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Try to solve killerSudoku with the principle of exclusion. By examining the block length and the sum of the colored block you can see that there can be only a fixed set of solutions.
In one sum area (one colored block) one number can only appear once! It does not matter, how many sectors (3x3 Fields) it covers.
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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