actually do any work?
Every board this page deals is built so that the answer depends on them: the generator removes digits until the puzzle has one answer with the signs, then checks the same givens without the signs and keeps digging until they no longer have one. On the board above:
We checked 160 fresh boards, 40 per level: every one has a single answer with its signs and more than one without them. Without the signs, Easy givens have a median of 4 answers, Medium 38, and Hard and Expert a median of more than 200.
That was not true before this rewrite. The old generator blanked random squares, showed a random share of the signs, and kept the board if its search counted one answer; after five tries it dealt whatever it had. On Expert that fallback fired on 32 boards in 40, and 31 of those had more than one answer — a median of 21 — so a correct solve could be marked wrong. On Easy, 5 boards in 40 did not need their signs at all. The generator now checks every removal, never deals an unchecked board, and deals each level in about 1 to 3 milliseconds.
How do the four levels differ?
We ran 40 fresh boards per level through a solver that knows one technique at a time, then took techniques away to see which boards stopped. Reading the signs is the variant’s own move, and the solver does it for free before each step.
| Level | Given digits | Signs shown | Squares the signs settle at first look | Singles finish it | Beyond our solver |
|---|---|---|---|---|---|
| Easy | 30–36 | 100 | 18 | 100% | 0% |
| Medium | 29–30 | 72 | 11 | 100% | 0% |
| Hard | 22 | 44 | 3 | 85% | 15% |
| Expert | 21 | 32 | 2 | 45% | 35% |
40 boards per level from this page’s generator, fixed seed; medians, and shares rounded. The solver knows naked and hidden singles, locked candidates, naked pairs and triples, and the X-Wing; “beyond our solver” boards still have exactly one answer. Easy sometimes comes in a few givens under 36, when that is what it takes for the signs to matter.
The signs do most of the work on the easier levels. With 100 signs, an Easy board settles 18 squares before you place a digit, and singles finish every Easy and Medium board once the signs are read. Hard is where it starts to bite: 34 of 40 boards still fall to singles. Expert gives only 32 signs and 21 digits, and 14 of its 40 boards go beyond everything our solver knows. Hard used to give 25 digits and 35% of the signs, and every Hard board fell to singles like Easy; it now gives 22 and 30%, between Medium and Expert.
The generator fills a grid, reads the signs off it, and removes digits one at a time, keeping a removal only while the puzzle still has exactly one answer with those signs; a search it cannot finish answers “not proven” and the digit stays. We re-solved 160 fresh boards with a separate counter written for the purpose: every one had exactly one answer. The deepest uniqueness check took 33 search steps of the 4,000 it is allowed.
Which level should you play?
If you already play sudoku, start on Medium. It is ordinary sudoku in which the signs do a good share of the work, and every board falls to singles once you read them. Easy is for learning to read signs quickly: it settles 18 squares before you begin.
Hard asks for more patience than technique; most boards still fall to singles once the signs are read, but there are fewer of them to read. Expert is the real step: one board in three goes beyond singles, locked candidates and pairs, though every one has exactly one answer.
What goes wrong on a Greater Than Sudoku
- Reading a sign backwards. The open side faces the larger digit, the point faces the smaller. Down a column the same shape is turned on its side, so check which way it opens.
- Treating a missing sign as a clue. On this page a border without a sign says nothing at all about its two squares.
- Only reading signs next to givens. A sign between two empty squares still cuts both: the larger can never be 1, the smaller never 9, and each is bounded by what the other can still hold.
- Stopping after one pass. A mark struck in one square can cut the next square along a chain. Go round the signs until nothing changes.
- Forgetting how far a chain reaches. In a chain of four squares, A > B > C > D, the first is at least 4 and the last at most 6.
Where does Greater Than Sudoku come from?
The idea comes from Futoshiki, a Japanese puzzle whose name means “inequality”. It was developed by Tamaki Seto in 2001 and uses a Latin square — each row and column holds every digit once, with no boxes — and signs between some neighbouring squares. It now runs in several British newspapers, including The Guardian and The Times. This page used to say Futoshiki had been popular in Japan since the 1990s; it did not exist until 2001.
Putting Futoshiki’s signs on a sudoku grid gives Greater Than Sudoku, also called Comparison Sudoku. By August 2006 it was already circulating under both names — a Wikipedia illustration from that month calls it “a new version of sudoku” — but we have not found a well-sourced account of who first made one.
What do the buttons do?
Select a square, then a digit from 1 to 9; the page opens on Medium. Selecting a square highlights its row, column and box, and a wrong digit is marked the moment it goes in. Under the grid:
- Notes turns pencil marks on and off. A correct digit clears itself from the notes of its row, its column and its box; a wrong one leaves your notes alone.
- Erase clears the selected square, and pressing the same digit twice does the same.
- Undo takes back the last change to a square, though not the notes a correct digit cleared elsewhere, and not the Mistakes count.
- Hint fills one square with its answer, picked at random rather than the square you could work out next.
- Solve asks first, then fills the grid and stops the timer.
- New Game deals another board at the level you are on; the level buttons deal one at theirs.
Digits 1–9, the arrow keys, Backspace or Delete and Ctrl+Z all work from a keyboard. The board is saved in this browser after every move, so it is waiting when you come back.
Where to go next
Greater Than Sudoku compares neighbours one pair at a time. Thermo Sudoku runs the same idea along a whole line, each digit larger than the one before. Kropki Sudoku also marks the border between neighbours, with dots that say the two differ by one or that one is double the other, and Consecutive Sudoku keeps only the first of those two relations.