Analysis of xx-top500-357-base.sdk
Contents
Original Sudoku
level: medium
position: ......2.1.8.4........7........54..8.3.2......1........5...326...7.....4.......... initial
Autosolve
position: 4.53.827178142..3..2371.4.8..75413823.2.87.1.1.82.37..51483269727.15.84383..74125 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # F3: 6,9 => SOL * DIS # F3: 5 => CTR => F3: 6,9 * PRF # F3: 6,9 => SOL * DIS # F3: 5 => CTR => F3: 6,9 * DIS # F3: 5,6 => CTR => F3: 9 * PRF # F3: 9 => SOL * PRF # I5: 6,9 => SOL * DIS # I5: 4 => CTR => I5: 6,9 * DIS # I6: 6,9 => CTR => I6: 4 * PRF # I6: 4 => SOL * DIS # F3: 5,6 => CTR => F3: 9 * PRF # F3: 9 => SOL * PRF # I5: 6,9 => SOL * DIS # I5: 4 => CTR => I5: 6,9 * DIS # I6: 6,9 => CTR => I6: 4 * PRF # I6: 4 => SOL * PRF # F3: 6,9 => SOL * DIS # F3: 5 => CTR => F3: 6,9 * CNT 18 HDP CHAINS / 18 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # F3: 6,9 => SOL * STA F3: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ......2.1.8.4........7........54..8.3.2......1........5...326...7.....4.......... | initial |
| 4.53.827178142..3..2371.4.8..75413823.2.87.1.1.82.37..51483269727.15.84383..74125 | autosolve |
| 495368271781425936623719458967541382342687519158293764514832697279156843836974125 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) B1: 6,9 A3: 6,9 E1: 6,9 F2: 5,6 G2: 5,9 I2: 6,9 H3: 5,6 A4: 6,9 B4: 6,9 B5: 4,5 B6: 4,5 D5: 6,9 E6: 6,9 G5: 5,9 H6: 5,6 C8: 6,9 C9: 6,9 F8: 6,9 D9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B5,B6: 4.. / B5 = 4 => 0 pairs (*) / B6 = 4 => 0 pairs (X) I5,I6: 4.. / I5 = 4 => 0 pairs (X) / I6 = 4 => 0 pairs (_) B5,I5: 4.. / B5 = 4 => 0 pairs (*) / I5 = 4 => 0 pairs (X) B6,I6: 4.. / B6 = 4 => 0 pairs (X) / I6 = 4 => 0 pairs (_) F2,F3: 5.. / F2 = 5 => 0 pairs (*) / F3 = 5 => 0 pairs (X) G2,H3: 5.. / G2 = 5 => 0 pairs (X) / H3 = 5 => 0 pairs (_) B5,B6: 5.. / B5 = 5 => 0 pairs (X) / B6 = 5 => 0 pairs (_) G5,H6: 5.. / G5 = 5 => 0 pairs (*) / H6 = 5 => 0 pairs (X) F2,G2: 5.. / F2 = 5 => 0 pairs (*) / G2 = 5 => 0 pairs (X) F3,H3: 5.. / F3 = 5 => 0 pairs (X) / H3 = 5 => 0 pairs (_) B5,G5: 5.. / B5 = 5 => 0 pairs (X) / G5 = 5 => 0 pairs (_) B6,H6: 5.. / B6 = 5 => 0 pairs (*) / H6 = 5 => 0 pairs (X) G2,G5: 5.. / G2 = 5 => 0 pairs (X) / G5 = 5 => 0 pairs (_) H3,H6: 5.. / H3 = 5 => 0 pairs (*) / H6 = 5 => 0 pairs (X) B1,A3: 6.. / B1 = 6 => 0 pairs (X) / A3 = 6 => 0 pairs (_) I2,H3: 6.. / I2 = 6 => 0 pairs (*) / H3 = 6 => 0 pairs (X) A4,B4: 6.. / A4 = 6 => 0 pairs (X) / B4 = 6 => 0 pairs (_) D5,E6: 6.. / D5 = 6 => 0 pairs (*) / E6 = 6 => 0 pairs (X) C8,C9: 6.. / C8 = 6 => 0 pairs (X) / C9 = 6 => 0 pairs (_) F8,D9: 6.. / F8 = 6 => 0 pairs (*) / D9 = 6 => 0 pairs (X) B1,E1: 6.. / B1 = 6 => 0 pairs (X) / E1 = 6 => 0 pairs (_) F2,I2: 6.. / F2 = 6 => 0 pairs (X) / I2 = 6 => 0 pairs (_) D5,I5: 6.. / D5 = 6 => 0 pairs (*) / I5 = 6 => 0 pairs (X) C8,F8: 6.. / C8 = 6 => 0 pairs (X) / F8 = 6 => 0 pairs (_) C9,D9: 6.. / C9 = 6 => 0 pairs (*) / D9 = 6 => 0 pairs (X) A3,A4: 6.. / A3 = 6 => 0 pairs (*) / A4 = 6 => 0 pairs (X) B1,B4: 6.. / B1 = 6 => 0 pairs (X) / B4 = 6 => 0 pairs (_) D5,D9: 6.. / D5 = 6 => 0 pairs (*) / D9 = 6 => 0 pairs (X) E1,E6: 6.. / E1 = 6 => 0 pairs (*) / E6 = 6 => 0 pairs (X) H3,H6: 6.. / H3 = 6 => 0 pairs (X) / H6 = 6 => 0 pairs (_) B1,A3: 9.. / B1 = 9 => 0 pairs (*) / A3 = 9 => 0 pairs (X) E1,F3: 9.. / E1 = 9 => 0 pairs (X) / F3 = 9 => 0 pairs (_) G2,I2: 9.. / G2 = 9 => 0 pairs (*) / I2 = 9 => 0 pairs (X) A4,B4: 9.. / A4 = 9 => 0 pairs (*) / B4 = 9 => 0 pairs (X) D5,E6: 9.. / D5 = 9 => 0 pairs (X) / E6 = 9 => 0 pairs (_) C8,C9: 9.. / C8 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) F8,D9: 9.. / F8 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) B1,E1: 9.. / B1 = 9 => 0 pairs (*) / E1 = 9 => 0 pairs (X) A3,F3: 9.. / A3 = 9 => 0 pairs (X) / F3 = 9 => 0 pairs (_) E6,I6: 9.. / E6 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) C8,F8: 9.. / C8 = 9 => 0 pairs (*) / F8 = 9 => 0 pairs (X) C9,D9: 9.. / C9 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) A3,A4: 9.. / A3 = 9 => 0 pairs (X) / A4 = 9 => 0 pairs (_) B1,B4: 9.. / B1 = 9 => 0 pairs (*) / B4 = 9 => 0 pairs (X) D5,D9: 9.. / D5 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) E1,E6: 9.. / E1 = 9 => 0 pairs (X) / E6 = 9 => 0 pairs (_) F3,F8: 9.. / F3 = 9 => 0 pairs (*) / F8 = 9 => 0 pairs (X) G2,G5: 9.. / G2 = 9 => 0 pairs (*) / G5 = 9 => 0 pairs (X) * DURATION: 0:01:27.164943 START: 14:57:10.123048 END: 14:58:37.287991 2017-05-04 * CP COUNT: (48) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B1,B4,B5,B6,C8,C9,D5,D9,E1,E6,F2,F8,G2,G5,H3,H6,I2) * 4.53.827178142..3..2371.4.8..75413823.2.87.1.1.82.37..51483269727.15.84383..74125 * PAIR A3: 6,9 ROW 3 F3: 6,9,5 # reduction candidate for 6,9 F3: 6,9 => SOLVED * 495368271781425936623719458967541382342687519158293764514832697279156843836974125 F3: 5 => CTR * 4.5398271781426539923715468697541382352987.1.1.82.37..51483269727.15.84383..74125 * PAIR E1: 6,9 BLK 2 F3: 6,9,5 # reduction candidate for 6,9 F3: 6,9 => SOLVED * 495368271781425936623719458967541382342687519158293764514832697279156843836974125 F3: 5 => CTR * 4.5398271781426539923715468697541382352987.1.1.82.37..51483269727.15.84383..74125 * PAIR F2: 5,6 BLK 2 F3: 5,6,9 # reduction candidate for 5,6 F3: 5,6 => CTR * 4.539827178142..3.92371.4.86975413823.29875161.82.37..51483269727.15.84383..74125 F3: 9 => SOLVED * 495368271781425936623719458967541382342687519158293764514832697279156843836974125 * PAIR I2: 6,9 COL I I5: 6,9,4 # reduction candidate for 6,9 I5: 6,9 => SOLVED * 495368271781425936623719458967541382342687519158293764514832697279156843836974125 I5: 4 => CTR * 4.53.827178142..3..2371.4.8..75413823.268791414829375651483269727.15684383..74125 I6: 6,9,4 # reduction candidate for 6,9 I6: 6,9 => CTR * 4.5368271781425.3..2371.4.8..75413823.2.87.141482.375651483269727.15.84383..74125 I6: 4 => SOLVED * 495368271781425936623719458967541382342687519158293764514832697279156843836974125 * PAIR H3: 5,6 ROW 3 F3: 5,6,9 # reduction candidate for 5,6 F3: 5,6 => CTR * 4.539827178142..3.92371.4.86975413823.29875161.82.37..51483269727.15.84383..74125 F3: 9 => SOLVED * 495368271781425936623719458967541382342687519158293764514832697279156843836974125 * PAIR D5: 6,9 ROW 5 I5: 6,9,4 # reduction candidate for 6,9 I5: 6,9 => SOLVED * 495368271781425936623719458967541382342687519158293764514832697279156843836974125 I5: 4 => CTR * 4.53.827178142..3..2371.4.8..75413823.268791414829375651483269727.15684383..74125 * PAIR E6: 6,9 ROW 6 I6: 6,9,4 # reduction candidate for 6,9 I6: 6,9 => CTR * 4.5368271781425.3..2371.4.8..75413823.2.87.141482.375651483269727.15.84383..74125 I6: 4 => SOLVED * 495368271781425936623719458967541382342687519158293764514832697279156843836974125 * PAIR F8: 6,9 COL F F3: 6,9,5 # reduction candidate for 6,9 F3: 6,9 => SOLVED * 495368271781425936623719458967541382342687519158293764514832697279156843836974125 F3: 5 => CTR * 4.5398271781426539923715468697541382352987.1.1.82.37..51483269727.15.84383..74125 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-357-base-pr-000.dot * REASONING * PRF # F3: 6,9 => SOL * DIS # F3: 5 => CTR => F3: 6,9 * PRF # F3: 6,9 => SOL * DIS # F3: 5 => CTR => F3: 6,9 * DIS # F3: 5,6 => CTR => F3: 9 * PRF # F3: 9 => SOL * PRF # I5: 6,9 => SOL * DIS # I5: 4 => CTR => I5: 6,9 * DIS # I6: 6,9 => CTR => I6: 4 * PRF # I6: 4 => SOL * DIS # F3: 5,6 => CTR => F3: 9 * PRF # F3: 9 => SOL * PRF # I5: 6,9 => SOL * DIS # I5: 4 => CTR => I5: 6,9 * DIS # I6: 6,9 => CTR => I6: 4 * PRF # I6: 4 => SOL * PRF # F3: 6,9 => SOL * DIS # F3: 5 => CTR => F3: 6,9 * CNT 18 HDP CHAINS / 18 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B1,B4,B5,B6,C8,C9,D5,D9,E1,E6,F2,F8,G2,G5,H3,H6,I2) * 4.53.827178142..3..2371.4.8..75413823.2.87.1.1.82.37..51483269727.15.84383..74125 * PAIR A3: 6,9 ROW 3 F3: 6,9,5 # reduction candidate for 6,9 F3: 6,9 => SOLVED * 495368271781425936623719458967541382342687519158293764514832697279156843836974125 * DURATION: 0:00:02.024625 START: 14:59:00.570499 END: 14:59:02.595124 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-357-base-pr-001.dot * REASONING * PRF # F3: 6,9 => SOL * STA F3: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 357 solution: 495368271781425936623719458967541382342687519158293764514832697279156843836974125 info: 4893 FNBWY S8.f 982 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 495368271781425936623719458967541382342687519158293764514832697279156843836974125 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 # F3: 6,9 => SOL * DIS # F3: 5 => CTR => F3: 6,9 * PRF # F3: 6,9 => SOL * DIS # F3: 5 => CTR => F3: 6,9 * DIS # F3: 5,6 => CTR => F3: 9 * PRF # F3: 9 => SOL * PRF # I5: 6,9 => SOL * DIS # I5: 4 => CTR => I5: 6,9 * DIS # I6: 6,9 => CTR => I6: 4 * PRF # I6: 4 => SOL * DIS # F3: 5,6 => CTR => F3: 9 * PRF # F3: 9 => SOL * PRF # I5: 6,9 => SOL * DIS # I5: 4 => CTR => I5: 6,9 * DIS # I6: 6,9 => CTR => I6: 4 * PRF # I6: 4 => SOL * PRF # F3: 6,9 => SOL * DIS # F3: 5 => CTR => F3: 6,9 * CNT 18 HDP CHAINS / 18 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # F3: 6,9 => SOL * STA F3: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED