Kakuro combinations chart

In kakuro, every run of white squares must add up to its clue, and no digit can appear twice in a run. That means only a few sets of digits can make each clue. This chart lists all of them, for runs of 2 to 9 squares.

How to use it: find the table for the length of the run, then the row for its clue. The digits in the run must be one of the sets in that row. When two runs cross, the square they share must use a digit that appears in a possible set of both runs.

Sums marked like this have only one possible set. They are the best place to start any puzzle. Try them on today’s Daily Kakuro.

Sums with only one combination

Learn these and most puzzles get much easier.

Squares	Sum	Digits
2	3	12
2	4	13
2	16	79
2	17	89
3	6	123
3	7	124
3	23	689
3	24	789
4	10	1234
4	11	1235
4	29	5789
4	30	6789
5	15	12345
5	16	12346
5	34	46789
5	35	56789
6	21	123456
6	22	123457
6	38	356789
6	39	456789
7	28	1234567
7	29	1234568
7	41	2456789
7	42	3456789
8	36	12345678
8	37	12345679
8	38	12345689
8	39	12345789
8	40	12346789
8	41	12356789
8	42	12456789
8	43	13456789
8	44	23456789
9	45	123456789

2 squares

Sum	Possible digits
3	12
4	13
5	23 14
6	24 15
7	34 25 16
8	35 26 17
9	45 36 27 18
10	46 37 28 19
11	56 47 38 29
12	57 48 39
13	67 58 49
14	68 59
15	78 69
16	79
17	89

3 squares

Sum	Possible digits
6	123
7	124
8	134 125
9	234 135 126
10	235 145 136 127
11	245 236 146 137 128
12	345 246 156 237 147 138 129
13	346 256 247 157 238 148 139
14	356 347 257 167 248 158 239 149
15	456 357 267 348 258 168 249 159
16	457 367 358 268 178 349 259 169
17	467 458 368 278 359 269 179
18	567 468 378 459 369 279 189
19	568 478 469 379 289
20	578 569 479 389
21	678 579 489
22	679 589
23	689
24	789

4 squares

Sum	Possible digits
10	1234
11	1235
12	1245 1236
13	1345 1246 1237
14	2345 1346 1256 1247 1238
15	2346 1356 1347 1257 1248 1239
16	2356 1456 2347 1357 1267 1348 1258 1249
17	2456 2357 1457 1367 2348 1358 1268 1349 1259
18	3456 2457 2367 1467 2358 1458 1368 1278 2349 1359 1269
19	3457 2467 1567 2458 2368 1468 1378 2359 1459 1369 1279
20	3467 2567 3458 2468 1568 2378 1478 2459 2369 1469 1379 1289
21	3567 3468 2568 2478 1578 3459 2469 1569 2379 1479 1389
22	4567 3568 3478 2578 1678 3469 2569 2479 1579 2389 1489
23	4568 3578 2678 3569 3479 2579 1679 2489 1589
24	4578 3678 4569 3579 2679 3489 2589 1689
25	4678 4579 3679 3589 2689 1789
26	5678 4679 4589 3689 2789
27	5679 4689 3789
28	5689 4789
29	5789
30	6789

5 squares

Sum	Possible digits
15	12345
16	12346
17	12356 12347
18	12456 12357 12348
19	13456 12457 12367 12358 12349
20	23456 13457 12467 12458 12368 12359
21	23457 13467 12567 13458 12468 12378 12459 12369
22	23467 13567 23458 13468 12568 12478 13459 12469 12379
23	23567 14567 23468 13568 13478 12578 23459 13469 12569 12479 12389
24	24567 23568 14568 23478 13578 12678 23469 13569 13479 12579 12489
25	34567 24568 23578 14578 13678 23569 14569 23479 13579 12679 13489 12589
26	34568 24578 23678 14678 24569 23579 14579 13679 23489 13589 12689
27	34578 24678 15678 34569 24579 23679 14679 23589 14589 13689 12789
28	34678 25678 34579 24679 15679 24589 23689 14689 13789
29	35678 34679 25679 34589 24689 15689 23789 14789
30	45678 35679 34689 25689 24789 15789
31	45679 35689 34789 25789 16789
32	45689 35789 26789
33	45789 36789
34	46789
35	56789

6 squares

Sum	Possible digits
21	123456
22	123457
23	123467 123458
24	123567 123468 123459
25	124567 123568 123478 123469
26	134567 124568 123578 123569 123479
27	234567 134568 124578 123678 124569 123579 123489
28	234568 134578 124678 134569 124579 123679 123589
29	234578 134678 125678 234569 134579 124679 124589 123689
30	234678 135678 234579 134679 125679 134589 124689 123789
31	235678 145678 234679 135679 234589 134689 125689 124789
32	245678 235679 145679 234689 135689 134789 125789
33	345678 245679 235689 145689 234789 135789 126789
34	345679 245689 235789 145789 136789
35	345689 245789 236789 146789
36	345789 246789 156789
37	346789 256789
38	356789
39	456789

7 squares

Sum	Possible digits
28	1234567
29	1234568
30	1234578 1234569
31	1234678 1234579
32	1235678 1234679 1234589
33	1245678 1235679 1234689
34	1345678 1245679 1235689 1234789
35	2345678 1345679 1245689 1235789
36	2345679 1345689 1245789 1236789
37	2345689 1345789 1246789
38	2345789 1346789 1256789
39	2346789 1356789
40	2356789 1456789
41	2456789
42	3456789

8 squares

Sum	Possible digits
36	12345678
37	12345679
38	12345689
39	12345789
40	12346789
41	12356789
42	12456789
43	13456789
44	23456789

9 squares

Sum	Possible digits
45	123456789

Tips for using combinations

A 2-square run with clue 3 must be 1 and 2; with 17 it must be 8 and 9. The same goes for 4 (1+3) and 16 (7+9).
A 9-square run always uses every digit once, so its clue is always 45.
For long runs, think about the missing digits instead: a 8-square run with clue 41 uses every digit except 4.
If every possible set for a run contains a digit, that digit is somewhere in the run, even if you don’t know where yet.

Play today’s Daily Kakuro · Past puzzles