SudokuBoku

Killer sudoku Cages & sums

Not one digit is given. Every square belongs to a coloured cage, every cage shows its total, and from those totals alone the whole grid follows.

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Puzzle —
Rules
  • Fill every row, every column and every 3×3 box with the digits 1 to 9.
  • A digit can appear once in each of those — never twice.
  • There is exactly one solution, and logic alone will reach it.
  • Rows and columns each take the digits 1 to 9, once apiece.
  • The boxes are irregular shapes, drawn with the heavy outlines.
  • However a region bends, no digit repeats inside it.
  • The colour patches are cages; the small number is what a cage's digits add up to.
  • No digit repeats within a cage — nor in any row, column or 3×3 box.
  • There are no given digits: the sums alone pin down the whole grid.
  • Everything from classic applies: rows, columns and 3×3 boxes take 1 to 9.
  • The two tinted diagonals must each hold 1 to 9 exactly once as well.
  • All the classic constraints hold — rows, columns and 3×3 boxes take 1 to 9.
  • Each of the four shaded windows must also contain 1 to 9 exactly once.
  • The windows sit a step in from the corners, overlapping four boxes apiece.
  • Rows, columns and 3×3 boxes work exactly as they always have.
  • On top of that, two squares a chess knight's move apart may not hold the same digit.
  • Select a square and its knight partners are ringed with a dashed outline.
  • Every row, column and 3×3 box holds 1 to 9, exactly as in classic.
  • Along each grey path, digits strictly climb from the round bulb to the far end.
  • They don't have to be consecutive — each square just beats the one before it.
  • Rows, columns and 3×3 boxes take 1 to 9, exactly as in classic.
  • The digits along each arrow add up to the digit in the circle it comes from.
  • Digits may repeat along an arrow — as long as no row, column or box objects.
  • Fill every row, column and 3×3 box with the digits 1 to 9, as usual.
  • Between squares in the same box you'll find a sign; its point aims at the smaller digit.
  • Every comparison inside every box is shown — a hundred and eight of them.
  • The higher levels hand you fewer digits, not fewer signs. Expert gives you four.
  • Fill every row, column and 3×3 box with the digits 1 to 9, as usual.
  • A white dot between two squares means their digits differ by one.
  • A black dot means one digit is exactly double the other. 1 and 2 are both, and always show black.
  • A boundary with no dot is a clue too — those two digits are neither one apart nor double and half. Every boundary is marked or deliberately bare.
  • Expert hands you no digits at all. The dots and the gaps are the whole puzzle.
  • Fill every row, column and 3×3 box with the digits 1 to 9, as usual.
  • A square with a ring behind it holds an odd digit — 1, 3, 5, 7 or 9.
  • A square with a frame behind it holds an even one — 2, 4, 6 or 8.
  • Most squares are marked with neither, and those are genuinely unrestricted.
  • Every square switches to the fully marked board — one level, gentler than it looks, and two puzzles sharing a grid rather than one.
  • Every row, column and box holds five odd digits and four even ones — so once five squares of a house are known odd, the rest of it is even, marked or not.
  • Solve the 9×9 sudoku as usual — every row, column and box takes 1 to 9.
  • Ten ships are hidden on the same squares: one of four, two of three, three of two and four single squares.
  • Ships are straight, and no two of them touch — not even at a corner.
  • The numbers beside and below say how many ship squares each row and column holds.
  • A ship listed with digits sits on exactly those digits, in order — so the grid is your map.
  • Five 9×9 grids interlock: four corners and a centre, each corner sharing one 3×3 box with it.
  • Every grid obeys ordinary sudoku on its own — rows, columns and boxes each take 1 to 9 once.
  • A tinted box belongs to two grids at once, and only together do the five have one solution.
  • Fill every row, every column and every box with the digits 1 to 6.
  • The boxes are three squares wide and two tall.
  • Nothing repeats in any row, column or box.
  • Put 1, 2, 3 and 4 into each row, each column and each 2×2 box.
  • No digit may appear twice in any of them.
  • Every square can be worked out — no guessing needed.
Keyboard shortcuts
1–9
Place a digit, or toggle a pencil mark
Arrows
Move around the grid
N
Notes mode on or off
Backspace
Clear the square
Ctrl + Z
Undo · Ctrl + Y redo

Killer packs for the printer

On paper the cages print with dashed boundaries and a small total in each corner — ink beats colour on a page. Every grid in the pack is generated on your machine and proved to have a single solution before it's drawn.

Difficulty

The grid starts empty on purpose

Killer sudoku keeps every rule of the classic game — digits 1 to 9 once per row, once per column, once per box — and then takes away all the starting digits. In their place, the 81 squares are carved into cages: small connected groups, each printed with a total. Digits inside a cage must add up to that total, and a cage never repeats a digit. Those two facts are the entire clue set.

That opening — a blank grid that is nonetheless fully determined — is what gives killer its particular flavour. You aren't extending given information outward; you're squeezing digits into existence from pure arithmetic. The first placement of a solve often takes longer than the next ten, and it's the most satisfying one on this site.

A complete killer layout from this page's own generator. Forty-three cages, forty-three totals, no digits — and exactly one way to finish it.

The sums are a vocabulary, not a maths test

Sets you learn once and use forever

Nothing here needs more than addition, and after a few grids you barely do that. What a killer solver actually carries around is a short vocabulary of forced sets: which totals, in which number of squares, can only be built one way. Two squares adding to 17 are 8 and 9 — there is no other pair of different digits that reaches it. Two adding to 3 are 1 and 2. Four squares totalling 30 must be 6, 7, 8 and 9. When one of these cages appears, you know its contents before you know their order, and every one of its squares starts policing its row, column and box.

A cage's total often tells you which digits it holds long before it tells you where each one sits.

From the same layout: a two-square cage totalling 3. Its digits are 1 and 2 in some order — settled before a single square of the grid is filled.

When several sets survive

Most totals are less obliging. Three squares making 12 could be 1-2-9, 1-3-8, 1-4-7, 2-3-7, 2-4-6 or 3-4-5, and the real work of the harder levels is whittling such lists down. The digits already placed in the cage strike out some sets; the pencil marks in each square strike out more; and what survives, square by square, is often narrower than any single rule suggests. Done thoroughly this cross-checking is genuinely demanding — our hardest level leans on it — but it's the same vocabulary, applied with more patience.

Everything adds to forty-five

The digits 1 to 9 total 45, so every row, every column and every box is a 45 waiting to be used. Where the cage boundaries nearly respect a row, that fact turns into free digits. Suppose the cages that touch a row fit inside it except for a single square hanging below: add up their totals, subtract 45, and whatever is left over is sitting in that square. Solvers call these spare squares innies and outies — one square poking in, or one poking out — and hunting them along the edges of the grid is the single most profitable habit in killer.

Six cages cover the washed row; five fit inside and one dangles a single square below it. Their totals reach 51, the row accounts for 45, so the dangling square holds a 6.

The same subtraction works across two or three rows at once — ninety in place of forty-five — and inside any box. The wider versions are harder to spot and harder to trust, which is precisely why our grading treats a one-unit 45 as everyday killer skill and the multi-unit kind as a mark of a genuinely hard puzzle.

What the four levels actually measure

Every puzzle on this page is built and proved in your browser. A finished grid is carved into cages; if that layout would allow a second solution, a cage is split exactly where the two solutions disagree — the impostor's sums stop working, yours don't — until uniqueness is proved, not assumed. Then the puzzle is solved back the way a person would, technique by technique, and the hardest step it forced becomes its level. Easy means the arithmetic and singles carry you. Medium asks for the combination vocabulary and the first innies and outies. Hard stretches the 45 rule across several units and expects real pencil-mark work. Expert demands full combination cross-checks, or the grid-spanning patterns classic experts know.

There is no Evil or Extreme chip here for the same reason the jigsaw board stops at four levels: those two classic bands are drawn from curated banks we've verified puzzle by puzzle, and no such banks exist for cage layouts. The ladder ends where our evidence does. If you're after that tier of pain, the classic evil and extreme pages are the honest place to find it.

Reading this board

Why the cages are colours, not dashes

Screens usually draw killer cages as dashed outlines threaded inside the cells, which turns a small grid into a thicket of competing lines. Here each cage is a solid wash of colour instead, and the layout engine guarantees touching cages never share a shade, so a cage's territory reads at a glance even where it crosses a box border. The total sits on a small chip in the cage's top-left square. Print is the one place dashes win — less ink, no colour needed — so the pack builder above draws them the traditional way on paper.

Notes that already know the sums

The Fill button on this board writes pencil marks that respect the cages: a square in a two-cell 17 fills with 8 and 9 only, not with everything its row would allow. The hint button plays by this page's own ladder — it will point out the cage arithmetic you missed, name a combination, or walk you through an innie, rather than blurting a digit. And the share button copies a link that carries the entire cage layout in the address itself, so whoever opens it gets your exact puzzle with nothing stored on any server — their progress and yours saved separately, as everywhere on this site.