Analysis of xx-top500-121-base.sdk
Contents
Original Sudoku
level: medium
position: .3.....2.....4.5..6..7......8.3.2.........4.1.........4.5.6.......5...3.1........ initial
Autosolve
position: 539681724817249563642735819.84312.5.326.5.4.1.514.63824.51632.82.85.413.1.3.2..45 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B8: 7,9 => CTR => B8: 6 * PRF # B8: 6 => SOL * PRF # B9: 7,9 => SOL * DIS # B9: 6 => CTR => B9: 7,9 * DIS # B8: 7,9 => CTR => B8: 6 * PRF # B8: 6 => SOL * PRF # B8: 6,7 => SOL * DIS # B8: 9 => CTR => B8: 6,7 * PRF # B9: 6,9 => SOL * DIS # B9: 7 => CTR => B9: 6,9 * CNT 10 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B8: 7,9 => CTR => B8: 6 * PRF B8: 6 => SOL * STA B8: 6 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .3.....2.....4.5..6..7......8.3.2.........4.1.........4.5.6.......5...3.1........ | initial |
| 539681724817249563642735819.84312.5.326.5.4.1.514.63824.51632.82.85.413.1.3.2..45 | autosolve |
| 539681724817249563642735819784312956326958471951476382475163298268594137193827645 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) A4: 7,9 A6: 7,9 D5: 8,9 F5: 7,8 E6: 7,9 G4: 6,9 I4: 6,7 H5: 7,9 B7: 7,9 E8: 7,9 D9: 8,9 F9: 7,8 H7: 7,9 I8: 6,7 G9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G4,I4: 6.. / G4 = 6 => 0 pairs (X) / I4 = 6 => 0 pairs (_) B8,B9: 6.. / B8 = 6 => 0 pairs (*) / B9 = 6 => 0 pairs (X) I8,G9: 6.. / I8 = 6 => 0 pairs (X) / G9 = 6 => 0 pairs (_) B8,I8: 6.. / B8 = 6 => 0 pairs (*) / I8 = 6 => 0 pairs (X) B9,G9: 6.. / B9 = 6 => 0 pairs (X) / G9 = 6 => 0 pairs (_) G4,G9: 6.. / G4 = 6 => 0 pairs (X) / G9 = 6 => 0 pairs (_) I4,I8: 6.. / I4 = 6 => 0 pairs (*) / I8 = 6 => 0 pairs (X) A4,A6: 7.. / A4 = 7 => 0 pairs (*) / A6 = 7 => 0 pairs (X) F5,E6: 7.. / F5 = 7 => 0 pairs (X) / E6 = 7 => 0 pairs (_) I4,H5: 7.. / I4 = 7 => 0 pairs (X) / H5 = 7 => 0 pairs (_) E8,F9: 7.. / E8 = 7 => 0 pairs (X) / F9 = 7 => 0 pairs (_) H7,I8: 7.. / H7 = 7 => 0 pairs (X) / I8 = 7 => 0 pairs (_) A4,I4: 7.. / A4 = 7 => 0 pairs (*) / I4 = 7 => 0 pairs (X) F5,H5: 7.. / F5 = 7 => 0 pairs (X) / H5 = 7 => 0 pairs (_) A6,E6: 7.. / A6 = 7 => 0 pairs (X) / E6 = 7 => 0 pairs (_) B7,H7: 7.. / B7 = 7 => 0 pairs (*) / H7 = 7 => 0 pairs (X) B9,F9: 7.. / B9 = 7 => 0 pairs (X) / F9 = 7 => 0 pairs (_) E6,E8: 7.. / E6 = 7 => 0 pairs (*) / E8 = 7 => 0 pairs (X) F5,F9: 7.. / F5 = 7 => 0 pairs (X) / F9 = 7 => 0 pairs (_) H5,H7: 7.. / H5 = 7 => 0 pairs (*) / H7 = 7 => 0 pairs (X) I4,I8: 7.. / I4 = 7 => 0 pairs (X) / I8 = 7 => 0 pairs (_) D5,F5: 8.. / D5 = 8 => 0 pairs (X) / F5 = 8 => 0 pairs (_) D9,F9: 8.. / D9 = 8 => 0 pairs (*) / F9 = 8 => 0 pairs (X) D5,D9: 8.. / D5 = 8 => 0 pairs (X) / D9 = 8 => 0 pairs (_) F5,F9: 8.. / F5 = 8 => 0 pairs (*) / F9 = 8 => 0 pairs (X) A4,A6: 9.. / A4 = 9 => 0 pairs (X) / A6 = 9 => 0 pairs (_) D5,E6: 9.. / D5 = 9 => 0 pairs (*) / E6 = 9 => 0 pairs (X) G4,H5: 9.. / G4 = 9 => 0 pairs (*) / H5 = 9 => 0 pairs (X) E8,D9: 9.. / E8 = 9 => 0 pairs (*) / D9 = 9 => 0 pairs (X) H7,G9: 9.. / H7 = 9 => 0 pairs (*) / G9 = 9 => 0 pairs (X) A4,G4: 9.. / A4 = 9 => 0 pairs (X) / G4 = 9 => 0 pairs (_) D5,H5: 9.. / D5 = 9 => 0 pairs (*) / H5 = 9 => 0 pairs (X) A6,E6: 9.. / A6 = 9 => 0 pairs (*) / E6 = 9 => 0 pairs (X) B7,H7: 9.. / B7 = 9 => 0 pairs (X) / H7 = 9 => 0 pairs (_) B8,E8: 9.. / B8 = 9 => 0 pairs (X) / E8 = 9 => 0 pairs (_) D5,D9: 9.. / D5 = 9 => 0 pairs (*) / D9 = 9 => 0 pairs (X) E6,E8: 9.. / E6 = 9 => 0 pairs (X) / E8 = 9 => 0 pairs (_) G4,G9: 9.. / G4 = 9 => 0 pairs (*) / G9 = 9 => 0 pairs (X) H5,H7: 9.. / H5 = 9 => 0 pairs (X) / H7 = 9 => 0 pairs (_) * DURATION: 0:01:04.977217 START: 06:55:00.550701 END: 06:56:05.527918 2017-05-04 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B7,D5,D9,E6,E8,F5,F9,G4,G9,H5,H7,I4,I8) * 539681724817249563642735819.84312.5.326.5.4.1.514.63824.51632.82.85.413.1.3.2..45 * PAIR B7: 7,9 BLK 7 B8: 7,9,6 # reduction candidate for 7,9 B8: 7,9 => CTR * 539681724817249563642735819.84312.5.326.5.4.1.514.63824.51632.82.85.4136163.27945 B8: 6 => SOLVED * 539681724817249563642735819784312956326958471951476382475163298268594137193827645 B9: 7,9,6 # reduction candidate for 7,9 B9: 7,9 => SOLVED * 539681724817249563642735819784312956326958471951476382475163298268594137193827645 B9: 6 => CTR * 539681724817249563642735819.84312.5.326.5.4.1.514.63824.51632.82.85.413.163.27945 * PAIR E8: 7,9 ROW 8 B8: 7,9,6 # reduction candidate for 7,9 B8: 7,9 => CTR * 539681724817249563642735819.84312.5.326.5.4.1.514.63824.51632.82.85.4136163.27945 B8: 6 => SOLVED * 539681724817249563642735819784312956326958471951476382475163298268594137193827645 * PAIR I8: 6,7 ROW 8 B8: 6,7,9 # reduction candidate for 6,7 B8: 6,7 => SOLVED * 539681724817249563642735819784312956326958471951476382475163298268594137193827645 B8: 9 => CTR * 539681724817249563642735819.84312.5.326.5.4.1.514.63824.51632.82985741361.3.2..45 * PAIR G9: 6,9 ROW 9 B9: 6,9,7 # reduction candidate for 6,9 B9: 6,9 => SOLVED * 539681724817249563642735819784312956326958471951476382475163298268594137193827645 B9: 7 => CTR * 539681724817249563642735819.84312.5.326.5.4.1.514.63824.51632.82685941371.3.2..45 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-121-base-pr-000.dot * REASONING * DIS # B8: 7,9 => CTR => B8: 6 * PRF # B8: 6 => SOL * PRF # B9: 7,9 => SOL * DIS # B9: 6 => CTR => B9: 7,9 * DIS # B8: 7,9 => CTR => B8: 6 * PRF # B8: 6 => SOL * PRF # B8: 6,7 => SOL * DIS # B8: 9 => CTR => B8: 6,7 * PRF # B9: 6,9 => SOL * DIS # B9: 7 => CTR => B9: 6,9 * CNT 10 HDP CHAINS / 10 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B7,D5,D9,E6,E8,F5,F9,G4,G9,H5,H7,I4,I8) * 539681724817249563642735819.84312.5.326.5.4.1.514.63824.51632.82.85.413.1.3.2..45 * PAIR B7: 7,9 BLK 7 B8: 7,9,6 # reduction candidate for 7,9 B8: 7,9 => CTR * 539681724817249563642735819.84312.5.326.5.4.1.514.63824.51632.82.85.4136163.27945 B8: 6 => SOLVED * 539681724817249563642735819784312956326958471951476382475163298268594137193827645 * DURATION: 0:00:01.797356 START: 06:56:17.516486 END: 06:56:19.313842 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-121-base-pr-001.dot * REASONING * DIS # B8: 7,9 => CTR => B8: 6 * PRF B8: 6 => SOL * STA B8: 6 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 121 solution: 539681724817249563642735819784312956326958471951476382475163298268594137193827645 info: 1803 FNWX S8.f 17390 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 539681724817249563642735819784312956326958471951476382475163298268594137193827645 solved
See section Pair Reduction for the HDP chains leading to this result.
Appendix: Full HDP Chains
A1. Pair Reduction Analysis
Full list of HDP chains traversed:
* DIS # B8: 7,9 => CTR => B8: 6 * PRF # B8: 6 => SOL * PRF # B9: 7,9 => SOL * DIS # B9: 6 => CTR => B9: 7,9 * DIS # B8: 7,9 => CTR => B8: 6 * PRF # B8: 6 => SOL * PRF # B8: 6,7 => SOL * DIS # B8: 9 => CTR => B8: 6,7 * PRF # B9: 6,9 => SOL * DIS # B9: 7 => CTR => B9: 6,9 * CNT 10 HDP CHAINS / 10 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B8: 7,9 => CTR => B8: 6 * PRF B8: 6 => SOL * STA B8: 6 * CNT 2 HDP CHAINS / 1 HYP OPENED