How to Play Killer Sudoku
Fill the 9 × 9 grid so every row, column and 3 × 3 box holds 1 to 9 once. On top of that, the dashed cages each carry a total their cells must add up to, and no digit may repeat within a cage. Because every row, column and box totals 45, the sums of the cages inside one tell you what the cells they miss must come to.
The rules, step by step
- 1Fill every cell with 1 to 9The grid has 81 cells. When it is full and every rule below holds, the puzzle is solved.
- 2No repeats in a row, column or boxThe ordinary sudoku constraints are unchanged: each of the nine rows, nine columns and nine 3 × 3 boxes holds every digit from 1 to 9 exactly once.
- 3Each cage adds up to its corner numberThe small number printed at the top-left of a dashed outline is the total its cells must reach. Cages cover the whole grid and never overlap.
- 4No digit repeats inside a cageA cage holds distinct digits even where its cells sit in different rows, columns and boxes. This is the rule that turns a total into a short list of possible digit sets.
- 5Printed clues are fixedAny digits already on the board at the start are part of the puzzle and cannot be changed. The hardest level starts with none of them.
- 6There is exactly one solutionEvery puzzle here is run through a solver before it is dealt, and only layouts with a single completion are used. Nothing on this board needs a guess.
Try it — the rules above, running
New puzzle deals a fresh grid at the level you last chose; the cage layout is chosen so that the first Hint names a real deduction — a cage with one cell left, the 45 rule, or a single. Deeper into a hard puzzle it may run out of rules it knows and take the digit from the solution instead; it says so when it does. If a digit you have entered is wrong, it corrects that first and tells you which square, because no deduction from a board that cannot be finished is worth making. The three-dot menu holds pencil marks, fill-in-all-marks, check-as-you-go, today’s shared puzzle and the level.
Your statistics · Gentle
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This level
20 digits printed, and cages of two or three cells — one or two of four per grid, where a stray cell had to be rehomed into a full cage. Enough of the grid is already there that ordinary sudoku scanning gets you moving before the sums matter.
Keyboard
- Arrows
- Move the selected cell
- 1 – 9
- Enter a digit
- Backspace
- Clear the cell
- P
- Pencil marks on or off
- U
- Undo
- H
- Hint
- C
- Check as you go
- F
- Full screen
Where do you start a killer sudoku?
- 1Write in the cages that only have one answerFind every cage whose total names its digits: 3, 4, 16 or 17 in two cells; 6, 7, 23 or 24 in three; 10, 11, 29 or 30 in four. Pencil those digits into every cell of the cage before doing anything else.
- 2Run the 45 rule on every boxFor each 3 × 3 box, add the totals of the cages lying entirely inside it. If they cover eight of the nine cells, 45 minus that sum is the ninth digit. Do the same down the columns and across the rows.
- 3Look for outiesTake a box and add up every cage that touches it, spill included. Subtract 45. That is the total of the cells hanging outside the box — and if only one cell hangs out, you have just solved it.
- 4Now play it as a sudokuWith a handful of digits placed, ordinary scanning starts to work: a digit with one home left in a row, a cell with one candidate left. Go back to the cages every time you fill something in.
How do cage totals narrow down digits?
A cage total is not a range, it is a short list of digit sets — and because no digit repeats inside a cage, that list is shorter than arithmetic alone would suggest. Two cells totalling 5 are 1+4 or 2+3, never 2.5 twice and never 5+0. Three cells totalling 8 are 1+2+5 or 1+3+4. The board's fill-in-all-marks button computes exactly this list for every cell and intersects it with what the row, column and box allow.
- Two cells total between 3 and 17. Nine is the worst of them, with four possible pairs.
- Three cells total between 6 and 24. Fourteen is the worst, with eight possible sets.
- Four cells total between 10 and 30. Twenty is the worst, with twelve possible sets.
- In every size, the two lowest and the two highest totals have exactly one set each.
What is the difference from ordinary sudoku?
The grid, the three constraints and the guarantee of a single answer are identical — if you can finish an ordinary sudoku you already know most of this. What is added is a partition of the grid into cages with totals, and one extra prohibition: no repeat inside a cage. What is usually taken away is the clues. An ordinary sudoku cannot have fewer than 17 of them; a killer can have none at all, because thirty cage totals carry more information than seventeen digits do.
How do you check your own work?
A cage is the cheapest place to catch a mistake, because it fails early: the moment its filled cells add up to more than its total, or repeat a digit, something upstream is wrong. This board marks those cells in red as you type, along with any ordinary row, column or box clash, and the Check option in the menu will also flag a digit that disagrees with the puzzle's one true solution.
How do you win more often?
- Start with the 45 rule, not with the cellsScan the nine boxes for one where the cages inside it cover eight cells. The difference between 45 and their totals is the ninth digit, handed over in one subtraction. On a no-clue grid this is the only way in, and there is almost always one box where it works.
- Learn the four totals per cage sizeTwo cells: 3, 4, 16 and 17. Three cells: 6, 7, 23 and 24. Four cells: 10, 11, 29 and 30. Each of those totals has exactly one possible set of digits, so a cage carrying one is a set of pencil marks you can write immediately without thinking about anything else.
- Hunt for cages that cross a box boundaryA cage sticking one cell out of a box is an outie: add every cage touching that box, subtract 45, and the remainder is the digit in the cell that sticks out. Beginners treat boundary-crossing cages as a nuisance; they are the fastest source of free digits on the board.
- Use a settled digit to collapse its whole cageA 20-in-four cage has twelve possible digit sets and tells you nothing. Place one digit in it and most of those sets die at once — put a 9 in and only sets containing 9 survive, which usually leaves two or three. Always re-read a cage immediately after filling any cell in it.
- Pencil in a cage at a time, never a cell at a timeCandidates in killer sudoku come from two directions — the peers and the cage total — and a half-filled set of marks leads straight to a false deduction. The fill-in-all-marks button here applies both constraints together, which is the only honest version of that list.
Common questions about killer sudoku
- Does a cage have to be a rectangle?
- No. A cage is any connected group of cells — an L, a T, a diagonal staircase, a straight line of four. Only the total and the no-repeat rule matter, never the shape.
- What does the small number in the corner mean?
- It is the total of every cell inside that dashed outline, printed once in the cage's top-left cell. It is not a clue about the cell it sits in; that cell is usually still empty.
- Can two cages have the same total?
- Yes, and every grid does — the fewest repeats seen on a board here is seven. Totals are not unique and cannot be: two-cell cages have only fifteen totals available to them (3 to 17) and three-cell cages nineteen (6 to 24), while a grid carries around thirty cages. Collisions are arithmetic, not coincidence, and a repeated total says nothing about the two cages sharing digits.
- Is the 45 rule ever wrong?
- Never, because it is arithmetic rather than a heuristic: nine distinct digits from 1 to 9 always add to 45. It only fails to help when too many cages cross the unit's boundary for the sums to resolve to a single cell.
Ready to stop reading? Play killer sudoku on the full board, with controls and statistics tailored to that game.