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Try to solve kakuro with the principle of exclusion. By examining the block length and the sum of the bordering black field you can see that there can be only a fixed set of solutions. We prepared the tables with possible combinations of sums by the block length.
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Tables with possible sums:
with field number: 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9
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with 2 fields:
sum ( reference number ) : possible solution
| 03: |
12 |
| 04: |
13 |
| 05: |
14 - 23 |
| 06: |
15 - 24 |
| 07: |
16 - 25 - 34 |
| 08: |
17 - 26 - 35 |
| 09: |
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: |
79 |
| 17: |
89 |
sum ( reference number ) : possible solution
| 06: |
123 |
| 07: |
124 |
| 08: |
125 - 134 |
| 09: |
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: |
689 |
| 24: |
789 |
sum ( reference number ) : possible solution
| 10: |
1234 |
| 11: |
1235 |
| 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: |
5789 |
| 30: |
6789 |
sum ( reference number ) : possible solution
| 15: |
12345 |
| 16: |
12346 |
| 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: |
46789 |
| 35: |
56789 |
sum ( reference number ) : possible solution
| 21: |
123456 |
| 22: |
123457 |
| 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: |
356789 |
| 39: |
456789 |
sum ( reference number ) : possible solution
| 28: |
1234567 |
| 29: |
1234568 |
| 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: |
2456789 |
| 42: |
3456789 |
sum ( reference number ) : possible solution
| 36: |
12345678 |
| 37: |
12345679 |
| 38: |
12345689 |
| 39: |
12345789 |
| 40: |
12346789 |
| 41: |
12356789 |
| 42: |
12456789 |
| 43: |
13456789 |
| 44: |
23456789 |
sum ( reference number ) : possible solution
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