Analysis of xx-top500-395-base.sdk
Contents
Original Sudoku
level: medium
position: 24......6...51.8............3.8..9..4......1....3.....1....2.....5...3......4.... initial
Autosolve
position: 24...31563..51.8..51.42.739.318.49..48.2...13.523.14..1.4.32....25...3..8.3.452.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D8: 7,9 => CTR => D8: 1,6 * DIS # A6: 6,7 => CTR => A6: 9 * DIS # A8: 9 => CTR => A8: 6,7 * PRF # E5: 7,9 => SOL * PRF # C5: 6 => SOL * PRF # E5: 7,9 => SOL * CNT 6 HDP CHAINS / 32 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D8: 7,9 => CTR => D8: 1,6 * DIS D8: 1,6 # A6: 6,7 => CTR => A6: 9 * DIS D8: 1,6 + A6: 9 # E4: 6,7 => CTR => E4: 5 * DIS D8: 1,6 + A6: 9 + E4: 5 # H4: 2 => CTR => H4: 6,7 * PRF D8: 1,6 + A6: 9 + E4: 5 + H4: 6,7 # E5: 7,9 => SOL * STA D8: 1,6 + A6: 9 + E4: 5 + H4: 6,7 + E5: 7,9 * CNT 5 HDP CHAINS / 20 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 24......6...51.8............3.8..9..4......1....3.....1....2.....5...3......4.... | initial |
| 24...31563..51.8..51.42.739.318.49..48.2...13.523.14..1.4.32....25...3..8.3.452.. | autosolve |
| 247983156369517824518426739731854962486279513952361478194732685625198347873645291 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) C3: 6,8 D1: 7,9 F3: 6,8 H2: 2,4 I2: 2,4 A4: 6,7 F5: 7,9 G5: 5,6 I6: 7,8 G7: 5,6 I9: 1,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D8,D9: 1.. / D8 = 1 => 11 pairs (_) / D9 = 1 => 13 pairs (_) I8,I9: 1.. / I8 = 1 => 13 pairs (_) / I9 = 1 => 11 pairs (_) D8,I8: 1.. / D8 = 1 => 11 pairs (_) / I8 = 1 => 13 pairs (_) D9,I9: 1.. / D9 = 1 => 13 pairs (_) / I9 = 1 => 11 pairs (_) H2,I2: 2.. / H2 = 2 => 14 pairs (_) / I2 = 2 => 9 pairs (_) H4,I4: 2.. / H4 = 2 => 9 pairs (_) / I4 = 2 => 14 pairs (_) H2,H4: 2.. / H2 = 2 => 14 pairs (_) / H4 = 2 => 9 pairs (_) I2,I4: 2.. / I2 = 2 => 9 pairs (_) / I4 = 2 => 14 pairs (_) H2,I2: 4.. / H2 = 4 => 9 pairs (_) / I2 = 4 => 14 pairs (_) H8,I8: 4.. / H8 = 4 => 14 pairs (_) / I8 = 4 => 9 pairs (_) H2,H8: 4.. / H2 = 4 => 9 pairs (_) / H8 = 4 => 14 pairs (_) I2,I8: 4.. / I2 = 4 => 14 pairs (_) / I8 = 4 => 9 pairs (_) E4,E5: 5.. / E4 = 5 => 15 pairs (_) / E5 = 5 => 15 pairs (_) I4,G5: 5.. / I4 = 5 => 15 pairs (_) / G5 = 5 => 15 pairs (_) G7,I7: 5.. / G7 = 5 => 15 pairs (_) / I7 = 5 => 15 pairs (_) E4,I4: 5.. / E4 = 5 => 15 pairs (_) / I4 = 5 => 15 pairs (_) E5,G5: 5.. / E5 = 5 => 15 pairs (_) / G5 = 5 => 15 pairs (_) G5,G7: 5.. / G5 = 5 => 15 pairs (_) / G7 = 5 => 15 pairs (_) I4,I7: 5.. / I4 = 5 => 15 pairs (_) / I7 = 5 => 15 pairs (_) F2,F3: 6.. / F2 = 6 => 19 pairs (_) / F3 = 6 => 12 pairs (_) C3,F3: 6.. / C3 = 6 => 19 pairs (_) / F3 = 6 => 12 pairs (_) G5,G7: 6.. / G5 = 6 => 15 pairs (_) / G7 = 6 => 15 pairs (_) C1,C3: 8.. / C1 = 8 => 19 pairs (_) / C3 = 8 => 12 pairs (_) E1,F3: 8.. / E1 = 8 => 12 pairs (_) / F3 = 8 => 19 pairs (_) H6,I6: 8.. / H6 = 8 => 13 pairs (_) / I6 = 8 => 12 pairs (_) E8,F8: 8.. / E8 = 8 => 19 pairs (_) / F8 = 8 => 12 pairs (_) H7,I7: 8.. / H7 = 8 => 12 pairs (_) / I7 = 8 => 13 pairs (_) C1,E1: 8.. / C1 = 8 => 19 pairs (_) / E1 = 8 => 12 pairs (_) C3,F3: 8.. / C3 = 8 => 12 pairs (_) / F3 = 8 => 19 pairs (_) E1,E8: 8.. / E1 = 8 => 12 pairs (_) / E8 = 8 => 19 pairs (_) F3,F8: 8.. / F3 = 8 => 19 pairs (_) / F8 = 8 => 12 pairs (_) H6,H7: 8.. / H6 = 8 => 13 pairs (_) / H7 = 8 => 12 pairs (_) I6,I7: 8.. / I6 = 8 => 12 pairs (_) / I7 = 8 => 13 pairs (_) C5,A6: 9.. / C5 = 9 => 0 pairs (X) / A6 = 9 => 15 pairs (_) A6,E6: 9.. / A6 = 9 => 15 pairs (_) / E6 = 9 => 0 pairs (X) A6,A8: 9.. / A6 = 9 => 15 pairs (_) / A8 = 9 => 0 pairs (X) * DURATION: 0:01:02.355479 START: 16:19:41.971051 END: 16:20:44.326530 2017-05-04 * CP COUNT: (36) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,C3,D1,F3,F5,G5,G7,H2,I2,I6,I9) * 24...31563..51.8..51.42.739.318.49..48.2...13.523.14..1.4.32....25...3..8.3.452.. * PAIR D1: 7,9 BLK 2 E1: 7,9,8 # reduction candidate for 7,9 E1: 7,9 # 19 pairs F2: 7,9,6 # reduction candidate for 7,9 F2: 7,9 # 12 pairs * PAIR D1: 7,9 ROW 1 C1: 7,9,8 # reduction candidate for 7,9 C1: 8 # 19 pairs C1: 7,9 # 12 pairs * PAIR D1: 7,9 COL D D7: 7,9,6 # reduction candidate for 7,9 D7: 7,9 # 14 pairs D8: 7,9,1,6 # reduction candidate for 7,9 D8: 7,9 => CTR * 24...31563..51.8.451.42.739.318.49.248.2..513.523.14.81.4632....25...3.18.31452.7 D8: 1,6 # 12 pairs D9: 7,9,1,6 # reduction candidate for 7,9 D9: 7,9 # 17 pairs * PAIR A4: 6,7 BLK 4 C5: 6,7,9 # reduction candidate for 6,7 C5: 6,7 # 15 pairs A6: 6,7,9 # reduction candidate for 6,7 A6: 6,7 => CTR * 24.9.31563..51.8..51.42.739.318.49..4892.7.13.523914..1.4.32...925..83..8.3.452.. A6: 9 # 15 pairs * PAIR A4: 6,7 ROW 4 E4: 6,7,5 # reduction candidate for 6,7 E4: 6,7 # 15 pairs H4: 6,7,2 # reduction candidate for 6,7 H4: 6,7 # 14 pairs * PAIR A4: 6,7 COL A A8: 6,7,9 # reduction candidate for 6,7 A8: 9 => CTR * 24...315639.51.8..51.42.739.318.49..4892.7.13.523914..1.4.32...925..83..8.3.452.. A8: 6,7 # 15 pairs * PAIR F5: 7,9 BLK 5 E5: 7,9,5,6 # reduction candidate for 7,9 E5: 7,9 => SOLVED * 247983156369517824518426739731854962486279513952361478194732685625198347873645291 E5: 5,6 # 18 pairs E6: 7,9,6 # reduction candidate for 7,9 E6: 7,9 # 20 pairs * PAIR F5: 7,9 ROW 5 C5: 7,9,6 # reduction candidate for 7,9 C5: 6 => SOLVED * 247983156369517824518426739731854962486279513952361478194732685625198347873645291 C5: 7,9 # 18 pairs * PAIR F5: 7,9 COL F F2: 7,9,6 # reduction candidate for 7,9 F2: 7,9 # 12 pairs F8: 7,9,8 # reduction candidate for 7,9 F8: 7,9 # 19 pairs * PAIR G5: 5,6 ROW 5 E5: 5,6,7,9 # reduction candidate for 5,6 E5: 7,9 => SOLVED * 247983156369517824518426739731854962486279513952361478194732685625198347873645291 E5: 5,6 # 18 pairs * PAIR I6: 7,8 BLK 6 H6: 7,8,6 # reduction candidate for 7,8 H6: 7,8 # 16 pairs H6: 6 # 11 pairs * PAIR I6: 7,8 COL I I7: 7,8,5 # reduction candidate for 7,8 I7: 7,8 # 15 pairs I7: 5 # 15 pairs * PAIR I9: 1,7 BLK 9 I8: 1,7,4 # reduction candidate for 1,7 I8: 1,7 # 14 pairs I8: 4 # 9 pairs * PAIR I9: 1,7 ROW 9 D9: 1,7,6,9 # reduction candidate for 1,7 D9: 1,7 # 14 pairs D9: 6,9 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-395-base-pr-000.dot * REASONING * DIS # D8: 7,9 => CTR => D8: 1,6 * DIS # A6: 6,7 => CTR => A6: 9 * DIS # A8: 9 => CTR => A8: 6,7 * PRF # E5: 7,9 => SOL * PRF # C5: 6 => SOL * PRF # E5: 7,9 => SOL * CNT 6 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,C3,D1,F3,F5,G5,G7,H2,I2,I6,I9) * 24...31563..51.8..51.42.739.318.49..48.2...13.523.14..1.4.32....25...3..8.3.452.. * PAIR D1: 7,9 BLK 2 E1: 7,9,8 # reduction candidate for 7,9 E1: 7,9 # 19 pairs F2: 7,9,6 # reduction candidate for 7,9 F2: 7,9 # 12 pairs * PAIR D1: 7,9 ROW 1 C1: 7,9,8 # reduction candidate for 7,9 C1: 8 # 19 pairs C1: 7,9 # 12 pairs * PAIR D1: 7,9 COL D D7: 7,9,6 # reduction candidate for 7,9 D7: 7,9 # 14 pairs D8: 7,9,1,6 # reduction candidate for 7,9 D8: 7,9 => CTR * 24...31563..51.8.451.42.739.318.49.248.2..513.523.14.81.4632....25...3.18.31452.7 D9: 7,9,1,6 # reduction candidate for 7,9 D9: 7,9 # 17 pairs * PAIR RESTART * PAIR D1: 7,9 BLK 2 E1: 7,9,8 # reduction candidate for 7,9 E1: 7,9 # 19 pairs F2: 7,9,6 # reduction candidate for 7,9 F2: 7,9 # 13 pairs * PAIR D1: 7,9 ROW 1 C1: 7,9,8 # reduction candidate for 7,9 C1: 8 # 19 pairs C1: 7,9 # 13 pairs * PAIR D1: 7,9 COL D D7: 7,9,6 # reduction candidate for 7,9 D7: 7,9 # 14 pairs D9: 7,9,1,6 # reduction candidate for 7,9 D9: 7,9 # 17 pairs * PAIR A4: 6,7 BLK 4 C5: 6,7,9 # reduction candidate for 6,7 C5: 6,7 # 16 pairs A6: 6,7,9 # reduction candidate for 6,7 A6: 6,7 => CTR * 24.9.31563..51.8..51.42.739.318.49..4892.7.13.523914..1.4.32...925..83..8.3.452.. * RESTART * PAIR A4: 6,7 ROW 4 E4: 6,7,5 # reduction candidate for 6,7 E4: 6,7 => CTR * 24...31563.951.8.25164287396318749254872596139523614..1.4.325..725...3..8.3.452.. H4: 6,7,2 # reduction candidate for 6,7 H4: 6,7 # 20 pairs * RESTART * PAIR A4: 6,7 ROW 4 H4: 6,7,2 # reduction candidate for 6,7 H4: 2 => CTR * 24...31563..51.8..51.42.7396318549274872695139523714681.4.326857256.83.18.3.452.. * PAIR RESTART * PAIR F5: 7,9 BLK 5 E5: 7,9,6 # reduction candidate for 7,9 E5: 7,9 => SOLVED * 247983156369517824518426739731854962486279513952361478194732685625198347873645291 * DURATION: 0:00:20.479497 START: 16:21:15.199557 END: 16:21:35.679054 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-395-base-pr-001.dot * REASONING * DIS # D8: 7,9 => CTR => D8: 1,6 * DIS D8: 1,6 # A6: 6,7 => CTR => A6: 9 * DIS D8: 1,6 + A6: 9 # E4: 6,7 => CTR => E4: 5 * DIS D8: 1,6 + A6: 9 + E4: 5 # H4: 2 => CTR => H4: 6,7 * PRF D8: 1,6 + A6: 9 + E4: 5 + H4: 6,7 # E5: 7,9 => SOL * STA D8: 1,6 + A6: 9 + E4: 5 + H4: 6,7 + E5: 7,9 * CNT 5 HDP CHAINS / 20 HYP OPENED
Header Info
Top 500 Minimum 17 395 solution: 247983156369517824518426739731854962486279513952361478194732685625198347873645291 info: 66841 FNBYK S8.f 44969 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 247983156369517824518426739731854962486279513952361478194732685625198347873645291 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 # E1: 7,9 => UNS * INC # F2: 7,9 => UNS * INC # C1: 7,9 => UNS * INC # C1: 8 => UNS * INC # D7: 7,9 => UNS * DIS # D8: 7,9 => CTR => D8: 1,6 * INC # D8: 1,6 => UNS * INC # D9: 7,9 => UNS * INC # C5: 6,7 => UNS * DIS # A6: 6,7 => CTR => A6: 9 * INC # A6: 9 => UNS * INC # E4: 6,7 => UNS * INC # H4: 6,7 => UNS * INC # A8: 6,7 => UNS * DIS # A8: 9 => CTR => A8: 6,7 * PRF # E5: 7,9 => SOL * INC # E5: 5,6 => UNS * INC # E6: 7,9 => UNS * INC # C5: 7,9 => UNS * PRF # C5: 6 => SOL * INC # F2: 7,9 => UNS * INC # F8: 7,9 => UNS * INC # E5: 5,6 => UNS * PRF # E5: 7,9 => SOL * INC # H6: 7,8 => UNS * INC # H6: 6 => UNS * INC # I7: 7,8 => UNS * INC # I7: 5 => UNS * INC # I8: 1,7 => UNS * INC # I8: 4 => UNS * INC # D9: 1,7 => UNS * INC # D9: 6,9 => UNS * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E1: 7,9 => UNS * INC # F2: 7,9 => UNS * INC # C1: 7,9 => UNS * INC # C1: 8 => UNS * INC # D7: 7,9 => UNS * DIS # D8: 7,9 => CTR => D8: 1,6 * INC D8: 1,6 # D9: 7,9 => UNS * INC D8: 1,6 # E1: 7,9 => UNS * INC D8: 1,6 # F2: 7,9 => UNS * INC D8: 1,6 # C1: 7,9 => UNS * INC D8: 1,6 # C1: 8 => UNS * INC D8: 1,6 # D7: 7,9 => UNS * INC D8: 1,6 # D9: 7,9 => UNS * INC D8: 1,6 # C5: 6,7 => UNS * DIS D8: 1,6 # A6: 6,7 => CTR => A6: 9 * DIS D8: 1,6 + A6: 9 # E4: 6,7 => CTR => E4: 5 * INC D8: 1,6 + A6: 9 + E4: 5 # H4: 6,7 => UNS * INC D8: 1,6 + A6: 9 + E4: 5 # H4: 6,7 => UNS * DIS D8: 1,6 + A6: 9 + E4: 5 # H4: 2 => CTR => H4: 6,7 * PRF D8: 1,6 + A6: 9 + E4: 5 + H4: 6,7 # E5: 7,9 => SOL * STA D8: 1,6 + A6: 9 + E4: 5 + H4: 6,7 + E5: 7,9 * CNT 20 HDP CHAINS / 20 HYP OPENED