Kakuro

Kakuro Combinations

In Kakuro, each run of white cells holds different digits from 1 to 9 that add up to the clue. Because the digits can’t repeat, most sums allow only a handful of digit sets — and the extreme sums allow just one. Knowing these combinations is the fastest way to solve.

Below are the sets worth memorising first, then the complete table for every run length and sum.

Unique combinations

These clue sums have only one possible digit set — fill them in on sight.

2 cells = 31 2
2 cells = 41 3
2 cells = 167 9
2 cells = 178 9
3 cells = 61 2 3
3 cells = 71 2 4
3 cells = 236 8 9
3 cells = 247 8 9
4 cells = 101 2 3 4
4 cells = 111 2 3 5
4 cells = 295 7 8 9
4 cells = 306 7 8 9
5 cells = 151 2 3 4 5
5 cells = 161 2 3 4 6
5 cells = 344 6 7 8 9
5 cells = 355 6 7 8 9
6 cells = 211 2 3 4 5 6
6 cells = 221 2 3 4 5 7
6 cells = 383 5 6 7 8 9
6 cells = 394 5 6 7 8 9
7 cells = 281 2 3 4 5 6 7
7 cells = 291 2 3 4 5 6 8
7 cells = 412 4 5 6 7 8 9
7 cells = 423 4 5 6 7 8 9
8 cells = 361 2 3 4 5 6 7 8
8 cells = 371 2 3 4 5 6 7 9
8 cells = 381 2 3 4 5 6 8 9
8 cells = 391 2 3 4 5 7 8 9
8 cells = 401 2 3 4 6 7 8 9
8 cells = 411 2 3 5 6 7 8 9
8 cells = 421 2 4 5 6 7 8 9
8 cells = 431 3 4 5 6 7 8 9
8 cells = 442 3 4 5 6 7 8 9
9 cells = 451 2 3 4 5 6 7 8 9

Full combination table

2 cells sums 3–17

Sum	Possible digits
3	1 2
4	1 3
5	1 42 3
6	1 52 4
7	1 62 53 4
8	1 72 63 5
9	1 82 73 64 5
10	1 92 83 74 6
11	2 93 84 75 6
12	3 94 85 7
13	4 95 86 7
14	5 96 8
15	6 97 8
16	7 9
17	8 9

3 cells sums 6–24

Sum	Possible digits
6	1 2 3
7	1 2 4
8	1 2 51 3 4
9	1 2 61 3 52 3 4
10	1 2 71 3 61 4 52 3 5
11	1 2 81 3 71 4 62 3 62 4 5
12	1 2 91 3 81 4 71 5 62 3 72 4 63 4 5
13	1 3 91 4 81 5 72 3 82 4 72 5 63 4 6
14	1 4 91 5 81 6 72 3 92 4 82 5 73 4 73 5 6
15	1 5 91 6 82 4 92 5 82 6 73 4 83 5 74 5 6
16	1 6 91 7 82 5 92 6 83 4 93 5 83 6 74 5 7
17	1 7 92 6 92 7 83 5 93 6 84 5 84 6 7
18	1 8 92 7 93 6 93 7 84 5 94 6 85 6 7
19	2 8 93 7 94 6 94 7 85 6 8
20	3 8 94 7 95 6 95 7 8
21	4 8 95 7 96 7 8
22	5 8 96 7 9
23	6 8 9
24	7 8 9

4 cells sums 10–30

Sum	Possible digits
10	1 2 3 4
11	1 2 3 5
12	1 2 3 61 2 4 5
13	1 2 3 71 2 4 61 3 4 5
14	1 2 3 81 2 4 71 2 5 61 3 4 62 3 4 5
15	1 2 3 91 2 4 81 2 5 71 3 4 71 3 5 62 3 4 6
16	1 2 4 91 2 5 81 2 6 71 3 4 81 3 5 71 4 5 62 3 4 72 3 5 6
17	1 2 5 91 2 6 81 3 4 91 3 5 81 3 6 71 4 5 72 3 4 82 3 5 72 4 5 6
18	1 2 6 91 2 7 81 3 5 91 3 6 81 4 5 81 4 6 72 3 4 92 3 5 82 3 6 72 4 5 73 4 5 6
19	1 2 7 91 3 6 91 3 7 81 4 5 91 4 6 81 5 6 72 3 5 92 3 6 82 4 5 82 4 6 73 4 5 7
20	1 2 8 91 3 7 91 4 6 91 4 7 81 5 6 82 3 6 92 3 7 82 4 5 92 4 6 82 5 6 73 4 5 83 4 6 7
21	1 3 8 91 4 7 91 5 6 91 5 7 82 3 7 92 4 6 92 4 7 82 5 6 83 4 5 93 4 6 83 5 6 7
22	1 4 8 91 5 7 91 6 7 82 3 8 92 4 7 92 5 6 92 5 7 83 4 6 93 4 7 83 5 6 84 5 6 7
23	1 5 8 91 6 7 92 4 8 92 5 7 92 6 7 83 4 7 93 5 6 93 5 7 84 5 6 8
24	1 6 8 92 5 8 92 6 7 93 4 8 93 5 7 93 6 7 84 5 6 94 5 7 8
25	1 7 8 92 6 8 93 5 8 93 6 7 94 5 7 94 6 7 8
26	2 7 8 93 6 8 94 5 8 94 6 7 95 6 7 8
27	3 7 8 94 6 8 95 6 7 9
28	4 7 8 95 6 8 9
29	5 7 8 9
30	6 7 8 9

5 cells sums 15–35

Sum	Possible digits
15	1 2 3 4 5
16	1 2 3 4 6
17	1 2 3 4 71 2 3 5 6
18	1 2 3 4 81 2 3 5 71 2 4 5 6
19	1 2 3 4 91 2 3 5 81 2 3 6 71 2 4 5 71 3 4 5 6
20	1 2 3 5 91 2 3 6 81 2 4 5 81 2 4 6 71 3 4 5 72 3 4 5 6
21	1 2 3 6 91 2 3 7 81 2 4 5 91 2 4 6 81 2 5 6 71 3 4 5 81 3 4 6 72 3 4 5 7
22	1 2 3 7 91 2 4 6 91 2 4 7 81 2 5 6 81 3 4 5 91 3 4 6 81 3 5 6 72 3 4 5 82 3 4 6 7
23	1 2 3 8 91 2 4 7 91 2 5 6 91 2 5 7 81 3 4 6 91 3 4 7 81 3 5 6 81 4 5 6 72 3 4 5 92 3 4 6 82 3 5 6 7
24	1 2 4 8 91 2 5 7 91 2 6 7 81 3 4 7 91 3 5 6 91 3 5 7 81 4 5 6 82 3 4 6 92 3 4 7 82 3 5 6 82 4 5 6 7
25	1 2 5 8 91 2 6 7 91 3 4 8 91 3 5 7 91 3 6 7 81 4 5 6 91 4 5 7 82 3 4 7 92 3 5 6 92 3 5 7 82 4 5 6 83 4 5 6 7
26	1 2 6 8 91 3 5 8 91 3 6 7 91 4 5 7 91 4 6 7 82 3 4 8 92 3 5 7 92 3 6 7 82 4 5 6 92 4 5 7 83 4 5 6 8
27	1 2 7 8 91 3 6 8 91 4 5 8 91 4 6 7 91 5 6 7 82 3 5 8 92 3 6 7 92 4 5 7 92 4 6 7 83 4 5 6 93 4 5 7 8
28	1 3 7 8 91 4 6 8 91 5 6 7 92 3 6 8 92 4 5 8 92 4 6 7 92 5 6 7 83 4 5 7 93 4 6 7 8
29	1 4 7 8 91 5 6 8 92 3 7 8 92 4 6 8 92 5 6 7 93 4 5 8 93 4 6 7 93 5 6 7 8
30	1 5 7 8 92 4 7 8 92 5 6 8 93 4 6 8 93 5 6 7 94 5 6 7 8
31	1 6 7 8 92 5 7 8 93 4 7 8 93 5 6 8 94 5 6 7 9
32	2 6 7 8 93 5 7 8 94 5 6 8 9
33	3 6 7 8 94 5 7 8 9
34	4 6 7 8 9
35	5 6 7 8 9

6 cells sums 21–39

Sum	Possible digits
21	1 2 3 4 5 6
22	1 2 3 4 5 7
23	1 2 3 4 5 81 2 3 4 6 7
24	1 2 3 4 5 91 2 3 4 6 81 2 3 5 6 7
25	1 2 3 4 6 91 2 3 4 7 81 2 3 5 6 81 2 4 5 6 7
26	1 2 3 4 7 91 2 3 5 6 91 2 3 5 7 81 2 4 5 6 81 3 4 5 6 7
27	1 2 3 4 8 91 2 3 5 7 91 2 3 6 7 81 2 4 5 6 91 2 4 5 7 81 3 4 5 6 82 3 4 5 6 7
28	1 2 3 5 8 91 2 3 6 7 91 2 4 5 7 91 2 4 6 7 81 3 4 5 6 91 3 4 5 7 82 3 4 5 6 8
29	1 2 3 6 8 91 2 4 5 8 91 2 4 6 7 91 2 5 6 7 81 3 4 5 7 91 3 4 6 7 82 3 4 5 6 92 3 4 5 7 8
30	1 2 3 7 8 91 2 4 6 8 91 2 5 6 7 91 3 4 5 8 91 3 4 6 7 91 3 5 6 7 82 3 4 5 7 92 3 4 6 7 8
31	1 2 4 7 8 91 2 5 6 8 91 3 4 6 8 91 3 5 6 7 91 4 5 6 7 82 3 4 5 8 92 3 4 6 7 92 3 5 6 7 8
32	1 2 5 7 8 91 3 4 7 8 91 3 5 6 8 91 4 5 6 7 92 3 4 6 8 92 3 5 6 7 92 4 5 6 7 8
33	1 2 6 7 8 91 3 5 7 8 91 4 5 6 8 92 3 4 7 8 92 3 5 6 8 92 4 5 6 7 93 4 5 6 7 8
34	1 3 6 7 8 91 4 5 7 8 92 3 5 7 8 92 4 5 6 8 93 4 5 6 7 9
35	1 4 6 7 8 92 3 6 7 8 92 4 5 7 8 93 4 5 6 8 9
36	1 5 6 7 8 92 4 6 7 8 93 4 5 7 8 9
37	2 5 6 7 8 93 4 6 7 8 9
38	3 5 6 7 8 9
39	4 5 6 7 8 9

7 cells sums 28–42

Sum	Possible digits
28	1 2 3 4 5 6 7
29	1 2 3 4 5 6 8
30	1 2 3 4 5 6 91 2 3 4 5 7 8
31	1 2 3 4 5 7 91 2 3 4 6 7 8
32	1 2 3 4 5 8 91 2 3 4 6 7 91 2 3 5 6 7 8
33	1 2 3 4 6 8 91 2 3 5 6 7 91 2 4 5 6 7 8
34	1 2 3 4 7 8 91 2 3 5 6 8 91 2 4 5 6 7 91 3 4 5 6 7 8
35	1 2 3 5 7 8 91 2 4 5 6 8 91 3 4 5 6 7 92 3 4 5 6 7 8
36	1 2 3 6 7 8 91 2 4 5 7 8 91 3 4 5 6 8 92 3 4 5 6 7 9
37	1 2 4 6 7 8 91 3 4 5 7 8 92 3 4 5 6 8 9
38	1 2 5 6 7 8 91 3 4 6 7 8 92 3 4 5 7 8 9
39	1 3 5 6 7 8 92 3 4 6 7 8 9
40	1 4 5 6 7 8 92 3 5 6 7 8 9
41	2 4 5 6 7 8 9
42	3 4 5 6 7 8 9

8 cells sums 36–44

Sum	Possible digits
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 cells sums 45–45

Sum	Possible digits
45	1 2 3 4 5 6 7 8 9

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