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A General Logic for Sudoku Golden Nugget |
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Elimination 19 Elimination 19 again takes the form of a layered structure like elimination 1. In this case, 3 of the 4 single digit layers form strong inference sets that combine in a group 4 vertical linksets. Each of the layers guarantees that 1 candidate is in the linksets thus 3 of the 4 nodes at digit layer 2 must be empty. This raises the rank in level 2 and forces linkset 2c4 to be rank 0, thus eliminating 2r1c4. Linkset 2r4 is highlighted black in the diagrams below.
Another view of the elimination showing rank 0 linkset 2r4 highlighted black and the SIS at level 4 highlighted with pink cubes.
Logic Diagram Below is a set/linkset logic diagram for the elimination showing
the 4 logical layers for (top to bottom) digits 1, 2, 4, and 7. Each of the 3
strong inference sets is indicated as SIS. The added effect of the 3 SIS is input to
digit layer 4. All nodes are rcn notation p321=p121A==p131 \_____|_____/ /
\ |
p171B=========================p391==p381
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| | p721========p771==p741=====================|=====|==========p791 | | | | |
p471==p441=====================|=====|====p481 | SIS 1 ----> | |
| |
| | |
| p632========p132
| | |
| | p232 | |
| +--+ | | Level 2 ----> |
| | | p792H=====|====p742 |
| | |
| \ |
| |
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p382C=p482===|====p982==p682
| |
| | |
| | |
p392==p382C==|=====|================p342==p312 SIS 2 ----> | |
| |
p174==============p394F=p384D
| | p274 | |
| | | | |
| | | p324==p364==p394F=p384D |
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| |
| | |
| |
p474==p424===|=====|=====|====p484
| | | |
| | |
p774========p764===|=====|=====|====p794 SIS 3 ----> | |
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p397G=p387E==|======================p367
| | | |
p397G=p387E==|================p277
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p487==============p477==p467 Logic and Grid rank 2: S15={247r3 147r4 124r7 2c38 1b1 147b3}, L17={1r1 2r6 14c2 12c4 47c6 147c7 3n89 4n8 7n9 2b19} => (2c4) => r1c4<>2 ------------------------------------------------------------------------------- |
25678 458*1 457*12
| 268 2467
4678 | 2*14 3
9 | |
289 489 47*2
| 389 2347 1
| 2*47 6 5
| |
69*2 69*14 3
| 69*2 5 9*47
| 8 *1247 *1247
| ------------------------------------------------------------------------------- |
235 35*4 8
| 5*1 9 35*7
| 235*147 *1247 6 | |
3569 7 456
| 13568 136 2
| 13459 1489 1348
| |
1 3569 56*2
| 4 367 35678
| 23579 789*2 378
| ------------------------------------------------------------------------------- |
367 36*1 9
| 6*12 8 36*4
| 37*14 5 *124
| |
3578 2 157
| 1359 134 3459
| 6 14789 13478
| |
4 13568 156
| 7 1236 3569
| 139 189*2 1238
| ------------------------------------------------------------------------------- |
