Analysis of xx-top500-305-base.sdk
Contents
Original Sudoku
level: medium
position: 36.....4.2..5........1..7...41.........2....8......3......6..1.7...4............5 initial
Autosolve
position: 365.7.14.2175.4..64..1.675..416.35275..21.4686..45.391...765.14756.412..1.43..675 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F1: 8,9 => CTR => F1: 2 * PRF # F1: 2 => SOL * PRF # F1: 2,9 => SOL * DIS # F1: 8 => CTR => F1: 2,9 * DIS # E9: 8,9 => CTR => E9: 2 * PRF # E9: 2 => SOL * DIS # E9: 8,9 => CTR => E9: 2 * PRF # E9: 2 => SOL * PRF # F9: 8,9 => SOL * DIS # F9: 2 => CTR => F9: 8,9 * DIS # E9: 8,9 => CTR => E9: 2 * PRF # E9: 2 => SOL * PRF # F9: 8,9 => SOL * DIS # F9: 2 => CTR => F9: 8,9 * CNT 14 HDP CHAINS / 14 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F1: 8,9 => CTR => F1: 2 * PRF F1: 2 => SOL * STA F1: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 36.....4.2..5........1..7...41.........2....8......3......6..1.7...4............5 | initial |
| 365.7.14.2175.4..64..1.675..416.35275..21.4686..45.391...765.14756.412..1.43..675 | autosolve |
| 365872149217594836489136752941683527573219468628457391832765914756941283194328675 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (25) B3: 8,9 C3: 8,9 D1: 8,9 E2: 3,9 E3: 2,3 I1: 2,9 G2: 8,9 H2: 3,8 I3: 2,3 A4: 8,9 B5: 3,7 C5: 3,9 B6: 2,7 C6: 2,8 E4: 8,9 F5: 7,9 F6: 7,8 A7: 8,9 B7: 2,3 C7: 2,3 B9: 8,9 D8: 8,9 G7: 8,9 H8: 3,8 I8: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F1,E3: 2.. / F1 = 2 => 0 pairs (*) / E3 = 2 => 0 pairs (X) I1,I3: 2.. / I1 = 2 => 0 pairs (X) / I3 = 2 => 0 pairs (_) B6,C6: 2.. / B6 = 2 => 0 pairs (*) / C6 = 2 => 0 pairs (X) B7,C7: 2.. / B7 = 2 => 0 pairs (X) / C7 = 2 => 0 pairs (_) E9,F9: 2.. / E9 = 2 => 0 pairs (*) / F9 = 2 => 0 pairs (X) F1,I1: 2.. / F1 = 2 => 0 pairs (*) / I1 = 2 => 0 pairs (X) E3,I3: 2.. / E3 = 2 => 0 pairs (X) / I3 = 2 => 0 pairs (_) B6,B7: 2.. / B6 = 2 => 0 pairs (*) / B7 = 2 => 0 pairs (X) C6,C7: 2.. / C6 = 2 => 0 pairs (X) / C7 = 2 => 0 pairs (_) E3,E9: 2.. / E3 = 2 => 0 pairs (X) / E9 = 2 => 0 pairs (_) F1,F9: 2.. / F1 = 2 => 0 pairs (*) / F9 = 2 => 0 pairs (X) E2,E3: 3.. / E2 = 3 => 0 pairs (X) / E3 = 3 => 0 pairs (_) H2,I3: 3.. / H2 = 3 => 0 pairs (*) / I3 = 3 => 0 pairs (X) B5,C5: 3.. / B5 = 3 => 0 pairs (X) / C5 = 3 => 0 pairs (_) B7,C7: 3.. / B7 = 3 => 0 pairs (*) / C7 = 3 => 0 pairs (X) H8,I8: 3.. / H8 = 3 => 0 pairs (X) / I8 = 3 => 0 pairs (_) E2,H2: 3.. / E2 = 3 => 0 pairs (X) / H2 = 3 => 0 pairs (_) E3,I3: 3.. / E3 = 3 => 0 pairs (*) / I3 = 3 => 0 pairs (X) B5,B7: 3.. / B5 = 3 => 0 pairs (X) / B7 = 3 => 0 pairs (_) C5,C7: 3.. / C5 = 3 => 0 pairs (*) / C7 = 3 => 0 pairs (X) H2,H8: 3.. / H2 = 3 => 0 pairs (*) / H8 = 3 => 0 pairs (X) I3,I8: 3.. / I3 = 3 => 0 pairs (X) / I8 = 3 => 0 pairs (_) B5,B6: 7.. / B5 = 7 => 0 pairs (*) / B6 = 7 => 0 pairs (X) F5,F6: 7.. / F5 = 7 => 0 pairs (X) / F6 = 7 => 0 pairs (_) B5,F5: 7.. / B5 = 7 => 0 pairs (*) / F5 = 7 => 0 pairs (X) B6,F6: 7.. / B6 = 7 => 0 pairs (X) / F6 = 7 => 0 pairs (_) B3,C3: 8.. / B3 = 8 => 0 pairs (*) / C3 = 8 => 0 pairs (X) D1,F1: 8.. / D1 = 8 => 0 pairs (*) / F1 = 8 => 0 pairs (X) G2,H2: 8.. / G2 = 8 => 0 pairs (*) / H2 = 8 => 0 pairs (X) A4,C6: 8.. / A4 = 8 => 0 pairs (X) / C6 = 8 => 0 pairs (_) E4,F6: 8.. / E4 = 8 => 0 pairs (*) / F6 = 8 => 0 pairs (X) A7,B9: 8.. / A7 = 8 => 0 pairs (*) / B9 = 8 => 0 pairs (X) G7,H8: 8.. / G7 = 8 => 0 pairs (X) / H8 = 8 => 0 pairs (_) A4,E4: 8.. / A4 = 8 => 0 pairs (X) / E4 = 8 => 0 pairs (_) C6,F6: 8.. / C6 = 8 => 0 pairs (*) / F6 = 8 => 0 pairs (X) A7,G7: 8.. / A7 = 8 => 0 pairs (*) / G7 = 8 => 0 pairs (X) D8,H8: 8.. / D8 = 8 => 0 pairs (X) / H8 = 8 => 0 pairs (_) A4,A7: 8.. / A4 = 8 => 0 pairs (X) / A7 = 8 => 0 pairs (_) B3,B9: 8.. / B3 = 8 => 0 pairs (*) / B9 = 8 => 0 pairs (X) C3,C6: 8.. / C3 = 8 => 0 pairs (X) / C6 = 8 => 0 pairs (_) D1,D8: 8.. / D1 = 8 => 0 pairs (*) / D8 = 8 => 0 pairs (X) E4,E9: 8.. / E4 = 8 => 0 pairs (*) / E9 = 8 => 0 pairs (X) G2,G7: 8.. / G2 = 8 => 0 pairs (*) / G7 = 8 => 0 pairs (X) H2,H8: 8.. / H2 = 8 => 0 pairs (X) / H8 = 8 => 0 pairs (_) B3,C3: 9.. / B3 = 9 => 0 pairs (X) / C3 = 9 => 0 pairs (_) I1,G2: 9.. / I1 = 9 => 0 pairs (*) / G2 = 9 => 0 pairs (X) A4,C5: 9.. / A4 = 9 => 0 pairs (*) / C5 = 9 => 0 pairs (X) E4,F5: 9.. / E4 = 9 => 0 pairs (X) / F5 = 9 => 0 pairs (_) A7,B9: 9.. / A7 = 9 => 0 pairs (X) / B9 = 9 => 0 pairs (_) G7,I8: 9.. / G7 = 9 => 0 pairs (*) / I8 = 9 => 0 pairs (X) E2,G2: 9.. / E2 = 9 => 0 pairs (*) / G2 = 9 => 0 pairs (X) A4,E4: 9.. / A4 = 9 => 0 pairs (*) / E4 = 9 => 0 pairs (X) C5,F5: 9.. / C5 = 9 => 0 pairs (X) / F5 = 9 => 0 pairs (_) A7,G7: 9.. / A7 = 9 => 0 pairs (X) / G7 = 9 => 0 pairs (_) D8,I8: 9.. / D8 = 9 => 0 pairs (*) / I8 = 9 => 0 pairs (X) A4,A7: 9.. / A4 = 9 => 0 pairs (*) / A7 = 9 => 0 pairs (X) B3,B9: 9.. / B3 = 9 => 0 pairs (X) / B9 = 9 => 0 pairs (_) C3,C5: 9.. / C3 = 9 => 0 pairs (*) / C5 = 9 => 0 pairs (X) D1,D8: 9.. / D1 = 9 => 0 pairs (X) / D8 = 9 => 0 pairs (_) G2,G7: 9.. / G2 = 9 => 0 pairs (X) / G7 = 9 => 0 pairs (_) I1,I8: 9.. / I1 = 9 => 0 pairs (*) / I8 = 9 => 0 pairs (X) * DURATION: 0:01:54.384267 START: 13:23:56.350476 END: 13:25:50.734743 2017-05-04 * CP COUNT: (61) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,B3,B5,B6,B7,B9,C3,C5,C6,C7,D1,D8,E2,E3,E4,F5,F6,G2,G7,H2,H8,I1,I3,I8) * 365.7.14.2175.4..64..1.675..416.35275..21.4686..45.391...765.14756.412..1.43..675 * PAIR D1: 8,9 BLK 2 F1: 8,9,2 # reduction candidate for 8,9 F1: 8,9 => CTR * 365.7.1422175.49864..126753.416.35275..21.4686..45.3919..76581475684123918439.675 F1: 2 => SOLVED * 365872149217594836489136752941683527573219468628457391832765914756941283194328675 * PAIR I1: 2,9 ROW 1 F1: 2,9,8 # reduction candidate for 2,9 F1: 2,9 => SOLVED * 365872149217594836489136752941683527573219468628457391832765914756941283194328675 F1: 8 => CTR * 365.781422175.49864..126753.416835275..2194686.8457391...765.14756.412..1.43..675 * PAIR E4: 8,9 COL E E9: 8,9,2 # reduction candidate for 8,9 E9: 8,9 => CTR * 3659781422175349864..126753.416835275..2194686.8457391...765.14756.412391.43.2675 E9: 2 => SOLVED * 365872149217594836489136752941683527573219468628457391832765914756941283194328675 * PAIR B9: 8,9 ROW 9 E9: 8,9,2 # reduction candidate for 8,9 E9: 8,9 => CTR * 3659781422175349864..126753.416835275..2194686.8457391...765.14756.412391.43.2675 E9: 2 => SOLVED * 365872149217594836489136752941683527573219468628457391832765914756941283194328675 F9: 8,9,2 # reduction candidate for 8,9 F9: 8,9 => SOLVED * 365872149217594836489136752941683527573219468628457391832765914756941283194328675 F9: 2 => CTR * 365.7.1422175.49864..126753.416.35275..21.4686..45.3919..765814756841239184392675 * PAIR D8: 8,9 BLK 8 E9: 8,9,2 # reduction candidate for 8,9 E9: 8,9 => CTR * 3659781422175349864..126753.416835275..2194686.8457391...765.14756.412391.43.2675 E9: 2 => SOLVED * 365872149217594836489136752941683527573219468628457391832765914756941283194328675 F9: 8,9,2 # reduction candidate for 8,9 F9: 8,9 => SOLVED * 365872149217594836489136752941683527573219468628457391832765914756941283194328675 F9: 2 => CTR * 365.7.1422175.49864..126753.416.35275..21.4686..45.3919..765814756841239184392675 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-305-base-pr-000.dot * REASONING * DIS # F1: 8,9 => CTR => F1: 2 * PRF # F1: 2 => SOL * PRF # F1: 2,9 => SOL * DIS # F1: 8 => CTR => F1: 2,9 * DIS # E9: 8,9 => CTR => E9: 2 * PRF # E9: 2 => SOL * DIS # E9: 8,9 => CTR => E9: 2 * PRF # E9: 2 => SOL * PRF # F9: 8,9 => SOL * DIS # F9: 2 => CTR => F9: 8,9 * DIS # E9: 8,9 => CTR => E9: 2 * PRF # E9: 2 => SOL * PRF # F9: 8,9 => SOL * DIS # F9: 2 => CTR => F9: 8,9 * CNT 14 HDP CHAINS / 14 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,B3,B5,B6,B7,B9,C3,C5,C6,C7,D1,D8,E2,E3,E4,F5,F6,G2,G7,H2,H8,I1,I3,I8) * 365.7.14.2175.4..64..1.675..416.35275..21.4686..45.391...765.14756.412..1.43..675 * PAIR D1: 8,9 BLK 2 F1: 8,9,2 # reduction candidate for 8,9 F1: 8,9 => CTR * 365.7.1422175.49864..126753.416.35275..21.4686..45.3919..76581475684123918439.675 F1: 2 => SOLVED * 365872149217594836489136752941683527573219468628457391832765914756941283194328675 * DURATION: 0:00:03.236102 START: 13:26:10.085289 END: 13:26:13.321391 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-305-base-pr-001.dot * REASONING * DIS # F1: 8,9 => CTR => F1: 2 * PRF F1: 2 => SOL * STA F1: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 305 solution: 365872149217594836489136752941683527573219468628457391832765914756941283194328675 info: 2592 FNBTWX S8.f 30082 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 365872149217594836489136752941683527573219468628457391832765914756941283194328675 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 # F1: 8,9 => CTR => F1: 2 * PRF # F1: 2 => SOL * PRF # F1: 2,9 => SOL * DIS # F1: 8 => CTR => F1: 2,9 * DIS # E9: 8,9 => CTR => E9: 2 * PRF # E9: 2 => SOL * DIS # E9: 8,9 => CTR => E9: 2 * PRF # E9: 2 => SOL * PRF # F9: 8,9 => SOL * DIS # F9: 2 => CTR => F9: 8,9 * DIS # E9: 8,9 => CTR => E9: 2 * PRF # E9: 2 => SOL * PRF # F9: 8,9 => SOL * DIS # F9: 2 => CTR => F9: 8,9 * CNT 14 HDP CHAINS / 14 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # F1: 8,9 => CTR => F1: 2 * PRF F1: 2 => SOL * STA F1: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED