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A General Logic for Sudoku Golden Nugget |
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Elimination 1, The Layer Cake
Logic Diagram Below is a set/linkset logic diagram for the elimination
showing the 5 logical layers for (top to bottom) digits 1, 2, 4, 6, and
7. Each of the 5 strong inference sets
is indicated as a SIS. Nodes are represented in NCR notation. (NOTE:
this diagram is an update, many of the older diagrams are in RCN notation) 1c7
2c7 1c2 1b1 2c1 1c4 2c4 7n9 3n9 3n8 2n8 4n8 4c6 7c1 4c2 7c6 4c7 7c7 1R1: 117=======112A=112A | |
113
} | |
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} 1R3: |
132B=132B=====================139==138 } | | |
| } SIS 1 1R7: 177=======172============174=======179 |
| } | | |
| | } 1R4: 147======================144========|====|====|========148 } | |
| | 2B3: 217============================|===239F=238C=228 |
} 227 | |
| | |
} | | |
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} 2R7: 277======================274==279 |
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} SIS 2 | | |
| | |
| } 2R3: | 231=======234===|===239F=238C |
| } | | | |
| | |
} 2R4: 247============241=============|====|====|====|===248 }
| | |
| | 6C8: | |
638==628 | } SIS 3
| | |
| | 4B3: { |
439G=438D=428===|=======================417 { | |
| | |
427 { | |
| | | | 4R4: SIS 4 {
| | |
| 448============442=======447 { | |
| | | | | 4R3: { |
439G=438D==|====|===436=======432 | { | |
| | |
| | 4R7: { 479===|====|====|====|===476=================477
| | |
| | 7B3: { |
739H=738E=728===|============================717 { |
| | | 727 { |
| | | | 7R4: SIS 5 {
| | |
748=================746=======747 { |
| | | | 7R3: { |
739H=738E================731=======736 | { |
| | 7R7: { 779===========================771=================777
Logic and Grid E1b 54 Nodes, Raw Rank = 1 (linksets - sets) 17 Sets = {1r1347 2r347 4r347 7r347 6c8 247b3} 18 Links = {27c1 14c2 12c4 47c6 1247c7 234n8 37n9 1b1} --> (7n9) => r7c9<>3
+--------------------------------------------------------------------------------------+ | 25678
4568(1) 24567(1) | 268 2467
4678 | (1247) 3
9 | | 26789
4689 2467 | 23689 23467
1 | (247) (2467)
5 | | 69(27)
69(14) 3 | 69(2) 5
69(47) | 8 (12467) (1247)
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+--------------------------------------------------------------------------------------+ | 35(2)
35(4) 8 | 35(1) 9
35(7) | 35(1247) (1247) 6
| | 3569
7 456 | 13568 136
2 | 13459
1489 1348 | | 1
3569 256 | 4 367 35678
| 23579 2789 2378
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+--------------------------------------------------------------------------------------+ | 36(7)
36(1) 9 | 36(12) 8
36(4) | 3(1247) 5
-3(1247) | | 3578
2 157 | 1359 134
3459 | 6 14789 13478
| | 4
13568 156 | 7 1236 3569
| 1239 1289 1238
|
+--------------------------------------------------------------------------------------+ |
This first
elimination takes the interesting form of a layered cake, as seen in the
small right image. Each of the 5 single digit layers forms a strong inference
set, all of which combine in the same group of 5 vertical linksets.
Each of the layers guarantees one candidate in the 5 linksets thus the
linksets must each have one to form a rank 0 region. The eliminatee sits in
one of the rank 0 linksets. Other eliminations from Golden Nugget show
similar layering effects so the layered method suggested by the solver might be
showing a weakness in the puzzle that can be exploited.