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How to play killer sudoku

Fill the grid so every row, column and 3 by 3 box has the numbers 1 to 9 once each, just like sudoku. On top of that, the grid is split into cages with dashed outlines: the numbers in each cage must add up to the small number in its corner, and no number can repeat inside a cage. Most killer sudokus start with an empty grid, so the sums are your only clues.

By Emre Özen, updated October 8, 2026

Want to try it straight away? Play an easy killer sudoku. Already know the rules? Jump to the killer sudoku combinations cheat sheet.

The rules

Each row, each column and each of the nine 3 by 3 boxes holds 1 to 9, once each.
Cages are groups of 2 or more squares next to each other, marked with a dashed line. The number in a cage's top-left corner is its sum.
The numbers in a cage add up to that sum.
A number can't appear twice in the same cage. That's true even when a cage spans two boxes.

That's all of it. A cage can cross the thick box lines, and cages don't have to be straight. Wikipedia's article on killer sudoku notes that some early puzzles didn't state rule 4, but every puzzle on this site follows it, and every one has exactly one solution.

Where to start: cages with only one answer

Some sums can only be made one way. Two squares adding up to 3 must be 1 and 2. Two squares adding up to 17 must be 8 and 9. Three squares adding up to 6 must be 1, 2 and 3, and three adding up to 24 must be 7, 8 and 9. You don't know the order yet, but you know which numbers go in, and that's enough to start crossing them off the rest of the box.

Out of the 120 possible sums for cages of 2 to 9 squares, 34 can only be made one way. They sit at the two ends of each size's range: the smallest two sums and the largest two (cages of 8 and 9 squares are always fixed). The full list is in the cheat sheet below, with those 34 marked.

Cage size	Sums with only one combination
2 squares	3, 4, 16, 17
3 squares	6, 7, 23, 24
4 squares	10, 11, 29, 30
5 squares	15, 16, 34, 35
6 squares	21, 22, 38, 39
7 squares	28, 29, 41, 42
8 squares	36, 37, 38, 39, 40, 41, 42, 43, 44
9 squares	45

The rule of 45

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45. Every row, every column and every box holds those nine numbers, so each one adds up to 45. That's the most useful fact in killer sudoku.

Pick a row. Add up the cages that sit completely inside it. Take that total from 45, and you get the sum of the squares that are left over. When only one square is left over, you know its number outright. Solvers call that square an innie.

The cages of 15, 12 and 11 sit fully inside the top row and add up to 38. The row must add up to 45, so the last square is 45 minus 38, which is 7. Its cage adds up to 16, so the square below it is 9.

It works the other way too. If the cages that touch a row stick out of it by one square, add those cages up, take away 45, and what's left is the number in the square that sticks out (an outie). The same goes for columns and boxes. Once you're comfortable, try it on two rows at once: they add up to 90.

A worked example in one box

Here's how the first few minutes in a box usually go. The box below has four cages: 3 and 17 in two squares each, 10 in two squares, and 15 in three.

Step 1: two squares adding up to 3 can only be 1 and 2. Two adding up to 17 can only be 8 and 9. That's four of the box's nine numbers placed in pairs.

Five numbers are left for the other five squares: 3, 4, 5, 6 and 7. The cage of 10 needs two of them adding up to 10, so it's 3 and 7 or 4 and 6 (1 and 9, and 2 and 8, are already used in this box). The cage of 15 needs three of them adding up to 15: 3, 5 and 7, or 4, 5 and 6.

Step 2: both ways of making 15 use a 5, so the 5 for this box is somewhere in the cage of 15. And the two cages split the five numbers between them: if the 10 is 3 and 7, the 15 is 4, 5 and 6.

That's as far as this box goes on its own. The next step comes from outside: a 4 or a 6 already sitting in the same column as the cage of 10 settles which pair it is, and then the 15 falls into place. This back and forth between cage sums and normal sudoku logic is the whole game.

Tips that save time

Small and large sums first. Look for 3, 4, 16 and 17 in two squares, and 6, 7, 23 and 24 in three. They each have one combination.
Look for numbers a cage can't use. A two-square cage of 10 can never hold a 5, because 5 + 5 repeats. The "never uses" column in the cheat sheet lists these.
Pencil in combinations, not guesses. Use Notes for the numbers a cage can hold. On this site, picking a square also shows every combination its cage can still make.
Run the rule of 45 on every row, column and box when you get stuck. It's slow, but it's often the only way forward on medium and hard.

Killer sudoku combinations cheat sheet

Every way to make every cage sum, for cages of 2 to 9 squares. Numbers in a cage are all different, so each combination is a set of different digits; the order inside a cage is up to the puzzle. "Always uses" lists digits found in every combination for that sum, and "never uses" lists digits found in none of them. Rows marked only one have a single combination.

In all there are 502 combinations over 120 sums. The busiest sum is 20 in 4 squares, with 12 different combinations. This table is generated from the same code the game uses, so it can't have a typo. Print this page and keep it next to your puzzles.

Cages of 2 squares (sums 3 to 17)

Sum	Combinations	Always uses	Never uses
3only one	12	1 2	3 4 5 6 7 8 9
4only one	13	1 3	2 4 5 6 7 8 9
5	1423	none	5 6 7 8 9
6	1524	none	3 6 7 8 9
7	162534	none	7 8 9
8	172635	none	4 8 9
9	18273645	none	9
10	19283746	none	5
11	29384756	none	1
12	394857	none	1 2 6
13	495867	none	1 2 3
14	5968	none	1 2 3 4 7
15	6978	none	1 2 3 4 5
16only one	79	7 9	1 2 3 4 5 6 8
17only one	89	8 9	1 2 3 4 5 6 7

Cages of 3 squares (sums 6 to 24)

Sum	Combinations	Always uses	Never uses
6only one	123	1 2 3	4 5 6 7 8 9
7only one	124	1 2 4	3 5 6 7 8 9
8	125134	1	6 7 8 9
9	126135234	none	7 8 9
10	127136145235	none	8 9
11	128137146236245	none	9
12	129138147156237246345	none	none
13	139148157238247256346	none	none
14	149158167239248257347356	none	none
15	159168249258267348357456	none	none
16	169178259268349358367457	none	none
17	179269278359368458467	none	none
18	189279369378459468567	none	none
19	289379469478568	none	1
20	389479569578	none	1 2
21	489579678	none	1 2 3
22	589679	9	1 2 3 4
23only one	689	6 8 9	1 2 3 4 5 7
24only one	789	7 8 9	1 2 3 4 5 6

Cages of 4 squares (sums 10 to 30)

Sum	Combinations	Always uses	Never uses
10only one	1234	1 2 3 4	5 6 7 8 9
11only one	1235	1 2 3 5	4 6 7 8 9
12	12361245	1 2	7 8 9
13	123712461345	1	8 9
14	12381247125613462345	none	9
15	123912481257134713562346	none	none
16	12491258126713481357145623472356	none	none
17	125912681349135813671457234823572456	none	none
18	12691278135913681458146723492358236724573456	none	none
19	12791369137814591468156723592368245824673457	none	none
20	128913791469147815682369237824592468256734583467	none	none
21	13891479156915782379246924782568345934683567	none	none
22	14891579167823892479256925783469347835684567	none	none
23	158916792489257926783479356935784568	none	none
24	16892589267934893579367845694578	none	none
25	178926893589367945794678	none	none
26	27893689458946795678	none	1
27	378946895679	9	1 2
28	47895689	8 9	1 2 3
29only one	5789	5 7 8 9	1 2 3 4 6
30only one	6789	6 7 8 9	1 2 3 4 5

Cages of 5 squares (sums 15 to 35)

Sum	Combinations	Always uses	Never uses
15only one	12345	1 2 3 4 5	6 7 8 9
16only one	12346	1 2 3 4 6	5 7 8 9
17	1234712356	1 2 3	8 9
18	123481235712456	1 2	9
19	1234912358123671245713456	1	none
20	123591236812458124671345723456	none	none
21	1236912378124591246812567134581346723457	none	none
22	123791246912478125681345913468135672345823467	none	none
23	1238912479125691257813469134781356814567234592346823567	none	none
24	1248912579126781347913569135781456823469234782356824567	none	none
25	125891267913489135791367814569145782347923569235782456834567	none	none
26	1268913589136791457914678234892357923678245692457834568	none	none
27	1278913689145891467915678235892367924579246783456934578	none	none
28	137891468915679236892458924679256783457934678	none	none
29	1478915689237892468925679345893467935678	none	none
30	157892478925689346893567945678	none	none
31	1678925789347893568945679	9	none
32	267893578945689	8 9	1
33	3678945789	7 8 9	1 2
34only one	46789	4 6 7 8 9	1 2 3 5
35only one	56789	5 6 7 8 9	1 2 3 4

Cages of 6 squares (sums 21 to 39)

Sum	Combinations	Always uses	Never uses
21only one	123456	1 2 3 4 5 6	7 8 9
22only one	123457	1 2 3 4 5 7	6 8 9
23	123458123467	1 2 3 4	9
24	123459123468123567	1 2 3	none
25	123469123478123568124567	1 2	none
26	123479123569123578124568134567	1	none
27	123489123579123678124569124578134568234567	none	none
28	123589123679124579124678134569134578234568	none	none
29	123689124589124679125678134579134678234569234578	none	none
30	123789124689125679134589134679135678234579234678	none	none
31	124789125689134689135679145678234589234679235678	none	none
32	125789134789135689145679234689235679245678	none	none
33	126789135789145689234789235689245679345678	none	none
34	136789145789235789245689345679	9	none
35	146789236789245789345689	8 9	none
36	156789246789345789	7 8 9	none
37	256789346789	6 7 8 9	1
38only one	356789	3 5 6 7 8 9	1 2 4
39only one	456789	4 5 6 7 8 9	1 2 3

Cages of 7 squares (sums 28 to 42)

Sum	Combinations	Always uses	Never uses
28only one	1234567	1 2 3 4 5 6 7	8 9
29only one	1234568	1 2 3 4 5 6 8	7 9
30	12345691234578	1 2 3 4 5	none
31	12345791234678	1 2 3 4 7	none
32	123458912346791235678	1 2 3	none
33	123468912356791245678	1 2 6	none
34	1234789123568912456791345678	1	none
35	1235789124568913456792345678	5	none
36	1236789124578913456892345679	9	none
37	124678913457892345689	4 8 9	none
38	125678913467892345789	7 8 9	none
39	13567892346789	3 6 7 8 9	none
40	14567892356789	5 6 7 8 9	none
41only one	2456789	2 4 5 6 7 8 9	1 3
42only one	3456789	3 4 5 6 7 8 9	1 2

Cages of 8 squares (sums 36 to 44)

Sum	Combinations	Always uses	Never uses
36only one	12345678	1 2 3 4 5 6 7 8	9
37only one	12345679	1 2 3 4 5 6 7 9	8
38only one	12345689	1 2 3 4 5 6 8 9	7
39only one	12345789	1 2 3 4 5 7 8 9	6
40only one	12346789	1 2 3 4 6 7 8 9	5
41only one	12356789	1 2 3 5 6 7 8 9	4
42only one	12456789	1 2 4 5 6 7 8 9	3
43only one	13456789	1 3 4 5 6 7 8 9	2
44only one	23456789	2 3 4 5 6 7 8 9	1

Cages of 9 squares (sums 45)

Sum	Combinations	Always uses	Never uses
45only one	123456789	1 2 3 4 5 6 7 8 9	none

Variations

Wikipedia's article describes two common variations. Killer sudoku X adds the diagonals: no number can repeat along either long diagonal. Killer jigsaw sudoku swaps the 3 by 3 boxes for irregular shapes of nine squares. The puzzles on this site are the standard version, with normal boxes and no diagonal rule.

The same article credits the puzzle's invention to the Tokyo puzzle setter Tetsuya Nishio, from an idea by his student Miyuki Nisawa, and says it first appeared outside Japan in The Times in 2005. In Japan it's called samunamupure ("sum number place"). Other names you may see are sumdoku and addoku.

Controls on this site

Notes lets you pencil small numbers into a square. Placing a number clears it from the notes in the same row, column, box and cage (you can switch that off in Settings).
Hint fills in one square and says why it had to be that number. You get 6 per puzzle.
Mistakes turn the square red with a "Wrong move" banner that says what went wrong, like a repeat in the cage or a sum that's too big. You get three; the third starts the puzzle over. Notes never count.
Undo goes back one move at a time, including notes. Pause hides the board and stops the clock.

Key	What it does
Arrow keys	Move around the grid
1 to 9	Place a number (or a note, when Notes is on)
Backspace, Delete or 0	Clear the square
N	Turn Notes on or off
H	Get a hint
Ctrl+Z (Cmd+Z on a Mac)	Undo

Ready? Play killer sudoku online, or try today's daily killer sudoku.

Sources

Wikipedia, "Killer sudoku" (rules, the rule of 45, innies and outies, variations, history and names).
The combinations table is computed by this site's own code: every set of 2 to 9 different digits from 1 to 9, grouped by size and sum.