Analysis of xx-top500-361-base.sdk
Contents
Original Sudoku
level: medium
position: ...6..3...24.......5......73..2........5....4.......1.5.....28.7...4........1.... initial
Autosolve
position: 1..65.342.24173.5..5342.1.73152.47.....531.244.27.65135493672817.1.42.3523..1547. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B1: 7,8 => SOL * DIS # B1: 9 => CTR => B1: 7,8 * PRF # A3: 6,9 => SOL * DIS # A3: 8 => CTR => A3: 6,9 * DIS # G2: 6,9 => CTR => G2: 8 * PRF # G2: 8 => SOL * PRF # I2: 6,9 => SOL * DIS # I2: 8 => CTR => I2: 6,9 * DIS # B1: 8,9 => CTR => B1: 7 * PRF # B1: 7 => SOL * DIS # A3: 8,9 => CTR => A3: 6 * PRF # A3: 6 => SOL * DIS # G2: 6,9 => CTR => G2: 8 * PRF # G2: 8 => SOL * PRF # I2: 6,9 => SOL * DIS # I2: 8 => CTR => I2: 6,9 * PRF # A3: 6,9 => SOL * DIS # A3: 8 => CTR => A3: 6,9 * DIS # A3: 8,9 => CTR => A3: 6 * PRF # A3: 6 => SOL * DIS # B1: 8,9 => CTR => B1: 7 * PRF # B1: 7 => SOL * PRF # I4: 8,9 => SOL * DIS # I4: 6 => CTR => I4: 8,9 * DIS # I4: 6,9 => CTR => I4: 8 * PRF # I4: 8 => SOL * PRF # I4: 8,9 => SOL * DIS # I4: 6 => CTR => I4: 8,9 * PRF # G2: 8,9 => SOL * DIS # G2: 6 => CTR => G2: 8,9 * DIS # G2: 6,9 => CTR => G2: 8 * PRF # G2: 8 => SOL * PRF # I2: 6,9 => SOL * DIS # I2: 8 => CTR => I2: 6,9 * DIS # I4: 6,9 => CTR => I4: 8 * PRF # I4: 8 => SOL * CNT 36 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B1: 7,8 => SOL * STA B1: 7,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...6..3...24.......5......73..2........5....4.......1.5.....28.7...4........1.... | initial |
| 1..65.342.24173.5..5342.1.73152.47.....531.244.27.65135493672817.1.42.3523..1547. | autosolve |
| 178659342924173856653428197315294768867531924492786513549367281781942635236815479 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) C1: 7,8 A2: 6,9 F1: 8,9 F3: 8,9 H3: 6,9 A5: 8,9 B5: 6,7 C5: 6,7 B6: 8,9 E4: 8,9 E6: 8,9 H4: 6,9 G5: 8,9 B8: 6,8 C9: 6,8 D8: 8,9 D9: 8,9 G8: 6,9 I9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,A3: 6.. / A2 = 6 => 0 pairs (X) / A3 = 6 => 0 pairs (_) B5,C5: 6.. / B5 = 6 => 0 pairs (*) / C5 = 6 => 0 pairs (X) H4,I4: 6.. / H4 = 6 => 0 pairs (*) / I4 = 6 => 0 pairs (X) B8,C9: 6.. / B8 = 6 => 0 pairs (X) / C9 = 6 => 0 pairs (_) G8,I9: 6.. / G8 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) A3,H3: 6.. / A3 = 6 => 0 pairs (*) / H3 = 6 => 0 pairs (X) B8,G8: 6.. / B8 = 6 => 0 pairs (X) / G8 = 6 => 0 pairs (_) C9,I9: 6.. / C9 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) B5,B8: 6.. / B5 = 6 => 0 pairs (*) / B8 = 6 => 0 pairs (X) C5,C9: 6.. / C5 = 6 => 0 pairs (X) / C9 = 6 => 0 pairs (_) G2,G8: 6.. / G2 = 6 => 0 pairs (X) / G8 = 6 => 0 pairs (_) H3,H4: 6.. / H3 = 6 => 0 pairs (X) / H4 = 6 => 0 pairs (_) B1,C1: 7.. / B1 = 7 => 0 pairs (*) / C1 = 7 => 0 pairs (X) B5,C5: 7.. / B5 = 7 => 0 pairs (X) / C5 = 7 => 0 pairs (_) B1,B5: 7.. / B1 = 7 => 0 pairs (*) / B5 = 7 => 0 pairs (X) C1,C5: 7.. / C1 = 7 => 0 pairs (X) / C5 = 7 => 0 pairs (_) F1,F3: 8.. / F1 = 8 => 0 pairs (X) / F3 = 8 => 0 pairs (_) G2,I2: 8.. / G2 = 8 => 0 pairs (*) / I2 = 8 => 0 pairs (X) A5,B6: 8.. / A5 = 8 => 0 pairs (*) / B6 = 8 => 0 pairs (X) E4,E6: 8.. / E4 = 8 => 0 pairs (X) / E6 = 8 => 0 pairs (_) I4,G5: 8.. / I4 = 8 => 0 pairs (*) / G5 = 8 => 0 pairs (X) B8,C9: 8.. / B8 = 8 => 0 pairs (*) / C9 = 8 => 0 pairs (X) D8,D9: 8.. / D8 = 8 => 0 pairs (X) / D9 = 8 => 0 pairs (_) A3,F3: 8.. / A3 = 8 => 0 pairs (X) / F3 = 8 => 0 pairs (_) E4,I4: 8.. / E4 = 8 => 0 pairs (X) / I4 = 8 => 0 pairs (_) A5,G5: 8.. / A5 = 8 => 0 pairs (*) / G5 = 8 => 0 pairs (X) B6,E6: 8.. / B6 = 8 => 0 pairs (X) / E6 = 8 => 0 pairs (_) B8,D8: 8.. / B8 = 8 => 0 pairs (*) / D8 = 8 => 0 pairs (X) C9,D9: 8.. / C9 = 8 => 0 pairs (X) / D9 = 8 => 0 pairs (_) A3,A5: 8.. / A3 = 8 => 0 pairs (X) / A5 = 8 => 0 pairs (_) C1,C9: 8.. / C1 = 8 => 0 pairs (*) / C9 = 8 => 0 pairs (X) G2,G5: 8.. / G2 = 8 => 0 pairs (*) / G5 = 8 => 0 pairs (X) I2,I4: 8.. / I2 = 8 => 0 pairs (X) / I4 = 8 => 0 pairs (_) F1,F3: 9.. / F1 = 9 => 0 pairs (*) / F3 = 9 => 0 pairs (X) A5,B6: 9.. / A5 = 9 => 0 pairs (X) / B6 = 9 => 0 pairs (_) E4,E6: 9.. / E4 = 9 => 0 pairs (*) / E6 = 9 => 0 pairs (X) D8,D9: 9.. / D8 = 9 => 0 pairs (*) / D9 = 9 => 0 pairs (X) G8,I9: 9.. / G8 = 9 => 0 pairs (X) / I9 = 9 => 0 pairs (_) B1,F1: 9.. / B1 = 9 => 0 pairs (X) / F1 = 9 => 0 pairs (_) A5,G5: 9.. / A5 = 9 => 0 pairs (X) / G5 = 9 => 0 pairs (_) B6,E6: 9.. / B6 = 9 => 0 pairs (*) / E6 = 9 => 0 pairs (X) D8,G8: 9.. / D8 = 9 => 0 pairs (*) / G8 = 9 => 0 pairs (X) D9,I9: 9.. / D9 = 9 => 0 pairs (X) / I9 = 9 => 0 pairs (_) B1,B6: 9.. / B1 = 9 => 0 pairs (X) / B6 = 9 => 0 pairs (_) H3,H4: 9.. / H3 = 9 => 0 pairs (*) / H4 = 9 => 0 pairs (X) * DURATION: 0:01:50.730894 START: 15:07:00.405071 END: 15:08:51.135965 2017-05-04 * CP COUNT: (45) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B5,B6,B8,C1,C5,C9,D8,D9,E4,E6,F1,F3,G5,G8,H3,H4,I9) * 1..65.342.24173.5..5342.1.73152.47.....531.244.27.65135493672817.1.42.3523..1547. * PAIR C1: 7,8 BLK 1 B1: 7,8,9 # reduction candidate for 7,8 B1: 7,8 => SOLVED * 178659342924173856653428197315294768867531924492786513549367281781942635236815479 B1: 9 => CTR * 197658342624173.5.8534291673152.4796976531.244.27.65135493672817.1.42.3523..1547. * PAIR A2: 6,9 BLK 1 A3: 6,9,8 # reduction candidate for 6,9 A3: 6,9 => SOLVED * 178659342924173856653428197315294768867531924492786513549367281781942635236815479 A3: 8 => CTR * 1..65.342624173.5.8534291673152.47969..531824482796513549367281761.42.3523..1547. * PAIR A2: 6,9 ROW 2 G2: 6,9,8 # reduction candidate for 6,9 G2: 6,9 => CTR * 197658342624173.58.5342.1.73152847.....531824482796513549367281761842935238915476 G2: 8 => SOLVED * 178659342924173856653428197315294768867531924492786513549367281781942635236815479 I2: 6,9,8 # reduction candidate for 6,9 I2: 6,9 => SOLVED * 178659342924173856653428197315294768867531924492786513549367281781942635236815479 I2: 8 => CTR * 197658342624173.58.5342.1.73152847.....531824482796513549367281761842935238915476 * PAIR F1: 8,9 ROW 1 B1: 8,9,7 # reduction candidate for 8,9 B1: 8,9 => CTR * 1.765.342.24173658653428197315284769.76531.244.27.6513549367281761842935238915476 B1: 7 => SOLVED * 178659342924173856653428197315294768867531924492786513549367281781942635236815479 * PAIR F3: 8,9 ROW 3 A3: 8,9,6 # reduction candidate for 8,9 A3: 8,9 => CTR * 1..65.342624173.5..5342.1673152.47969..531824482796513549367281761.42.3523..1547. A3: 6 => SOLVED * 178659342924173856653428197315294768867531924492786513549367281781942635236815479 * PAIR H3: 6,9 BLK 3 G2: 6,9,8 # reduction candidate for 6,9 G2: 6,9 => CTR * 197658342624173.58.5342.1.73152847.....531824482796513549367281761842935238915476 G2: 8 => SOLVED * 178659342924173856653428197315294768867531924492786513549367281781942635236815479 I2: 6,9,8 # reduction candidate for 6,9 I2: 6,9 => SOLVED * 178659342924173856653428197315294768867531924492786513549367281781942635236815479 I2: 8 => CTR * 197658342624173.58.5342.1.73152847.....531824482796513549367281761842935238915476 * PAIR H3: 6,9 ROW 3 A3: 6,9,8 # reduction candidate for 6,9 A3: 6,9 => SOLVED * 178659342924173856653428197315294768867531924492786513549367281781942635236815479 A3: 8 => CTR * 1..65.342624173.5.8534291673152.47969..531824482796513549367281761.42.3523..1547. * PAIR A5: 8,9 COL A A3: 8,9,6 # reduction candidate for 8,9 A3: 8,9 => CTR * 1..65.342624173.5..5342.1673152.47969..531824482796513549367281761.42.3523..1547. A3: 6 => SOLVED * 178659342924173856653428197315294768867531924492786513549367281781942635236815479 * PAIR B6: 8,9 COL B B1: 8,9,7 # reduction candidate for 8,9 B1: 8,9 => CTR * 1.765.342.24173658653428197315284769.76531.244.27.6513549367281761842935238915476 B1: 7 => SOLVED * 178659342924173856653428197315294768867531924492786513549367281781942635236815479 * PAIR E4: 8,9 ROW 4 I4: 8,9,6 # reduction candidate for 8,9 I4: 8,9 => SOLVED * 178659342924173856653428197315294768867531924492786513549367281781942635236815479 I4: 6 => CTR * 1..65.342.24173.58.5342.1.73152847969..531824482796513549367281761.42.3523..1547. * PAIR H4: 6,9 BLK 6 I4: 6,9,8 # reduction candidate for 6,9 I4: 6,9 => CTR * 197658342624173.58.5342.1.73152847.....531824482796513549367281761842935238915476 I4: 8 => SOLVED * 178659342924173856653428197315294768867531924492786513549367281781942635236815479 * PAIR G5: 8,9 BLK 6 I4: 8,9,6 # reduction candidate for 8,9 I4: 8,9 => SOLVED * 178659342924173856653428197315294768867531924492786513549367281781942635236815479 I4: 6 => CTR * 1..65.342.24173.58.5342.1.73152847969..531824482796513549367281761.42.3523..1547. * PAIR G5: 8,9 COL G G2: 8,9,6 # reduction candidate for 8,9 G2: 8,9 => SOLVED * 178659342924173856653428197315294768867531924492786513549367281781942635236815479 G2: 6 => CTR * 1..65.342.24173658653428197315284769...531.244.27.65135493672817.1.42.3523..1547. * PAIR G8: 6,9 COL G G2: 6,9,8 # reduction candidate for 6,9 G2: 6,9 => CTR * 197658342624173.58.5342.1.73152847.....531824482796513549367281761842935238915476 G2: 8 => SOLVED * 178659342924173856653428197315294768867531924492786513549367281781942635236815479 * PAIR I9: 6,9 COL I I2: 6,9,8 # reduction candidate for 6,9 I2: 6,9 => SOLVED * 178659342924173856653428197315294768867531924492786513549367281781942635236815479 I2: 8 => CTR * 197658342624173.58.5342.1.73152847.....531824482796513549367281761842935238915476 I4: 6,9,8 # reduction candidate for 6,9 I4: 6,9 => CTR * 197658342624173.58.5342.1.73152847.....531824482796513549367281761842935238915476 I4: 8 => SOLVED * 178659342924173856653428197315294768867531924492786513549367281781942635236815479 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-361-base-pr-000.dot * REASONING * PRF # B1: 7,8 => SOL * DIS # B1: 9 => CTR => B1: 7,8 * PRF # A3: 6,9 => SOL * DIS # A3: 8 => CTR => A3: 6,9 * DIS # G2: 6,9 => CTR => G2: 8 * PRF # G2: 8 => SOL * PRF # I2: 6,9 => SOL * DIS # I2: 8 => CTR => I2: 6,9 * DIS # B1: 8,9 => CTR => B1: 7 * PRF # B1: 7 => SOL * DIS # A3: 8,9 => CTR => A3: 6 * PRF # A3: 6 => SOL * DIS # G2: 6,9 => CTR => G2: 8 * PRF # G2: 8 => SOL * PRF # I2: 6,9 => SOL * DIS # I2: 8 => CTR => I2: 6,9 * PRF # A3: 6,9 => SOL * DIS # A3: 8 => CTR => A3: 6,9 * DIS # A3: 8,9 => CTR => A3: 6 * PRF # A3: 6 => SOL * DIS # B1: 8,9 => CTR => B1: 7 * PRF # B1: 7 => SOL * PRF # I4: 8,9 => SOL * DIS # I4: 6 => CTR => I4: 8,9 * DIS # I4: 6,9 => CTR => I4: 8 * PRF # I4: 8 => SOL * PRF # I4: 8,9 => SOL * DIS # I4: 6 => CTR => I4: 8,9 * PRF # G2: 8,9 => SOL * DIS # G2: 6 => CTR => G2: 8,9 * DIS # G2: 6,9 => CTR => G2: 8 * PRF # G2: 8 => SOL * PRF # I2: 6,9 => SOL * DIS # I2: 8 => CTR => I2: 6,9 * DIS # I4: 6,9 => CTR => I4: 8 * PRF # I4: 8 => SOL * CNT 36 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B5,B6,B8,C1,C5,C9,D8,D9,E4,E6,F1,F3,G5,G8,H3,H4,I9) * 1..65.342.24173.5..5342.1.73152.47.....531.244.27.65135493672817.1.42.3523..1547. * PAIR C1: 7,8 BLK 1 B1: 7,8,9 # reduction candidate for 7,8 B1: 7,8 => SOLVED * 178659342924173856653428197315294768867531924492786513549367281781942635236815479 * DURATION: 0:00:02.431159 START: 15:09:51.486973 END: 15:09:53.918132 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-361-base-pr-001.dot * REASONING * PRF # B1: 7,8 => SOL * STA B1: 7,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 361 solution: 178659342924173856653428197315294768867531924492786513549367281781942635236815479 info: 4911 FNBTWY S8.f 43409 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 178659342924173856653428197315294768867531924492786513549367281781942635236815479 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:
* PRF # B1: 7,8 => SOL * DIS # B1: 9 => CTR => B1: 7,8 * PRF # A3: 6,9 => SOL * DIS # A3: 8 => CTR => A3: 6,9 * DIS # G2: 6,9 => CTR => G2: 8 * PRF # G2: 8 => SOL * PRF # I2: 6,9 => SOL * DIS # I2: 8 => CTR => I2: 6,9 * DIS # B1: 8,9 => CTR => B1: 7 * PRF # B1: 7 => SOL * DIS # A3: 8,9 => CTR => A3: 6 * PRF # A3: 6 => SOL * DIS # G2: 6,9 => CTR => G2: 8 * PRF # G2: 8 => SOL * PRF # I2: 6,9 => SOL * DIS # I2: 8 => CTR => I2: 6,9 * PRF # A3: 6,9 => SOL * DIS # A3: 8 => CTR => A3: 6,9 * DIS # A3: 8,9 => CTR => A3: 6 * PRF # A3: 6 => SOL * DIS # B1: 8,9 => CTR => B1: 7 * PRF # B1: 7 => SOL * PRF # I4: 8,9 => SOL * DIS # I4: 6 => CTR => I4: 8,9 * DIS # I4: 6,9 => CTR => I4: 8 * PRF # I4: 8 => SOL * PRF # I4: 8,9 => SOL * DIS # I4: 6 => CTR => I4: 8,9 * PRF # G2: 8,9 => SOL * DIS # G2: 6 => CTR => G2: 8,9 * DIS # G2: 6,9 => CTR => G2: 8 * PRF # G2: 8 => SOL * PRF # I2: 6,9 => SOL * DIS # I2: 8 => CTR => I2: 6,9 * DIS # I4: 6,9 => CTR => I4: 8 * PRF # I4: 8 => SOL * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # B1: 7,8 => SOL * STA B1: 7,8 * CNT 1 HDP CHAINS / 1 HYP OPENED