Killer Sudoku calculator: every cage combination

Pick how many cells the cage has and its sum to list every set of digits that fits. Mark digits the cage must contain or cannot contain to narrow the list. The full cheat sheet is further down the page.

Killer Sudoku cheat sheet

Every combination for cages of 2 to 7 cells. Sums in bold have only one combination. An 8-cell cage is the nine digits minus one, so its sum is 45 minus the missing digit; a 9-cell cage always adds up to 45.

2 cells

Sum	Combinations
3	1 2
4	1 3
5	2 31 4
6	2 41 5
7	3 42 51 6
8	3 52 61 7
9	4 53 62 71 8
10	4 63 72 81 9
11	5 64 73 82 9
12	5 74 83 9
13	6 75 84 9
14	6 85 9
15	7 86 9
16	7 9
17	8 9

3 cells

Sum	Combinations
6	1 2 3
7	1 2 4
8	1 3 41 2 5
9	2 3 41 3 51 2 6
10	2 3 51 4 51 3 61 2 7
11	2 4 52 3 61 4 61 3 71 2 8
12	3 4 52 4 61 5 62 3 71 4 71 3 81 2 9
13	3 4 62 5 62 4 71 5 72 3 81 4 81 3 9
14	3 5 63 4 72 5 71 6 72 4 81 5 82 3 91 4 9
15	4 5 63 5 72 6 73 4 82 5 81 6 82 4 91 5 9
16	4 5 73 6 73 5 82 6 81 7 83 4 92 5 91 6 9
17	4 6 74 5 83 6 82 7 83 5 92 6 91 7 9
18	5 6 74 6 83 7 84 5 93 6 92 7 91 8 9
19	5 6 84 7 84 6 93 7 92 8 9
20	5 7 85 6 94 7 93 8 9
21	6 7 85 7 94 8 9
22	6 7 95 8 9
23	6 8 9
24	7 8 9

4 cells

Sum	Combinations
10	1 2 3 4
11	1 2 3 5
12	1 2 4 51 2 3 6
13	1 3 4 51 2 4 61 2 3 7
14	2 3 4 51 3 4 61 2 5 61 2 4 71 2 3 8
15	2 3 4 61 3 5 61 3 4 71 2 5 71 2 4 81 2 3 9
16	2 3 5 61 4 5 62 3 4 71 3 5 71 2 6 71 3 4 81 2 5 81 2 4 9
17	2 4 5 62 3 5 71 4 5 71 3 6 72 3 4 81 3 5 81 2 6 81 3 4 91 2 5 9
18	3 4 5 62 4 5 72 3 6 71 4 6 72 3 5 81 4 5 81 3 6 81 2 7 82 3 4 91 3 5 91 2 6 9
19	3 4 5 72 4 6 71 5 6 72 4 5 82 3 6 81 4 6 81 3 7 82 3 5 91 4 5 91 3 6 91 2 7 9
20	3 4 6 72 5 6 73 4 5 82 4 6 81 5 6 82 3 7 81 4 7 82 4 5 92 3 6 91 4 6 91 3 7 91 2 8 9
21	3 5 6 73 4 6 82 5 6 82 4 7 81 5 7 83 4 5 92 4 6 91 5 6 92 3 7 91 4 7 91 3 8 9
22	4 5 6 73 5 6 83 4 7 82 5 7 81 6 7 83 4 6 92 5 6 92 4 7 91 5 7 92 3 8 91 4 8 9
23	4 5 6 83 5 7 82 6 7 83 5 6 93 4 7 92 5 7 91 6 7 92 4 8 91 5 8 9
24	4 5 7 83 6 7 84 5 6 93 5 7 92 6 7 93 4 8 92 5 8 91 6 8 9
25	4 6 7 84 5 7 93 6 7 93 5 8 92 6 8 91 7 8 9
26	5 6 7 84 6 7 94 5 8 93 6 8 92 7 8 9
27	5 6 7 94 6 8 93 7 8 9
28	5 6 8 94 7 8 9
29	5 7 8 9
30	6 7 8 9

5 cells

Sum	Combinations
15	1 2 3 4 5
16	1 2 3 4 6
17	1 2 3 5 61 2 3 4 7
18	1 2 4 5 61 2 3 5 71 2 3 4 8
19	1 3 4 5 61 2 4 5 71 2 3 6 71 2 3 5 81 2 3 4 9
20	2 3 4 5 61 3 4 5 71 2 4 6 71 2 4 5 81 2 3 6 81 2 3 5 9
21	2 3 4 5 71 3 4 6 71 2 5 6 71 3 4 5 81 2 4 6 81 2 3 7 81 2 4 5 91 2 3 6 9
22	2 3 4 6 71 3 5 6 72 3 4 5 81 3 4 6 81 2 5 6 81 2 4 7 81 3 4 5 91 2 4 6 91 2 3 7 9
23	2 3 5 6 71 4 5 6 72 3 4 6 81 3 5 6 81 3 4 7 81 2 5 7 82 3 4 5 91 3 4 6 91 2 5 6 91 2 4 7 91 2 3 8 9
24	2 4 5 6 72 3 5 6 81 4 5 6 82 3 4 7 81 3 5 7 81 2 6 7 82 3 4 6 91 3 5 6 91 3 4 7 91 2 5 7 91 2 4 8 9
25	3 4 5 6 72 4 5 6 82 3 5 7 81 4 5 7 81 3 6 7 82 3 5 6 91 4 5 6 92 3 4 7 91 3 5 7 91 2 6 7 91 3 4 8 91 2 5 8 9
26	3 4 5 6 82 4 5 7 82 3 6 7 81 4 6 7 82 4 5 6 92 3 5 7 91 4 5 7 91 3 6 7 92 3 4 8 91 3 5 8 91 2 6 8 9
27	3 4 5 7 82 4 6 7 81 5 6 7 83 4 5 6 92 4 5 7 92 3 6 7 91 4 6 7 92 3 5 8 91 4 5 8 91 3 6 8 91 2 7 8 9
28	3 4 6 7 82 5 6 7 83 4 5 7 92 4 6 7 91 5 6 7 92 4 5 8 92 3 6 8 91 4 6 8 91 3 7 8 9
29	3 5 6 7 83 4 6 7 92 5 6 7 93 4 5 8 92 4 6 8 91 5 6 8 92 3 7 8 91 4 7 8 9
30	4 5 6 7 83 5 6 7 93 4 6 8 92 5 6 8 92 4 7 8 91 5 7 8 9
31	4 5 6 7 93 5 6 8 93 4 7 8 92 5 7 8 91 6 7 8 9
32	4 5 6 8 93 5 7 8 92 6 7 8 9
33	4 5 7 8 93 6 7 8 9
34	4 6 7 8 9
35	5 6 7 8 9

6 cells

Sum	Combinations
21	1 2 3 4 5 6
22	1 2 3 4 5 7
23	1 2 3 4 6 71 2 3 4 5 8
24	1 2 3 5 6 71 2 3 4 6 81 2 3 4 5 9
25	1 2 4 5 6 71 2 3 5 6 81 2 3 4 7 81 2 3 4 6 9
26	1 3 4 5 6 71 2 4 5 6 81 2 3 5 7 81 2 3 5 6 91 2 3 4 7 9
27	2 3 4 5 6 71 3 4 5 6 81 2 4 5 7 81 2 3 6 7 81 2 4 5 6 91 2 3 5 7 91 2 3 4 8 9
28	2 3 4 5 6 81 3 4 5 7 81 2 4 6 7 81 3 4 5 6 91 2 4 5 7 91 2 3 6 7 91 2 3 5 8 9
29	2 3 4 5 7 81 3 4 6 7 81 2 5 6 7 82 3 4 5 6 91 3 4 5 7 91 2 4 6 7 91 2 4 5 8 91 2 3 6 8 9
30	2 3 4 6 7 81 3 5 6 7 82 3 4 5 7 91 3 4 6 7 91 2 5 6 7 91 3 4 5 8 91 2 4 6 8 91 2 3 7 8 9
31	2 3 5 6 7 81 4 5 6 7 82 3 4 6 7 91 3 5 6 7 92 3 4 5 8 91 3 4 6 8 91 2 5 6 8 91 2 4 7 8 9
32	2 4 5 6 7 82 3 5 6 7 91 4 5 6 7 92 3 4 6 8 91 3 5 6 8 91 3 4 7 8 91 2 5 7 8 9
33	3 4 5 6 7 82 4 5 6 7 92 3 5 6 8 91 4 5 6 8 92 3 4 7 8 91 3 5 7 8 91 2 6 7 8 9
34	3 4 5 6 7 92 4 5 6 8 92 3 5 7 8 91 4 5 7 8 91 3 6 7 8 9
35	3 4 5 6 8 92 4 5 7 8 92 3 6 7 8 91 4 6 7 8 9
36	3 4 5 7 8 92 4 6 7 8 91 5 6 7 8 9
37	3 4 6 7 8 92 5 6 7 8 9
38	3 5 6 7 8 9
39	4 5 6 7 8 9

7 cells

Sum	Combinations
28	1 2 3 4 5 6 7
29	1 2 3 4 5 6 8
30	1 2 3 4 5 7 81 2 3 4 5 6 9
31	1 2 3 4 6 7 81 2 3 4 5 7 9
32	1 2 3 5 6 7 81 2 3 4 6 7 91 2 3 4 5 8 9
33	1 2 4 5 6 7 81 2 3 5 6 7 91 2 3 4 6 8 9
34	1 3 4 5 6 7 81 2 4 5 6 7 91 2 3 5 6 8 91 2 3 4 7 8 9
35	2 3 4 5 6 7 81 3 4 5 6 7 91 2 4 5 6 8 91 2 3 5 7 8 9
36	2 3 4 5 6 7 91 3 4 5 6 8 91 2 4 5 7 8 91 2 3 6 7 8 9
37	2 3 4 5 6 8 91 3 4 5 7 8 91 2 4 6 7 8 9
38	2 3 4 5 7 8 91 3 4 6 7 8 91 2 5 6 7 8 9
39	2 3 4 6 7 8 91 3 5 6 7 8 9
40	2 3 5 6 7 8 91 4 5 6 7 8 9
41	2 4 5 6 7 8 9
42	3 4 5 6 7 8 9

How to use cage combinations

Start with the cages that have only one combination. They tell you exactly which digits go in, so you only have to work out the order.
Every row, column and 3×3 box adds up to 45. Add up the cages that sit completely inside a box: what is left of the 45 is the total of the cells that are not covered yet.
If a digit is in every combination that is still possible, the cage must contain it. When the whole cage lies in one row, column or box, that digit cannot go anywhere else in it.

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