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 Anti-Knight Sudoku?
Anti-Knight Sudoku is ordinary sudoku with one rule borrowed from chess. Fill the grid so that:
- every row, column and 3×3 box holds 1 to 9 exactly once;
- and no two cells a knight’s move apart hold the same digit — two squares in one direction and one across, the chess knight’s L.
Nothing on the grid marks the rule. It applies everywhere, to every cell, and a cell may have anything from two to eight squares a knight’s move away. Diagonal neighbours are not knight squares: two cells touching at a corner may hold the same digit whenever they are in different boxes.
A knight’s move never stays in a row or a column, but it can stay inside a box: from R1C1 it reaches only R2C3 and R3C2, and both are already in R1C1’s own box. Every cell except the nine box centres has exactly two of its knight squares inside its own box, where the ordinary rules already forbid a repeat. Of the 224 knight pairs on the board, 72 are like that, so the rule really adds 152.
What does the knight rule tell you before you place anything?
Picture the knight squares of every given. Each one takes the given’s digit away from up to eight more cells than an ordinary sudoku would, and how many depends on where the cell sits:
| Cell | Where on the grid | Knight squares | Outside its box | Peers |
|---|---|---|---|---|
| R1C1 | The four corners (4 cells) | 2 | 0 | 20 |
| R1C2 | Edge squares next to a corner (8 cells) | 3 | 1 | 21 |
| R1C5 | The rest of the edge (20 cells) | 4 | 2 | 22 |
| R2C2 | One step in diagonally from a corner (4 cells) | 4 | 4 | 24 |
| R2C3 | The second ring, apart from those and its four middles (16 cells) | 6 | 4 | 24 |
| R2C5 | The middle of each side of the second ring (4 cells) | 6 | 6 | 26 |
| R3C3 | The inner 5×5, apart from its centre (24 cells) | 8 | 6 | 26 |
| R5C5 | The centre | 8 | 8 | 28 |
“Peers” are the cells that may not repeat a cell’s digit: the 20 in its row, column and box, plus its knight squares outside the box. Averaged over the 81 cells that is 23.75, about a fifth more than ordinary sudoku’s 20. The rule is strongest in the middle of the grid and does nothing at the corners.
So on a real board, keep the knight squares in your pencil marks from the start:
It is a steady trickle, not a flood. Across 40 boards per level, the knight squares of the givens strike a median of 17 pencil marks on Easy and 29 on Expert before any digit is placed, and settle four cells outright on Easy and two on Medium. An empty cell on Easy starts with 2.7 candidates from its row, column and box and 2.3 once the knight squares are counted. The real work comes later: every digit you place takes itself out of its knight squares too, so the rule keeps paying out all the way through the solve.
Does the knight rule actually do any work?
Every board this page deals is built so that the answer depends on it: the generator removes digits until the puzzle has one answer under the knight rule, then checks the same givens as ordinary sudoku 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 the knight rule and more than one without it. As ordinary sudoku, Easy givens have a median of three answers and up to 27, Medium a median of 20, and Hard and Expert more than 200 on every board we tried. A solver that ignores the knight rule stalls on every board at every level.
This page’s generator already got that right before this rewrite — its uniqueness check was complete, and 160 of 160 boards passed the same test. What it got wrong was speed: it filled the grid one cell at a time with no look-ahead, and the worst of 1,000 fills we timed needed over 100,000 steps. A board took 25 to 57 milliseconds at the median and up to 310 on a desktop, all of it while the page loaded; on a phone that is a visible freeze. The rewrite deals the same kind of board in about 2 to 4 milliseconds, 9 at worst.
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. The knight rule is not a technique here: like a row or a box, it simply clears a placed digit from the cells it reaches.
| Level | Given digits | Marks the knight rule strikes at first look | Cells it settles | Singles finish it | Needs locked candidates | Needs a subset | Beyond our solver |
|---|---|---|---|---|---|---|---|
| Easy | 34–38 | 17 | 4 | 100% | 0% | 0% | 0% |
| Medium | 29–30 | 21 | 2 | 98% | 3% | 0% | 0% |
| Hard | 25 | 26 | 0 | 83% | 15% | 0% | 3% |
| Expert | 21 | 29 | 0 | 28% | 53% | 3% | 18% |
40 boards per level from this page’s generator, fixed seed; medians, and shares rounded, so a row can add up to a little over 100. Our locked-candidates step includes the knight version: when every place left for a digit in a house sees one cell, by row, column, box or knight’s move, that cell loses the digit. The solver also knows naked pairs and triples and the X-Wing; “beyond our solver” boards still have exactly one answer. Easy and Medium come in a few givens under target when that is what it takes to make the knight rule load-bearing.
The levels are real steps, and Expert is a big one. Naked and hidden singles, with the knight squares cleared, finish every Easy board and 39 of 40 Medium. Hard is where locked candidates arrive, on about one board in seven. On Expert singles alone finish little more than one board in four: half need locked candidates, and about one in six goes beyond everything our solver knows. This page used to promise that Hard needed pairs and pointing pairs; measured, Hard is singles more than four times in five.
The generator fills a grid that already obeys the knight rule, then removes digits one at a time, keeping a removal only while the puzzle still has exactly one answer; 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, and every solution kept every knight pair apart. The deepest uniqueness check took 84 search steps of the 4,000 it is allowed.
Which level should you play?
Start on Easy, even if ordinary sudoku is easy for you. The knight rule is invisible, and the first few boards are about the habit of checking the L-shapes at all; on Easy every board falls to singles once you do. Medium is the same skill with fewer givens, so less comes free at the start and more comes from the knight squares of the digits you place.
Hard adds locked candidates on about one board in seven, including the knight version, where a digit squeezed into two or three cells of a box rules itself out of every cell all of them reach. Expert is a real step: fewer than a third of its boards fall to singles. Every board still has exactly one answer, and none needs guessing.
What goes wrong on an Anti-Knight Sudoku
- Forgetting the rule. Nothing on the grid reminds you. A board that stalls halfway is usually one where a digit was placed without clearing its knight squares.
- Counting the corners. A corner’s two knight squares are in its own box, so the rule tells you nothing new there. Look to the middle of the grid, where a cell reaches eight.
- Confusing it with a king’s move. Cells that touch diagonally are not a knight’s move apart. In different boxes they may hold the same digit.
- Checking one direction. The knight moves both ways: a 5 at R3C4 rules 5 out of R5C5, and a 5 at R5C5 would rule it out of R3C4. Every pair is checked from both ends, so clear the whole L-shape every time.
- Expecting the rule to replace the ordinary ones. It adds peers; it does not take any away. Rows, columns and boxes still do most of the work on every board.
Where does Anti-Knight Sudoku come from?
Michal Stajszczak introduced it on Ed Pegg’s puzzle site mathpuzzle.com on 20 August 2006, as “a new (I hope) variant of sudoku”: standard sudoku, with the same numbers never “knight move connected”. Competition setters picked it up under names such as “No Knight Step Sudoku”, and it became widely known in May 2020 through Mitchell Lee’s “Miracle Sudoku”, which combined the anti-knight rule with an anti-king rule and a ban on consecutive neighbours and started from just two given digits. Alex Bellos ran it as his Monday Puzzle in the Guardian on 18 May 2020, and the YouTube channel Cracking the Cryptic’s solve of it went viral.
What do the buttons do?
Select a cell, then a digit from 1 to 9; the page opens on Medium. Selecting a cell highlights its row, column and box and the squares a knight’s move away, and a digit that repeats in any of them is marked as a clash. Under the grid:
- Notes turns pencil marks on and off. A correct digit clears itself from the notes of its row, its column, its box and its knight squares; a wrong one leaves your notes alone.
- Erase clears the selected cell, and pressing the same digit twice does the same.
- Undo takes back the last change to a cell, though not the notes a correct digit cleared elsewhere, and not the Mistakes count.
- Hint fills one cell with its answer, picked at random rather than the cell 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
Anti-Knight Sudoku is the variant that adds an invisible rule rather than drawing one. X-Sudoku adds the two long diagonals as extra houses, and Hyper Sudoku adds four shaded boxes; both keep the new constraint in plain sight. Kropki Sudoku is the other variant here built on neighbouring cells, with dots that say how two touching digits relate, and Killer Sudoku is the one to try if you would rather have arithmetic than geometry.