Analysis of xx-top500-231-base.sdk
Contents
Original Sudoku
level: medium
position: .3..9....7.......4.......1.2...6.8.....5..9..1...........1.4....9....3...5.7..... initial
Autosolve
position: 534.917..71.3.5.949...47513279463851.4351.9.71.597.43.3.7154..9491..6375.5.73914. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # I1: 2,6 => SOL * PRF # D3: 6 => SOL * PRF # C2: 6 => SOL * PRF # I1: 2,6 => SOL * DIS # B3: 6,8 => CTR => B3: 2 * PRF # H7: 2,6 => SOL * PRF # I1: 2,6 => SOL * DIS # C9: 6,8 => CTR => C9: 2 * DIS # I9: 2 => CTR => I9: 6,8 * PRF # D3: 6 => SOL * PRF # H7: 2,6 => SOL * PRF # B7: 8 => SOL * CNT 12 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # I1: 2,6 => SOL * STA I1: 2,6 * CNT 1 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .3..9....7.......4.......1.2...6.8.....5..9..1...........1.4....9....3...5.7..... | initial |
| 534.917..71.3.5.949...47513279463851.4351.9.71.597.43.3.7154..9491..6375.5.73914. | autosolve |
| 534291786716385294928647513279463851843512967165978432387154629491826375652739148 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) D1: 2,6 E2: 2,8 G2: 2,6 A5: 6,8 B6: 6,8 F5: 2,8 F6: 2,8 H5: 2,6 I6: 2,6 A9: 6,8 D8: 2,8 E8: 2,8 G7: 2,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F5,F6: 2.. / F5 = 2 => 0 pairs (*) / F6 = 2 => 0 pairs (X) H5,I6: 2.. / H5 = 2 => 0 pairs (X) / I6 = 2 => 0 pairs (_) B7,C9: 2.. / B7 = 2 => 0 pairs (X) / C9 = 2 => 18 pairs (_) D8,E8: 2.. / D8 = 2 => 12 pairs (_) / E8 = 2 => 12 pairs (_) F5,H5: 2.. / F5 = 2 => 0 pairs (*) / H5 = 2 => 0 pairs (X) F6,I6: 2.. / F6 = 2 => 0 pairs (X) / I6 = 2 => 0 pairs (_) C9,I9: 2.. / C9 = 2 => 18 pairs (_) / I9 = 2 => 0 pairs (X) B3,B7: 2.. / B3 = 2 => 18 pairs (_) / B7 = 2 => 0 pairs (X) E2,E8: 2.. / E2 = 2 => 12 pairs (_) / E8 = 2 => 12 pairs (_) G2,G7: 2.. / G2 = 2 => 0 pairs (*) / G7 = 2 => 0 pairs (X) D1,D3: 6.. / D1 = 6 => 12 pairs (_) / D3 = 6 => 0 pairs (*) A5,B6: 6.. / A5 = 6 => 0 pairs (X) / B6 = 6 => 0 pairs (_) H5,I6: 6.. / H5 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) C2,G2: 6.. / C2 = 6 => 0 pairs (*) / G2 = 6 => 0 pairs (X) A5,H5: 6.. / A5 = 6 => 0 pairs (X) / H5 = 6 => 0 pairs (_) B6,I6: 6.. / B6 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) A5,A9: 6.. / A5 = 6 => 0 pairs (X) / A9 = 6 => 0 pairs (_) G2,G7: 6.. / G2 = 6 => 12 pairs (_) / G7 = 6 => 0 pairs (*) E2,D3: 8.. / E2 = 8 => 12 pairs (_) / D3 = 8 => 12 pairs (_) H1,I1: 8.. / H1 = 8 => 0 pairs (*) / I1 = 8 => 0 pairs (X) A5,B6: 8.. / A5 = 8 => 0 pairs (*) / B6 = 8 => 0 pairs (X) F5,F6: 8.. / F5 = 8 => 0 pairs (X) / F6 = 8 => 0 pairs (_) D8,E8: 8.. / D8 = 8 => 12 pairs (_) / E8 = 8 => 12 pairs (_) H7,I9: 8.. / H7 = 8 => 16 pairs (_) / I9 = 8 => 0 pairs (*) C2,E2: 8.. / C2 = 8 => 12 pairs (_) / E2 = 8 => 12 pairs (_) A5,F5: 8.. / A5 = 8 => 0 pairs (*) / F5 = 8 => 0 pairs (X) B6,F6: 8.. / B6 = 8 => 0 pairs (X) / F6 = 8 => 0 pairs (_) B7,H7: 8.. / B7 = 8 => 0 pairs (*) / H7 = 8 => 0 pairs (X) A5,A9: 8.. / A5 = 8 => 0 pairs (*) / A9 = 8 => 0 pairs (X) D3,D8: 8.. / D3 = 8 => 12 pairs (_) / D8 = 8 => 12 pairs (_) E2,E8: 8.. / E2 = 8 => 12 pairs (_) / E8 = 8 => 12 pairs (_) H1,H7: 8.. / H1 = 8 => 0 pairs (*) / H7 = 8 => 0 pairs (X) I1,I9: 8.. / I1 = 8 => 16 pairs (_) / I9 = 8 => 0 pairs (*) * DURATION: 0:00:55.167543 START: 10:43:54.408935 END: 10:44:49.576478 2017-05-04 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A9,B6,D1,D8,E2,E8,F5,F6,G2,G7,H5,I6) * 534.917..71.3.5.949...47513279463851.4351.9.71.597.43.3.7154..9491..6375.5.73914. * PAIR D1: 2,6 BLK 2 D3: 2,6,8 # reduction candidate for 2,6 D3: 8 # 12 pairs D3: 2,6 # 12 pairs * PAIR D1: 2,6 ROW 1 H1: 2,6,8 # reduction candidate for 2,6 H1: 2,6 # 16 pairs I1: 2,6,8 # reduction candidate for 2,6 I1: 2,6 => SOLVED * 534291786716385294928647513279463851843512967165978432387154629491826375652739148 I1: 8 # 16 pairs * PAIR E2: 2,8 BLK 2 D3: 2,8,6 # reduction candidate for 2,8 D3: 6 => SOLVED * 534291786716385294928647513279463851843512967165978432387154629491826375652739148 D3: 2,8 # 12 pairs * PAIR E2: 2,8 ROW 2 C2: 2,8,6 # reduction candidate for 2,8 C2: 6 => SOLVED * 534291786716385294928647513279463851843512967165978432387154629491826375652739148 C2: 2,8 # 12 pairs * PAIR G2: 2,6 BLK 3 H1: 2,6,8 # reduction candidate for 2,6 H1: 2,6 # 16 pairs I1: 2,6,8 # reduction candidate for 2,6 I1: 2,6 => SOLVED * 534291786716385294928647513279463851843512967165978432387154629491826375652739148 I1: 8 # 16 pairs * PAIR G2: 2,6 ROW 2 C2: 2,6,8 # reduction candidate for 2,6 C2: 8 # 12 pairs C2: 2,6 # 12 pairs * PAIR B6: 6,8 COL B B3: 6,8,2 # reduction candidate for 6,8 B3: 6,8 => CTR * 534.917.87163852949826475132794638518435129.71.597.43.327154689491..6375.5.739142 B3: 2 # 18 pairs B7: 6,8,2 # reduction candidate for 6,8 B7: 6,8 # 18 pairs * PAIR H5: 2,6 COL H H1: 2,6,8 # reduction candidate for 2,6 H1: 2,6 # 16 pairs H7: 2,6,8 # reduction candidate for 2,6 H7: 2,6 => SOLVED * 534291786716385294928647513279463851843512967165978432387154629491826375652739148 H7: 8 # 16 pairs * PAIR I6: 2,6 COL I I1: 2,6,8 # reduction candidate for 2,6 I1: 2,6 => SOLVED * 534291786716385294928647513279463851843512967165978432387154629491826375652739148 I1: 8 # 16 pairs I9: 2,6,8 # reduction candidate for 2,6 I9: 2,6 # 16 pairs * PAIR A9: 6,8 BLK 7 B7: 6,8,2 # reduction candidate for 6,8 B7: 6,8 # 18 pairs C9: 6,8,2 # reduction candidate for 6,8 C9: 6,8 => CTR * 534.917.87163852949826475132794638518435129.71.597.43.327154689491..6375.5.739142 C9: 2 # 18 pairs * PAIR A9: 6,8 ROW 9 I9: 6,8,2 # reduction candidate for 6,8 I9: 2 => CTR * 534.917687163852949.264751327946385164351892718597.4363.7154.89491..6375.5.739142 I9: 6,8 # 18 pairs * PAIR D8: 2,8 COL D D3: 2,8,6 # reduction candidate for 2,8 D3: 6 => SOLVED * 534291786716385294928647513279463851843512967165978432387154629491826375652739148 D3: 2,8 # 12 pairs * PAIR G7: 2,6 BLK 9 H7: 2,6,8 # reduction candidate for 2,6 H7: 2,6 => SOLVED * 534291786716385294928647513279463851843512967165978432387154629491826375652739148 H7: 8 # 16 pairs I9: 2,6,8 # reduction candidate for 2,6 I9: 2,6 # 16 pairs * PAIR G7: 2,6 ROW 7 B7: 2,6,8 # reduction candidate for 2,6 B7: 8 => SOLVED * 534291786716385294928647513279463851843512967165978432387154629491826375652739148 B7: 2,6 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-231-base-pr-000.dot * REASONING * PRF # I1: 2,6 => SOL * PRF # D3: 6 => SOL * PRF # C2: 6 => SOL * PRF # I1: 2,6 => SOL * DIS # B3: 6,8 => CTR => B3: 2 * PRF # H7: 2,6 => SOL * PRF # I1: 2,6 => SOL * DIS # C9: 6,8 => CTR => C9: 2 * DIS # I9: 2 => CTR => I9: 6,8 * PRF # D3: 6 => SOL * PRF # H7: 2,6 => SOL * PRF # B7: 8 => SOL * CNT 12 HDP CHAINS / 35 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A9,B6,D1,D8,E2,E8,F5,F6,G2,G7,H5,I6) * 534.917..71.3.5.949...47513279463851.4351.9.71.597.43.3.7154..9491..6375.5.73914. * PAIR D1: 2,6 BLK 2 D3: 2,6,8 # reduction candidate for 2,6 D3: 8 # 12 pairs D3: 2,6 # 12 pairs * PAIR D1: 2,6 ROW 1 H1: 2,6,8 # reduction candidate for 2,6 H1: 2,6 # 16 pairs I1: 2,6,8 # reduction candidate for 2,6 I1: 2,6 => SOLVED * 534291786716385294928647513279463851843512967165978432387154629491826375652739148 * DURATION: 0:00:04.741425 START: 10:45:25.736846 END: 10:45:30.478271 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-231-base-pr-001.dot * REASONING * PRF # I1: 2,6 => SOL * STA I1: 2,6 * CNT 1 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 231 solution: 534291786716385294928647513279463851843512967165978432387154629491826375652739148 info: 2065 FNBWXY S8.f 17843 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 534291786716385294928647513279463851843512967165978432387154629491826375652739148 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:
* INC # D3: 2,6 => UNS * INC # D3: 8 => UNS * INC # H1: 2,6 => UNS * PRF # I1: 2,6 => SOL * INC # I1: 8 => UNS * INC # D3: 2,8 => UNS * PRF # D3: 6 => SOL * INC # C2: 2,8 => UNS * PRF # C2: 6 => SOL * INC # H1: 2,6 => UNS * PRF # I1: 2,6 => SOL * INC # I1: 8 => UNS * INC # C2: 2,6 => UNS * INC # C2: 8 => UNS * DIS # B3: 6,8 => CTR => B3: 2 * INC # B3: 2 => UNS * INC # B7: 6,8 => UNS * INC # H1: 2,6 => UNS * PRF # H7: 2,6 => SOL * INC # H7: 8 => UNS * PRF # I1: 2,6 => SOL * INC # I1: 8 => UNS * INC # I9: 2,6 => UNS * INC # B7: 6,8 => UNS * DIS # C9: 6,8 => CTR => C9: 2 * INC # C9: 2 => UNS * INC # I9: 6,8 => UNS * DIS # I9: 2 => CTR => I9: 6,8 * INC # D3: 2,8 => UNS * PRF # D3: 6 => SOL * PRF # H7: 2,6 => SOL * INC # H7: 8 => UNS * INC # I9: 2,6 => UNS * INC # B7: 2,6 => UNS * PRF # B7: 8 => SOL * CNT 35 HDP CHAINS / 35 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D3: 2,6 => UNS * INC # D3: 8 => UNS * INC # H1: 2,6 => UNS * PRF # I1: 2,6 => SOL * STA I1: 2,6 * CNT 4 HDP CHAINS / 4 HYP OPENED