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Killer Sudoku
Cages that add up. Free, at five levels.
How to play killer sudoku
Killer sudoku draws dashed cages over the grid. The small number in each cage is the sum of its digits, and a digit can't repeat inside a cage. The usual sudoku rules still hold, and many killers start with no digits at all.
Our killers are set so the cages carry the solve: an early step always uses a cage total, a cage combination or the 45 rule. Pick a level above, look up any cage in the combination chart below, or try one of the hand-set killers from the setters on Cracking the Cryptic.
At a glance
- Digits in a cage add up to the small total in its corner.
- No digit repeats inside a cage, even when it crosses a box border.
- Every row, column and box adds up to 45.
- Many killers start with no given digits at all.
Killer sudoku combinations
Every way to make every cage total, from two cells to five. Totals with only one combination are highlighted: those are the cages to look at first. Use the finder to narrow a cage down by digits you know are in or out.
Tap a digit once if it must be in, twice to leave it out
2-cell cages 15 totals
| Total | Combinations | What it tells you |
|---|---|---|
| 3 | 12 | One way only |
| 4 | 13 | One way only |
| 5 | 14 23 | – |
| 6 | 15 24 | – |
| 7 | 16 25 34 | never 7, 8, 9 |
| 8 | 17 26 35 | never 4, 8, 9 |
| 9 | 18 27 36 45 | never 9 |
| 10 | 19 28 37 46 | never 5 |
| 11 | 29 38 47 56 | never 1 |
| 12 | 39 48 57 | never 1, 2, 6 |
| 13 | 49 58 67 | never 1, 2, 3 |
| 14 | 59 68 | – |
| 15 | 69 78 | – |
| 16 | 79 | One way only |
| 17 | 89 | One way only |
3-cell cages 19 totals
| Total | Combinations | What it tells you |
|---|---|---|
| 6 | 123 | One way only |
| 7 | 124 | One way only |
| 8 | 125 134 | Always has 1; never 6, 7, 8, 9 |
| 9 | 126 135 234 | never 7, 8, 9 |
| 10 | 127 136 145 235 | never 8, 9 |
| 11 | 128 137 146 236 245 | never 9 |
| 12 | 129 138 147 156 237 246 345 | – |
| 13 | 139 148 157 238 247 256 346 | – |
| 14 | 149 158 167 239 248 257 347 356 | – |
| 15 | 159 168 249 258 267 348 357 456 | – |
| 16 | 169 178 259 268 349 358 367 457 | – |
| 17 | 179 269 278 359 368 458 467 | – |
| 18 | 189 279 369 378 459 468 567 | – |
| 19 | 289 379 469 478 568 | never 1 |
| 20 | 389 479 569 578 | never 1, 2 |
| 21 | 489 579 678 | never 1, 2, 3 |
| 22 | 589 679 | Always has 9; never 1, 2, 3, 4 |
| 23 | 689 | One way only |
| 24 | 789 | One way only |
4-cell cages 21 totals
| Total | Combinations | What it tells you |
|---|---|---|
| 10 | 1234 | One way only |
| 11 | 1235 | One way only |
| 12 | 1236 1245 | Always has 1, 2; never 7, 8, 9 |
| 13 | 1237 1246 1345 | Always has 1; never 8, 9 |
| 14 | 1238 1247 1256 1346 2345 | never 9 |
| 15 | 1239 1248 1257 1347 1356 2346 | – |
| 16 | 1249 1258 1267 1348 1357 1456 2347 2356 | – |
| 17 | 1259 1268 1349 1358 1367 1457 2348 2357 2456 | – |
| 18 | 1269 1278 1359 1368 1458 1467 2349 2358 2367 2457 3456 | – |
| 19 | 1279 1369 1378 1459 1468 1567 2359 2368 2458 2467 3457 | – |
| 20 | 1289 1379 1469 1478 1568 2369 2378 2459 2468 2567 3458 3467 | – |
| 21 | 1389 1479 1569 1578 2379 2469 2478 2568 3459 3468 3567 | – |
| 22 | 1489 1579 1678 2389 2479 2569 2578 3469 3478 3568 4567 | – |
| 23 | 1589 1679 2489 2579 2678 3479 3569 3578 4568 | – |
| 24 | 1689 2589 2679 3489 3579 3678 4569 4578 | – |
| 25 | 1789 2689 3589 3679 4579 4678 | – |
| 26 | 2789 3689 4589 4679 5678 | never 1 |
| 27 | 3789 4689 5679 | Always has 9; never 1, 2 |
| 28 | 4789 5689 | Always has 8, 9; never 1, 2, 3 |
| 29 | 5789 | One way only |
| 30 | 6789 | One way only |
5-cell cages 21 totals
| Total | Combinations | What it tells you |
|---|---|---|
| 15 | 12345 | One way only |
| 16 | 12346 | One way only |
| 17 | 12347 12356 | Always has 1, 2, 3; never 8, 9 |
| 18 | 12348 12357 12456 | Always has 1, 2; never 9 |
| 19 | 12349 12358 12367 12457 13456 | Always has 1 |
| 20 | 12359 12368 12458 12467 13457 23456 | – |
| 21 | 12369 12378 12459 12468 12567 13458 13467 23457 | – |
| 22 | 12379 12469 12478 12568 13459 13468 13567 23458 23467 | – |
| 23 | 12389 12479 12569 12578 13469 13478 13568 14567 23459 23468 23567 | – |
| 24 | 12489 12579 12678 13479 13569 13578 14568 23469 23478 23568 24567 | – |
| 25 | 12589 12679 13489 13579 13678 14569 14578 23479 23569 23578 24568 34567 | – |
| 26 | 12689 13589 13679 14579 14678 23489 23579 23678 24569 24578 34568 | – |
| 27 | 12789 13689 14589 14679 15678 23589 23679 24579 24678 34569 34578 | – |
| 28 | 13789 14689 15679 23689 24589 24679 25678 34579 34678 | – |
| 29 | 14789 15689 23789 24689 25679 34589 34679 35678 | – |
| 30 | 15789 24789 25689 34689 35679 45678 | – |
| 31 | 16789 25789 34789 35689 45679 | Always has 9 |
| 32 | 26789 35789 45689 | Always has 8, 9; never 1 |
| 33 | 36789 45789 | Always has 7, 8, 9; never 1, 2 |
| 34 | 46789 | One way only |
| 35 | 56789 | One way only |
Six cells or more? Flip the cage: a 6-cell cage holds every digit except a 3-cell set that totals 45 minus the cage. A 7-cell 40 leaves out two digits that make 5, so it's missing 1 and 4 or 2 and 3. The finder above does any size.
How to start a killer sudoku
Mark the one-way cages
A two-cell 3 or 17, a three-cell 6 or 24, a four-cell 10 or 30: each can only be made one way. Pencil those digits in right away. The combination chart highlights every one.
Add up a box
A box holds 1 to 9, so its digits total 45. If whole cages cover all but one or two of its cells, 45 minus their totals is what's left. That's the 45 rule.
Look for innies and outies
When the cages over a row stick out by one cell, add their totals and take away 45: the result is the cell that sticks out.
Let the cage and the box share digits
If a two-cell 3 sits inside one box, that box's 1 and 2 are in the cage, so cross 1 and 2 off the rest of the box.
Come back to the cages
Each digit you place cuts down the combinations of the cages around it. When singles stall, look for a cage that now has only one way left.
Common mistakes
Forgetting the no-repeat rule
A two-cell 4 isn't 2 + 2. It can only be 1 + 3, and that's what makes it useful.
Counting a cage that pokes out
The 45 rule only adds cages that sit wholly inside the house. A cage that sticks out belongs in the innie and outie sum instead.
Missing the repeat ban across boxes
A cage that spans two boxes still can't repeat a digit, even though no row, column or box covers it.
Five levels, no guessing
Every puzzle has one solution, proved when it is set, and our solver finishes it by logic alone. The level is the hardest step the solve needs. Here is what each level asks of a killer puzzle:
- EasyOne-way cages and singles. A gentle way in.Play Easy
- MediumCombinations of up to three cells, the 45 rule on a single house, and digits locked inside a cage.Play Medium
- HardFour-cell and longer combinations, the 45 rule across several houses, and pairs and triples.Play Hard
- ExpertX-Wings, Skyscrapers and wings once the cages run dry.Play Expert
- FiendishChains, coloring, and testing every way a cage can be filled against its neighbors.Play Fiendish
The daily variant rotates through 11 kinds, so a killer daily comes round about every 11 days. Past dailies
Hand-set killer puzzles
Our levels are a good start. For more, Explore has 867 killer puzzles made by people, from Logic Masters and Cracking the Cryptic. A few of the most popular:
RAT RUN 9: Shock Valueby marty_sears
Chiaroscuro-dokuby yttrio
Beginner Palindromeby wuc
Chainedby arbitrary
TIC TAC TOE TIEby Will Power
One Killer Knightby meggen033
Even Cages Evenby kierownik
Minchen's Boxby Gerhard1963Setters with the most killer puzzles:
- meggen033 109
- lgastako 21
- Will Power 17
- Vythic 15
- Brandy New 14
- gUBBLOR 13
- Sudonym 12
- gwai77 12
- sujoyku 11
- Vitray 10
Often combined with:
- Killer + Kropki 347
- Killer + German Whispers 210
- Killer + Fog of War 183
- Killer + Arrow 178
- Killer + Renban 161
- Killer + Thermo 130
- Killer + XV 112
- Killer + Region Sum Lines 76
- Killer + Anti-Knight 70
- Killer + X-Sums 68
All 867 killer puzzles in Explore · Make your own killer sudoku
Questions
Is killer sudoku harder than normal sudoku?
Not necessarily. Easy killers fall to cage combinations alone. The hard ones lean on the 45 rule, where you add up whole rows and boxes to find a single cell.
Why does my killer sudoku have no given digits?
The cage totals pin down the solution on their own, so givens aren't needed. Start with the cages that can only be made one way, such as a two-cell 3 or 17.
Where can I learn the cage combinations?
The killer lesson lists the one-way cages and walks through the 45 rule on real boards.
Which killer cages can only be made one way?
Two cells: 3, 4, 16 and 17. Three cells: 6, 7, 23 and 24. Four cells: 10, 11, 29 and 30. Five cells: 15, 16, 34 and 35. The chart on this page lists every total and its combinations.
What are innies and outies?
After the 45 rule, the leftover cells. An innie is a cell inside a house that its whole cages don't cover; an outie is a cell outside the house that its cages spill into. Adding cage totals and comparing with 45 gives their sum.
How big can a killer cage be?
Up to nine cells. A nine-cell cage can only hold 1 to 9 once each, so it always totals 45.
More ways to play
Classic Sudoku1 to 9 in every row, column and boxThermo SudokuDigits climb from the bulbArrow SudokuThe arrow sums to its circleKropki SudokuWhite dots, black dotsXV SudokuX is 10, V is 5Sandwich SudokuSum between the 1 and the 9German Whispers SudokuNeighbors differ by 5 or moreDiagonal SudokuBoth diagonals hold 1 to 9Anti-Knight SudokuNo repeat a knight's move apartAnti-King SudokuTouching cells never repeat