Puzzle Genius

Killer Sudoku Cheat Sheet

Knowing the combination of digits that can fit into a killer sudoku cage isn’t just a useful technique, sometimes it is absolutely necessary in order to solve or start a puzzle. Remembering common unique combinations is essential if you want to improve your time for solving killer sudoku puzzles. Unless you have a photographic memory though, you probably won’t memorise all of them, which is why this cheat sheet can be handy.

As well as cell cage combinations, we've included required digits further down. Some cells always require particular digits, regardless of the number combination that goes into them. Knowing these is a great way to eliminate candidate numbers from blocks, rows, and columns.

Is it cheating? We call it a cheat sheet, but is it really cheating? Only you can decide! Our view is that a reference like this is no more cheating than using a dictionary to check your spelling. For us, puzzles like killer sudoku are all about the logic and not an exercise in memory or recall.

New to killer sudoku? Be sure to check out our Killer Sudoku From Scratch tutorial.

Looking for some excellent killer sudoku puzzles? We have plenty of lovely killer sudoku books to keep you busy!

Cell Cage Combinations

These are all possible combinations of digits for a given cage size and sum. Bolded sums have only one combination.

2-Cell Cage Combinations

3 — 12

4 — 13

5 — 14 23

6 — 15 24

7 — 16 25 34

8 — 17 26 35

9 — 18 27 36 45

10 — 19 28 37 46

11 — 29 38 47 56

12 — 39 48 57

13 — 49 58 67

14 — 59 68

15 — 69 78

16 — 79

17 — 89

3-Cell Cage Combinations

6 — 123

7 — 124

8 — 125 134

9 — 126 135 234

10 — 127 136 145 235

11 — 128 137 146 236 245

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

20 — 389 479 569 578

21 — 489 579 678

22 — 589 679

23 — 689

24 — 789

4-Cell Cage Combinations

10 — 1234

11 — 1235

12 — 1236 1245

13 — 1237 1246 1345

14 — 1238 1247 1256 1346 2345

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

27 — 3789 4689 5679

28 — 4789 5689

29 — 5789

30 — 6789

5-Cell Cage Combinations

15 — 12345

16 — 12346

17 — 12347 12356

18 — 12348 12357 12456

19 — 12349 12358 12367 12457 13456

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

32 — 26789 35789 45689

33 — 36789 45789

34 — 46789

35 — 56789

6-Cell Cage Combinations

21 — 123456

22 — 123457

23 — 123458 123467

24 — 123459 123468 123567

25 — 123469 123478 123568 124567

26 — 123479 123569 123578 124568 134567

27 — 123489 123579 123678 124569 124578 134568 234567

28 — 123589 123679 124579 124678 134569 134578 234568

29 — 123689 124589 124679 125678 134579 134678 234569 234578

30 — 123789 124689 125679 134589 134679 135678 234579 234678

31 — 124789 125689 134689 135679 145678 234589 234679 235678

32 — 125789 134789 135689 145679 234689 235679 245678

33 — 126789 135789 145689 234789 235689 245679 345678

34 — 136789 145789 235789 245689 345679

35 — 146789 236789 245789 345689

36 — 156789 246789 345789

37 — 256789 346789

38 — 356789

39 — 456789

7-Cell Cage Combinations

28 — 1234567

29 — 1234568

30 — 1234569 1234578

31 — 1234579 1234678

32 — 1234589 1234679 1235678

33 — 1234689 1235679 1245678

34 — 1234789 1235689 1245679 1345678

35 — 1235789 1245689 1345679 2345678

36 — 1236789 1245789 1345689 2345679

37 — 1246789 1345789 2345689

38 — 1256789 1346789 2345789

39 — 1356789 2346789

40 — 1456789 2356789

41 — 2456789

42 — 3456789

8-Cell Cage Combinations

36 — 12345678

37 — 12345679

38 — 12345689

39 — 12345789

40 — 12346789

41 — 12356789

42 — 12456789

43 — 13456789

44 — 23456789

9-Cell Cage Combinations

45 — 123456789




Required Digits

These are digits that must be present somewhere within a cage for a given sum.

3-Cell Cage Required Digits

8 — 1

22 - 9

4-Cell Cage Required Digits

12 — 1,2

13 — 1

27 — 9

28 — 8,9

5-Cell Cage Required Digits

17 — 1,2,3

18 — 1,2

18 — 1,2

19 — 1,2

20 — 1,2

21 — 1

31 — 9

32 — 8,9

33 — 7,8,9

6-Cell Cage Required Digits

23 — 1,2,3,4

24 — 1,2,3

25 — 1,2

26 — 1

34 — 9

35 — 8,9

36 — 7,8,9

37 — 6,7,8,9

7-Cell Cage Required Digits

30 — 1,2,3,4,5

31 — 1,2,3,4

32 — 1,2,3

33 — 1,2,6

34 — 1

36 — 9

37 — 8,9

38 — 7,8,9

39 — 3,6,7,8,9

40 — 5,6,7,8,9

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