Analysis of xx-top500-443-base.sdk
Contents
Original Sudoku
level: medium
position: 5.3......1..2..........6...4......35.6.7........8...1..2....7......3.2......1.... initial
Autosolve
position: 5.3......1.62........3.61..4......35.6.7........8...17.2....7......372......12... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D4: 1,9 => CTR => D4: 6 * PRF # F5: 1,9 => SOL * DIS # F5: 3,4,5 => CTR => F5: 1,9 * DIS # C4: 1,9 => CTR => C4: 2,7,8 * DIS # F1: 1,9 => CTR => F1: 4,8 * DIS # B9: 4,7,8,9 => CTR => B9: 3,5 * CNT 6 HDP CHAINS / 11 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D4: 1,9 => CTR => D4: 6 * PRF D4: 6 # F5: 1,9 => SOL * STA D4: 6 + F5: 1,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 5.3......1..2..........6...4......35.6.7........8...1..2....7......3.2......1.... | initial |
| 5.3......1.62........3.61..4......35.6.7........8...17.2....7......372......12... | autosolve |
| 573184962146295378892376154417629835368751429259843617921568743685437291734912586 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) H1: 2,6 I1: 2,6 G2: 3,5 F4: 1,9 G9: 3,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,F1: 1.. / D1 = 1 => 7 pairs (_) / F1 = 1 => 0 pairs (X) I7,I8: 1.. / I7 = 1 => 0 pairs (X) / I8 = 1 => 0 pairs (_) C5,F5: 1.. / C5 = 1 => 0 pairs (X) / F5 = 1 => 0 pairs (_) C7,I7: 1.. / C7 = 1 => 0 pairs (*) / I7 = 1 => 0 pairs (X) B4,B8: 1.. / B4 = 1 => 0 pairs (*) / B8 = 1 => 0 pairs (X) D1,D4: 1.. / D1 = 1 => 7 pairs (_) / D4 = 1 => 0 pairs (X) A3,C3: 2.. / A3 = 2 => 6 pairs (_) / C3 = 2 => 6 pairs (_) H1,I1: 2.. / H1 = 2 => 3 pairs (_) / I1 = 2 => 3 pairs (_) E4,E6: 2.. / E4 = 2 => 5 pairs (_) / E6 = 2 => 0 pairs (X) H5,I5: 2.. / H5 = 2 => 3 pairs (_) / I5 = 2 => 3 pairs (_) C4,E4: 2.. / C4 = 2 => 0 pairs (X) / E4 = 2 => 5 pairs (_) A3,A6: 2.. / A3 = 2 => 6 pairs (_) / A6 = 2 => 6 pairs (_) H1,H5: 2.. / H1 = 2 => 3 pairs (_) / H5 = 2 => 3 pairs (_) I1,I5: 2.. / I1 = 2 => 3 pairs (_) / I5 = 2 => 3 pairs (_) G2,I2: 3.. / G2 = 3 => 5 pairs (_) / I2 = 3 => 0 pairs (X) F5,F6: 3.. / F5 = 3 => 0 pairs (X) / F6 = 3 => 0 pairs (_) A5,F5: 3.. / A5 = 3 => 0 pairs (*) / F5 = 3 => 0 pairs (X) A7,I7: 3.. / A7 = 3 => 0 pairs (X) / I7 = 3 => 0 pairs (_) B6,B9: 3.. / B6 = 3 => 0 pairs (X) / B9 = 3 => 0 pairs (_) G2,G9: 3.. / G2 = 3 => 5 pairs (_) / G9 = 3 => 0 pairs (X) E3,H3: 5.. / E3 = 5 => 0 pairs (X) / H3 = 5 => 3 pairs (_) G2,G9: 5.. / G2 = 5 => 0 pairs (X) / G9 = 5 => 5 pairs (_) H1,I1: 6.. / H1 = 6 => 3 pairs (_) / I1 = 6 => 3 pairs (_) G4,G6: 6.. / G4 = 6 => 0 pairs (X) / G6 = 6 => 7 pairs (_) E6,G6: 6.. / E6 = 6 => 0 pairs (X) / G6 = 6 => 7 pairs (_) H2,H3: 7.. / H2 = 7 => 5 pairs (_) / H3 = 7 => 0 pairs (X) B4,C4: 7.. / B4 = 7 => 0 pairs (X) / C4 = 7 => 5 pairs (_) B1,E1: 7.. / B1 = 7 => 7 pairs (_) / E1 = 7 => 5 pairs (_) A3,A9: 7.. / A3 = 7 => 9 pairs (_) / A9 = 7 => 5 pairs (_) E7,F7: 8.. / E7 = 8 => 0 pairs (X) / F7 = 8 => 5 pairs (_) * DURATION: 0:00:48.478559 START: 17:53:46.450296 END: 17:54:34.928855 2017-05-04 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (F4,G2,G9,H1,I1) * 5.3......1.62........3.61..4......35.6.7........8...17.2....7......372......12... * PAIR F4: 1,9 BLK 5 D4: 1,9,6 # reduction candidate for 1,9 D4: 1,9 => CTR * 5.3......1.62.5......3.61..4......35.617.3....358.4.1732....7.1.1..372...5..123.. D4: 6 # 10 pairs F5: 1,9,3,4,5 # reduction candidate for 1,9 F5: 1,9 => SOLVED * 573184962146295378892376154417629835368751429259843617921568743685437291734912586 F5: 3,4,5 => CTR * 5.3......1.62.5......3.61..4......35.617.3....358...1732....7.1.1..372...5..123.. * PAIR F4: 1,9 ROW 4 B4: 1,9,7,8 # reduction candidate for 1,9 B4: 1,9 # 16 pairs C4: 1,9,2,7,8 # reduction candidate for 1,9 C4: 1,9 => CTR * 58317....1.62..573...3561..47.621835.6.7.3....3.8..61732..687.1.1..372...5..123.. C4: 2,7,8 # 5 pairs * PAIR F4: 1,9 COL F F1: 1,9,4,8 # reduction candidate for 1,9 F1: 1,9 => CTR * 5.3......1.62........3.61..4......35.617.3....358.4.1732...87.1.1..372...5..123.. F1: 4,8 # 8 pairs * PAIR G9: 3,5 ROW 9 B9: 3,5,4,7,8,9 # reduction candidate for 3,5 B9: 4,7,8,9 => CTR * 5.3......1.62........3.61..417.2..35.6.7......3.8...17.2....7...5..372......12... B9: 3,5 # 6 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-443-base-pr-000.dot * REASONING * DIS # D4: 1,9 => CTR => D4: 6 * PRF # F5: 1,9 => SOL * DIS # F5: 3,4,5 => CTR => F5: 1,9 * DIS # C4: 1,9 => CTR => C4: 2,7,8 * DIS # F1: 1,9 => CTR => F1: 4,8 * DIS # B9: 4,7,8,9 => CTR => B9: 3,5 * CNT 6 HDP CHAINS / 11 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (F4,G2,G9,H1,I1) * 5.3......1.62........3.61..4......35.6.7........8...17.2....7......372......12... * PAIR F4: 1,9 BLK 5 D4: 1,9,6 # reduction candidate for 1,9 D4: 1,9 => CTR * 5.3......1.62.5......3.61..4......35.617.3....358.4.1732....7.1.1..372...5..123.. F5: 1,9,3,5 # reduction candidate for 1,9 F5: 1,9 => SOLVED * 573184962146295378892376154417629835368751429259843617921568743685437291734912586 * DURATION: 0:00:03.890067 START: 17:54:45.248859 END: 17:54:49.138926 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-443-base-pr-001.dot * REASONING * DIS # D4: 1,9 => CTR => D4: 6 * PRF D4: 6 # F5: 1,9 => SOL * STA D4: 6 + F5: 1,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 443 solution: 573184962146295378892376154417629835368751429259843617921568743685437291734912586 info: 95317 FNBHYK S8.f 39355 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 573184962146295378892376154417629835368751429259843617921568743685437291734912586 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 # D4: 1,9 => CTR => D4: 6 * INC # D4: 6 => UNS * PRF # F5: 1,9 => SOL * DIS # F5: 3,4,5 => CTR => F5: 1,9 * INC # B4: 1,9 => UNS * DIS # C4: 1,9 => CTR => C4: 2,7,8 * INC # C4: 2,7,8 => UNS * DIS # F1: 1,9 => CTR => F1: 4,8 * INC # F1: 4,8 => UNS * INC # B9: 3,5 => UNS * DIS # B9: 4,7,8,9 => CTR => B9: 3,5 * CNT 11 HDP CHAINS / 11 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D4: 1,9 => CTR => D4: 6 * PRF D4: 6 # F5: 1,9 => SOL * STA D4: 6 + F5: 1,9 * CNT 2 HDP CHAINS / 2 HYP OPENED