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A General Logic for Sudoku Golden Nugget |
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Elimination 23x
Elimination 23x is an elimination from a previous solution to Golden Nugget. It is a rank 4 structure that uses all its triplets to raise the rank to 1 at the elimination side, in spite of the fact that two triplets cannot be occupied at the same time. This emphasizes that triplets can raise the rank whether occupied or not. Se the simplified logic diagram below for an explanation.
Set Logic and Grid E23[
24 Nodes, Rank 4: 8 Sets = {2479r3 247r4 2n7} 12 Links = {2c1 4c2 7c6 247c7 3n46 4n8 247b3} --> (7c7*7b3) => r1c7<>7
+--------------------------------------------------------------------+ | 257
145 12457 | 68
2467 678 | 1247
3 9 | | 89
89 2467 | 3
247 1 | (247)
267 5 | | 6(2)
16(4) 3 | (29)
5 (479) | 8
16(247 1(47) |
+--------------------------------------------------------------------+ | 3(2)
35(4) 8 | 15
9 35(7) | 15(247 1(247) 6 | | 3569
7 456 | 1568
136 2 | 13459
1489 138 | | 1
3569 256 | 4
367 35678 | 23579
2789 2378 |
+--------------------------------------------------------------------+ | 367
136 9 |
126 8 346
| 1347 5 124
| | 358
2 157 | 159
134 3459 | 6
14789 13478 | | 4
3568 156 | 7
1236 3569 | 1239
189 1238 |
+--------------------------------------------------------------------+ Logic Diagram The following is a simplified logic diagram to demonstrate the principle. The tri0plets p272 and p274 are the focus. One must be occupied and the other unoccupied. The occupied one reduces the overall rank by occupying 2 linksets simultaneously, while the unoccupied one must reduce the rank along its minor path, i.e., in the direction of the elimination. The pair lowers the rank by two, combined with the third triplet produces the elimination. p367C=====p387 /
\ | / \ |
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| +-----X (target) |
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p467==p487==p477 | | (|)
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<----Rank 1 region. | | | | p272A=======p274B | | / \
/ \ | | / \
/ \ | | | |
| | p369=========|===========|=====|=====|=====|====p349 | | | |
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p382===|=====|=====|====p342==p312
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| | | p482==============p472===|=====|==========p412 | | | | |
p484====================p474===|================p424 |
| | p364======================================p384==============p324 |
