Killer Sudoku Combinations

All 502 killer sudoku combinations, grouped by cage size and total. Each row lists the sets of different digits from 1 to 9 that add up to that total. Totals that can only be made one way are marked ONLY: they tell you exactly which digits are in the cage.

2 cells 36 combinations

Total	Combinations
3	12ONLY
4	13ONLY
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	79ONLY
17	89ONLY

3 cells 84 combinations

Total	Combinations
6	123ONLY
7	124ONLY
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	689ONLY
24	789ONLY

4 cells 126 combinations

Total	Combinations
10	1234ONLY
11	1235ONLY
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	5789ONLY
30	6789ONLY

5 cells 126 combinations

Total	Combinations
15	12345ONLY
16	12346ONLY
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	46789ONLY
35	56789ONLY

6 cells 84 combinations

Total	Combinations
21	123456ONLY
22	123457ONLY
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	356789ONLY
39	456789ONLY

7 cells 36 combinations

Total	Combinations
28	1234567ONLY
29	1234568ONLY
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	2456789ONLY
42	3456789ONLY

8 cells 9 combinations

Total	Combinations
36	12345678ONLY
37	12345679ONLY
38	12345689ONLY
39	12345789ONLY
40	12346789ONLY
41	12356789ONLY
42	12456789ONLY
43	13456789ONLY
44	23456789ONLY

9 cells 1 combination

Total	Combinations
45	123456789ONLY

How to use the chart

Find the cage's size, then its total. If the total has one combination, you know every digit in the cage, just not the order. If it has several, look for digits they all share, or digits none of them use. The killer sudoku calculator does that for you and lets you rule digits in or out as you solve.

Two patterns are worth remembering. The smallest and largest totals for each cage size have only one combination. And an 8-cell cage misses exactly one digit: the one equal to 45 minus its total. A 9-cell cage always totals 45.

The same chart works for kakuro: a run of cells is just like a cage, with different digits adding up to the clue. For a whole killer sudoku, try the step-by-step solver.