Kakuro combinations chart

This chart lists all 502 Kakuro combinations. Each one is a set of 2 to 9 different digits from 1 to 9. Find the clue and the number of cells, and the row shows the digits that can fill the run.

The same chart works for Killer Sudoku cages, because a cage also uses different digits. New to the puzzle? Read how to play Kakuro first.

Sums with only one combination

These 34 sums have exactly one set of digits. When you see one of them, you know the digits at once. Only the order is left to find. The solving guide shows how to use them.

Cells	Sum = digits
2	3 = 1+2 4 = 1+3 16 = 7+9 17 = 8+9
3	6 = 1+2+3 7 = 1+2+4 23 = 6+8+9 24 = 7+8+9
4	10 = 1+2+3+4 11 = 1+2+3+5 29 = 5+7+8+9 30 = 6+7+8+9
5	15 = 1+2+3+4+5 16 = 1+2+3+4+6 34 = 4+6+7+8+9 35 = 5+6+7+8+9
6	21 = 1+2+3+4+5+6 22 = 1+2+3+4+5+7 38 = 3+5+6+7+8+9 39 = 4+5+6+7+8+9
7	28 = 1+2+3+4+5+6+7 29 = 1+2+3+4+5+6+8 41 = 2+4+5+6+7+8+9 42 = 3+4+5+6+7+8+9
8	36 = 1+2+3+4+5+6+7+8 37 = 1+2+3+4+5+6+7+9 38 = 1+2+3+4+5+6+8+9 39 = 1+2+3+4+5+7+8+9 40 = 1+2+3+4+6+7+8+9 41 = 1+2+3+5+6+7+8+9 42 = 1+2+4+5+6+7+8+9 43 = 1+3+4+5+6+7+8+9 44 = 2+3+4+5+6+7+8+9
9	45 = 1+2+3+4+5+6+7+8+9

All 502 combinations

The rows go by the number of cells, then by the sum. A shaded row marked "Only one" is the single combination for that sum and cell count.

Sum	Cells	Digits	Note
3	2	1 2	Only one
4	2	1 3	Only one
5	2	1 4
5	2	2 3
6	2	1 5
6	2	2 4
7	2	1 6
7	2	2 5
7	2	3 4
8	2	1 7
8	2	2 6
8	2	3 5
9	2	1 8
9	2	2 7
9	2	3 6
9	2	4 5
10	2	1 9
10	2	2 8
10	2	3 7
10	2	4 6
11	2	2 9
11	2	3 8
11	2	4 7
11	2	5 6
12	2	3 9
12	2	4 8
12	2	5 7
13	2	4 9
13	2	5 8
13	2	6 7
14	2	5 9
14	2	6 8
15	2	6 9
15	2	7 8
16	2	7 9	Only one
17	2	8 9	Only one
6	3	1 2 3	Only one
7	3	1 2 4	Only one
8	3	1 2 5
8	3	1 3 4
9	3	1 2 6
9	3	1 3 5
9	3	2 3 4
10	3	1 2 7
10	3	1 3 6
10	3	1 4 5
10	3	2 3 5
11	3	1 2 8
11	3	1 3 7
11	3	1 4 6
11	3	2 3 6
11	3	2 4 5
12	3	1 2 9
12	3	1 3 8
12	3	1 4 7
12	3	1 5 6
12	3	2 3 7
12	3	2 4 6
12	3	3 4 5
13	3	1 3 9
13	3	1 4 8
13	3	1 5 7
13	3	2 3 8
13	3	2 4 7
13	3	2 5 6
13	3	3 4 6
14	3	1 4 9
14	3	1 5 8
14	3	1 6 7
14	3	2 3 9
14	3	2 4 8
14	3	2 5 7
14	3	3 4 7
14	3	3 5 6
15	3	1 5 9
15	3	1 6 8
15	3	2 4 9
15	3	2 5 8
15	3	2 6 7
15	3	3 4 8
15	3	3 5 7
15	3	4 5 6
16	3	1 6 9
16	3	1 7 8
16	3	2 5 9
16	3	2 6 8
16	3	3 4 9
16	3	3 5 8
16	3	3 6 7
16	3	4 5 7
17	3	1 7 9
17	3	2 6 9
17	3	2 7 8
17	3	3 5 9
17	3	3 6 8
17	3	4 5 8
17	3	4 6 7
18	3	1 8 9
18	3	2 7 9
18	3	3 6 9
18	3	3 7 8
18	3	4 5 9
18	3	4 6 8
18	3	5 6 7
19	3	2 8 9
19	3	3 7 9
19	3	4 6 9
19	3	4 7 8
19	3	5 6 8
20	3	3 8 9
20	3	4 7 9
20	3	5 6 9
20	3	5 7 8
21	3	4 8 9
21	3	5 7 9
21	3	6 7 8
22	3	5 8 9
22	3	6 7 9
23	3	6 8 9	Only one
24	3	7 8 9	Only one
10	4	1 2 3 4	Only one
11	4	1 2 3 5	Only one
12	4	1 2 3 6
12	4	1 2 4 5
13	4	1 2 3 7
13	4	1 2 4 6
13	4	1 3 4 5
14	4	1 2 3 8
14	4	1 2 4 7
14	4	1 2 5 6
14	4	1 3 4 6
14	4	2 3 4 5
15	4	1 2 3 9
15	4	1 2 4 8
15	4	1 2 5 7
15	4	1 3 4 7
15	4	1 3 5 6
15	4	2 3 4 6
16	4	1 2 4 9
16	4	1 2 5 8
16	4	1 2 6 7
16	4	1 3 4 8
16	4	1 3 5 7
16	4	1 4 5 6
16	4	2 3 4 7
16	4	2 3 5 6
17	4	1 2 5 9
17	4	1 2 6 8
17	4	1 3 4 9
17	4	1 3 5 8
17	4	1 3 6 7
17	4	1 4 5 7
17	4	2 3 4 8
17	4	2 3 5 7
17	4	2 4 5 6
18	4	1 2 6 9
18	4	1 2 7 8
18	4	1 3 5 9
18	4	1 3 6 8
18	4	1 4 5 8
18	4	1 4 6 7
18	4	2 3 4 9
18	4	2 3 5 8
18	4	2 3 6 7
18	4	2 4 5 7
18	4	3 4 5 6
19	4	1 2 7 9
19	4	1 3 6 9
19	4	1 3 7 8
19	4	1 4 5 9
19	4	1 4 6 8
19	4	1 5 6 7
19	4	2 3 5 9
19	4	2 3 6 8
19	4	2 4 5 8
19	4	2 4 6 7
19	4	3 4 5 7
20	4	1 2 8 9
20	4	1 3 7 9
20	4	1 4 6 9
20	4	1 4 7 8
20	4	1 5 6 8
20	4	2 3 6 9
20	4	2 3 7 8
20	4	2 4 5 9
20	4	2 4 6 8
20	4	2 5 6 7
20	4	3 4 5 8
20	4	3 4 6 7
21	4	1 3 8 9
21	4	1 4 7 9
21	4	1 5 6 9
21	4	1 5 7 8
21	4	2 3 7 9
21	4	2 4 6 9
21	4	2 4 7 8
21	4	2 5 6 8
21	4	3 4 5 9
21	4	3 4 6 8
21	4	3 5 6 7
22	4	1 4 8 9
22	4	1 5 7 9
22	4	1 6 7 8
22	4	2 3 8 9
22	4	2 4 7 9
22	4	2 5 6 9
22	4	2 5 7 8
22	4	3 4 6 9
22	4	3 4 7 8
22	4	3 5 6 8
22	4	4 5 6 7
23	4	1 5 8 9
23	4	1 6 7 9
23	4	2 4 8 9
23	4	2 5 7 9
23	4	2 6 7 8
23	4	3 4 7 9
23	4	3 5 6 9
23	4	3 5 7 8
23	4	4 5 6 8
24	4	1 6 8 9
24	4	2 5 8 9
24	4	2 6 7 9
24	4	3 4 8 9
24	4	3 5 7 9
24	4	3 6 7 8
24	4	4 5 6 9
24	4	4 5 7 8
25	4	1 7 8 9
25	4	2 6 8 9
25	4	3 5 8 9
25	4	3 6 7 9
25	4	4 5 7 9
25	4	4 6 7 8
26	4	2 7 8 9
26	4	3 6 8 9
26	4	4 5 8 9
26	4	4 6 7 9
26	4	5 6 7 8
27	4	3 7 8 9
27	4	4 6 8 9
27	4	5 6 7 9
28	4	4 7 8 9
28	4	5 6 8 9
29	4	5 7 8 9	Only one
30	4	6 7 8 9	Only one
15	5	1 2 3 4 5	Only one
16	5	1 2 3 4 6	Only one
17	5	1 2 3 4 7
17	5	1 2 3 5 6
18	5	1 2 3 4 8
18	5	1 2 3 5 7
18	5	1 2 4 5 6
19	5	1 2 3 4 9
19	5	1 2 3 5 8
19	5	1 2 3 6 7
19	5	1 2 4 5 7
19	5	1 3 4 5 6
20	5	1 2 3 5 9
20	5	1 2 3 6 8
20	5	1 2 4 5 8
20	5	1 2 4 6 7
20	5	1 3 4 5 7
20	5	2 3 4 5 6
21	5	1 2 3 6 9
21	5	1 2 3 7 8
21	5	1 2 4 5 9
21	5	1 2 4 6 8
21	5	1 2 5 6 7
21	5	1 3 4 5 8
21	5	1 3 4 6 7
21	5	2 3 4 5 7
22	5	1 2 3 7 9
22	5	1 2 4 6 9
22	5	1 2 4 7 8
22	5	1 2 5 6 8
22	5	1 3 4 5 9
22	5	1 3 4 6 8
22	5	1 3 5 6 7
22	5	2 3 4 5 8
22	5	2 3 4 6 7
23	5	1 2 3 8 9
23	5	1 2 4 7 9
23	5	1 2 5 6 9
23	5	1 2 5 7 8
23	5	1 3 4 6 9
23	5	1 3 4 7 8
23	5	1 3 5 6 8
23	5	1 4 5 6 7
23	5	2 3 4 5 9
23	5	2 3 4 6 8
23	5	2 3 5 6 7
24	5	1 2 4 8 9
24	5	1 2 5 7 9
24	5	1 2 6 7 8
24	5	1 3 4 7 9
24	5	1 3 5 6 9
24	5	1 3 5 7 8
24	5	1 4 5 6 8
24	5	2 3 4 6 9
24	5	2 3 4 7 8
24	5	2 3 5 6 8
24	5	2 4 5 6 7
25	5	1 2 5 8 9
25	5	1 2 6 7 9
25	5	1 3 4 8 9
25	5	1 3 5 7 9
25	5	1 3 6 7 8
25	5	1 4 5 6 9
25	5	1 4 5 7 8
25	5	2 3 4 7 9
25	5	2 3 5 6 9
25	5	2 3 5 7 8
25	5	2 4 5 6 8
25	5	3 4 5 6 7
26	5	1 2 6 8 9
26	5	1 3 5 8 9
26	5	1 3 6 7 9
26	5	1 4 5 7 9
26	5	1 4 6 7 8
26	5	2 3 4 8 9
26	5	2 3 5 7 9
26	5	2 3 6 7 8
26	5	2 4 5 6 9
26	5	2 4 5 7 8
26	5	3 4 5 6 8
27	5	1 2 7 8 9
27	5	1 3 6 8 9
27	5	1 4 5 8 9
27	5	1 4 6 7 9
27	5	1 5 6 7 8
27	5	2 3 5 8 9
27	5	2 3 6 7 9
27	5	2 4 5 7 9
27	5	2 4 6 7 8
27	5	3 4 5 6 9
27	5	3 4 5 7 8
28	5	1 3 7 8 9
28	5	1 4 6 8 9
28	5	1 5 6 7 9
28	5	2 3 6 8 9
28	5	2 4 5 8 9
28	5	2 4 6 7 9
28	5	2 5 6 7 8
28	5	3 4 5 7 9
28	5	3 4 6 7 8
29	5	1 4 7 8 9
29	5	1 5 6 8 9
29	5	2 3 7 8 9
29	5	2 4 6 8 9
29	5	2 5 6 7 9
29	5	3 4 5 8 9
29	5	3 4 6 7 9
29	5	3 5 6 7 8
30	5	1 5 7 8 9
30	5	2 4 7 8 9
30	5	2 5 6 8 9
30	5	3 4 6 8 9
30	5	3 5 6 7 9
30	5	4 5 6 7 8
31	5	1 6 7 8 9
31	5	2 5 7 8 9
31	5	3 4 7 8 9
31	5	3 5 6 8 9
31	5	4 5 6 7 9
32	5	2 6 7 8 9
32	5	3 5 7 8 9
32	5	4 5 6 8 9
33	5	3 6 7 8 9
33	5	4 5 7 8 9
34	5	4 6 7 8 9	Only one
35	5	5 6 7 8 9	Only one
21	6	1 2 3 4 5 6	Only one
22	6	1 2 3 4 5 7	Only one
23	6	1 2 3 4 5 8
23	6	1 2 3 4 6 7
24	6	1 2 3 4 5 9
24	6	1 2 3 4 6 8
24	6	1 2 3 5 6 7
25	6	1 2 3 4 6 9
25	6	1 2 3 4 7 8
25	6	1 2 3 5 6 8
25	6	1 2 4 5 6 7
26	6	1 2 3 4 7 9
26	6	1 2 3 5 6 9
26	6	1 2 3 5 7 8
26	6	1 2 4 5 6 8
26	6	1 3 4 5 6 7
27	6	1 2 3 4 8 9
27	6	1 2 3 5 7 9
27	6	1 2 3 6 7 8
27	6	1 2 4 5 6 9
27	6	1 2 4 5 7 8
27	6	1 3 4 5 6 8
27	6	2 3 4 5 6 7
28	6	1 2 3 5 8 9
28	6	1 2 3 6 7 9
28	6	1 2 4 5 7 9
28	6	1 2 4 6 7 8
28	6	1 3 4 5 6 9
28	6	1 3 4 5 7 8
28	6	2 3 4 5 6 8
29	6	1 2 3 6 8 9
29	6	1 2 4 5 8 9
29	6	1 2 4 6 7 9
29	6	1 2 5 6 7 8
29	6	1 3 4 5 7 9
29	6	1 3 4 6 7 8
29	6	2 3 4 5 6 9
29	6	2 3 4 5 7 8
30	6	1 2 3 7 8 9
30	6	1 2 4 6 8 9
30	6	1 2 5 6 7 9
30	6	1 3 4 5 8 9
30	6	1 3 4 6 7 9
30	6	1 3 5 6 7 8
30	6	2 3 4 5 7 9
30	6	2 3 4 6 7 8
31	6	1 2 4 7 8 9
31	6	1 2 5 6 8 9
31	6	1 3 4 6 8 9
31	6	1 3 5 6 7 9
31	6	1 4 5 6 7 8
31	6	2 3 4 5 8 9
31	6	2 3 4 6 7 9
31	6	2 3 5 6 7 8
32	6	1 2 5 7 8 9
32	6	1 3 4 7 8 9
32	6	1 3 5 6 8 9
32	6	1 4 5 6 7 9
32	6	2 3 4 6 8 9
32	6	2 3 5 6 7 9
32	6	2 4 5 6 7 8
33	6	1 2 6 7 8 9
33	6	1 3 5 7 8 9
33	6	1 4 5 6 8 9
33	6	2 3 4 7 8 9
33	6	2 3 5 6 8 9
33	6	2 4 5 6 7 9
33	6	3 4 5 6 7 8
34	6	1 3 6 7 8 9
34	6	1 4 5 7 8 9
34	6	2 3 5 7 8 9
34	6	2 4 5 6 8 9
34	6	3 4 5 6 7 9
35	6	1 4 6 7 8 9
35	6	2 3 6 7 8 9
35	6	2 4 5 7 8 9
35	6	3 4 5 6 8 9
36	6	1 5 6 7 8 9
36	6	2 4 6 7 8 9
36	6	3 4 5 7 8 9
37	6	2 5 6 7 8 9
37	6	3 4 6 7 8 9
38	6	3 5 6 7 8 9	Only one
39	6	4 5 6 7 8 9	Only one
28	7	1 2 3 4 5 6 7	Only one
29	7	1 2 3 4 5 6 8	Only one
30	7	1 2 3 4 5 6 9
30	7	1 2 3 4 5 7 8
31	7	1 2 3 4 5 7 9
31	7	1 2 3 4 6 7 8
32	7	1 2 3 4 5 8 9
32	7	1 2 3 4 6 7 9
32	7	1 2 3 5 6 7 8
33	7	1 2 3 4 6 8 9
33	7	1 2 3 5 6 7 9
33	7	1 2 4 5 6 7 8
34	7	1 2 3 4 7 8 9
34	7	1 2 3 5 6 8 9
34	7	1 2 4 5 6 7 9
34	7	1 3 4 5 6 7 8
35	7	1 2 3 5 7 8 9
35	7	1 2 4 5 6 8 9
35	7	1 3 4 5 6 7 9
35	7	2 3 4 5 6 7 8
36	7	1 2 3 6 7 8 9
36	7	1 2 4 5 7 8 9
36	7	1 3 4 5 6 8 9
36	7	2 3 4 5 6 7 9
37	7	1 2 4 6 7 8 9
37	7	1 3 4 5 7 8 9
37	7	2 3 4 5 6 8 9
38	7	1 2 5 6 7 8 9
38	7	1 3 4 6 7 8 9
38	7	2 3 4 5 7 8 9
39	7	1 3 5 6 7 8 9
39	7	2 3 4 6 7 8 9
40	7	1 4 5 6 7 8 9
40	7	2 3 5 6 7 8 9
41	7	2 4 5 6 7 8 9	Only one
42	7	3 4 5 6 7 8 9	Only one
36	8	1 2 3 4 5 6 7 8	Only one
37	8	1 2 3 4 5 6 7 9	Only one
38	8	1 2 3 4 5 6 8 9	Only one
39	8	1 2 3 4 5 7 8 9	Only one
40	8	1 2 3 4 6 7 8 9	Only one
41	8	1 2 3 5 6 7 8 9	Only one
42	8	1 2 4 5 6 7 8 9	Only one
43	8	1 3 4 5 6 7 8 9	Only one
44	8	2 3 4 5 6 7 8 9	Only one
45	9	1 2 3 4 5 6 7 8 9	Only one

How to use the chart

Count the white cells in the run, and read its clue.
Find the rows for that sum and cell count. Only these digits can go in the run.
Do the same for the crossing run. A cell can hold only a digit that is in both lists.
Remove the digits that the run already uses. Each digit goes in a run only once.

Example: an across clue of 3 in 2 cells can only be 1 and 2. A down clue of 4 in 2 cells can only be 1 and 3. The cell where the two runs meet must hold 1, the only digit in both lists.

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