Analysis of xx-top500-291-base.sdk
Contents
Original Sudoku
level: medium
position: ...2...6.5.....9......18...6..35............13.........8.7..4.....6...3...1...... initial
Autosolve
position: 1..2..8655.84..91..6.518...61.35..8.8..9..3.13..18.5.6.8673145....6..138.318.56.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 4,7 => CTR => C1: 3 * DIS # B5: 4,7 => CTR => B5: 2,5 * DIS # B6: 4,7 => CTR => B6: 2,9 * DIS # A3: 2,7 => CTR => A3: 9 * DIS # I2: 3 => CTR => I2: 2,7 * DIS # B5: 2,7 => CTR => B5: 4,5 * DIS # B8: 2,7 => CTR => B8: 5,9 * DIS # F1: 3 => CTR => F1: 7,9 * DIS # F2: 6,7 => CTR => F2: 3 * DIS # E5: 6,7 => CTR => E5: 2,4 * DIS # H3: 2,7 => CTR => H3: 4 * DIS # I3: 2,7 => CTR => I3: 3,4 * DIS # A3: 2,7 => CTR => A3: 9 * DIS # I4: 2,7 => CTR => I4: 4,9 * DIS # H6: 2,7 => CTR => H6: 4,9 * DIS # C4: 2,7 => CTR => C4: 4,9 * DIS # A8: 2,9 => CTR => A8: 4,7 * DIS # C8: 2,9 => CTR => C8: 5,7 * DIS # A9: 2,9 => CTR => A9: 4 * DIS # A3: 7 => CTR => A3: 2,9 * DIS # I9: 2,9 => CTR => I9: 7 * DIS # I4: 2,9 => CTR => I4: 4,7 * CNT 22 HDP CHAINS / 52 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 4,7 => CTR => C1: 3 * PRF C1: 3 # C6: 2,7 => SOL * STA C1: 3 + C6: 2,7 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...2...6.5.....9......18...6..35............13.........8.7..4.....6...3...1...... | initial |
| 1..2..8655.84..91..6.518...61.35..8.8..9..3.13..18.5.6.8673145....6..138.318.56.. | autosolve |
| 143279865578463912962518743619357284854926371327184596286731459795642138431895627 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) B1: 4,7 B2: 2,7 E1: 7,9 E2: 6,7 G3: 2,7 G4: 2,7 A7: 2,9 I7: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,I2: 2.. / B2 = 2 => 9 pairs (_) / I2 = 2 => 0 pairs (*) A7,I7: 2.. / A7 = 2 => 13 pairs (_) / I7 = 2 => 0 pairs (X) G3,G4: 2.. / G3 = 2 => 10 pairs (_) / G4 = 2 => 12 pairs (_) C1,C3: 3.. / C1 = 3 => 13 pairs (_) / C3 = 3 => 0 pairs (X) F1,F2: 3.. / F1 = 3 => 0 pairs (X) / F2 = 3 => 13 pairs (_) I2,I3: 3.. / I2 = 3 => 0 pairs (X) / I3 = 3 => 13 pairs (_) C1,F1: 3.. / C1 = 3 => 13 pairs (_) / F1 = 3 => 0 pairs (X) F2,I2: 3.. / F2 = 3 => 13 pairs (_) / I2 = 3 => 0 pairs (X) C3,I3: 3.. / C3 = 3 => 0 pairs (X) / I3 = 3 => 13 pairs (_) B1,C1: 4.. / B1 = 4 => 8 pairs (_) / C1 = 4 => 0 pairs (X) H3,I3: 4.. / H3 = 4 => 13 pairs (_) / I3 = 4 => 0 pairs (X) A8,A9: 4.. / A8 = 4 => 0 pairs (X) / A9 = 4 => 9 pairs (_) A9,E9: 4.. / A9 = 4 => 9 pairs (_) / E9 = 4 => 0 pairs (X) I3,I4: 4.. / I3 = 4 => 0 pairs (X) / I4 = 4 => 13 pairs (_) B5,C5: 5.. / B5 = 5 => 8 pairs (_) / C5 = 5 => 0 pairs (X) B8,C8: 5.. / B8 = 5 => 0 pairs (X) / C8 = 5 => 8 pairs (_) B5,B8: 5.. / B5 = 5 => 8 pairs (_) / B8 = 5 => 0 pairs (X) C5,C8: 5.. / C5 = 5 => 0 pairs (X) / C8 = 5 => 8 pairs (_) E2,F2: 6.. / E2 = 6 => 8 pairs (_) / F2 = 6 => 0 pairs (X) E5,F5: 6.. / E5 = 6 => 0 pairs (X) / F5 = 6 => 8 pairs (_) E2,E5: 6.. / E2 = 6 => 8 pairs (_) / E5 = 6 => 0 pairs (X) F2,F5: 6.. / F2 = 6 => 0 pairs (X) / F5 = 6 => 8 pairs (_) H9,I9: 7.. / H9 = 7 => 0 pairs (X) / I9 = 7 => 12 pairs (_) A3,A8: 7.. / A3 = 7 => 0 pairs (X) / A8 = 7 => 10 pairs (_) G3,G4: 7.. / G3 = 7 => 12 pairs (_) / G4 = 7 => 10 pairs (_) A3,C3: 9.. / A3 = 9 => 13 pairs (_) / C3 = 9 => 0 pairs (X) E1,F1: 9.. / E1 = 9 => 0 pairs (X) / F1 = 9 => 13 pairs (_) I4,H6: 9.. / I4 = 9 => 0 pairs (X) / H6 = 9 => 13 pairs (_) C4,I4: 9.. / C4 = 9 => 13 pairs (_) / I4 = 9 => 0 pairs (X) A7,I7: 9.. / A7 = 9 => 0 pairs (X) / I7 = 9 => 13 pairs (_) B6,B8: 9.. / B6 = 9 => 0 pairs (X) / B8 = 9 => 13 pairs (_) F1,F8: 9.. / F1 = 9 => 13 pairs (_) / F8 = 9 => 0 pairs (X) H6,H9: 9.. / H6 = 9 => 13 pairs (_) / H9 = 9 => 0 pairs (X) * DURATION: 0:01:04.786945 START: 12:53:38.491693 END: 12:54:43.278638 2017-05-04 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B1,B2,E1,E2,G3,G4,I7) * 1..2..8655.84..91..6.518...61.35..8.8..9..3.13..18.5.6.8673145....6..138.318.56.. * PAIR B1: 4,7 BLK 1 C1: 4,7,3 # reduction candidate for 4,7 C1: 4,7 => CTR * 1..2938655284..913963518...61.35..8.8..9..3.139.18.5.628673145975.6.9138.318.56.. C1: 3 # 13 pairs * PAIR B1: 4,7 COL B B5: 4,7,2,5 # reduction candidate for 4,7 B5: 4,7 => CTR * 1..2..8655284..913.63518...61.35..898.59..3.139.18.5.6986731452.5.6..138.318.5697 B5: 2,5 # 9 pairs B6: 4,7,2,9 # reduction candidate for 4,7 B6: 4,7 => CTR * 14327986552846391796751824361.35..8485.9.63.13..18.5962867314597956..1384318956.. B6: 2,9 # 9 pairs * PAIR B2: 2,7 BLK 1 A3: 2,7,9 # reduction candidate for 2,7 A3: 2,7 => CTR * 1..2..8655.84..91..69518..361.35..8.8..9..3.13..18.5.6.8673145....6..138.318.56.. A3: 9 # 13 pairs C3: 2,7,3,9 # reduction candidate for 2,7 C3: 2,7 # 13 pairs * PAIR B2: 2,7 ROW 2 I2: 2,7,3 # reduction candidate for 2,7 I2: 3 => CTR * 1..2.38655284..913963518...61.35..8.8..9..3.13..18.5.62867314597..6.91384318256.. I2: 2,7 # 13 pairs * PAIR B2: 2,7 COL B B5: 2,7,4,5 # reduction candidate for 2,7 B5: 2,7 => CTR * 14.2..8655284..91376.518...61.35..898.59..3.139.18.5.6986731452.5.6..138.318.5697 B5: 4,5 # 9 pairs B6: 2,7,4,9 # reduction candidate for 2,7 B6: 2,7 # 13 pairs B8: 2,7,5,9 # reduction candidate for 2,7 B8: 2,7 => CTR * 14.2..8655.84..91..69518..361.35..8.85.9..3.139.18.5.6.8673145...56..138.318.5697 B8: 5,9 # 9 pairs * PAIR E1: 7,9 BLK 2 F1: 7,9,3 # reduction candidate for 7,9 F1: 3 => CTR * 1..2938655284..913963518...61.35..8.8..9..3.139.18.5.628673145975.6.9138.318.56.. F1: 7,9 # 13 pairs * PAIR E2: 6,7 BLK 2 F2: 6,7,3 # reduction candidate for 6,7 F2: 6,7 => CTR * 1..2938655284..913963518...61.35..8.8..9..3.139.18.5.628673145975.6.9138.318.56.. F2: 3 # 13 pairs * PAIR E2: 6,7 COL E E5: 6,7,2,4 # reduction candidate for 6,7 E5: 6,7 => CTR * 1..29.8655.84..91..69518..361.35..8.8..9..3.139.18.5.6.8673145....6.9138.318.5697 E5: 2,4 # 13 pairs * PAIR G3: 2,7 BLK 3 I2: 2,7,3 # reduction candidate for 2,7 I2: 2,7 # 13 pairs H3: 2,7,4 # reduction candidate for 2,7 H3: 2,7 => CTR * 1..2.38655284..913963518..461.35..8.8..9..3.13..18.5.62867314597..6.91384318256.. H3: 4 # 13 pairs I3: 2,7,3,4 # reduction candidate for 2,7 I3: 2,7 => CTR * 1..2..8655.84..913.63518.4.61.35..848..9..3.13..18.596.8673145..956..138.318956.. I3: 3,4 # 9 pairs * PAIR G3: 2,7 ROW 3 A3: 2,7,9 # reduction candidate for 2,7 A3: 2,7 => CTR * 1..2..8655.84..91..69518..361.35..8.8..9..3.13..18.5.6.8673145....6..138.318.56.. A3: 9 # 13 pairs C3: 2,7,3,9 # reduction candidate for 2,7 C3: 2,7 # 13 pairs * PAIR G4: 2,7 BLK 6 I4: 2,7,4,9 # reduction candidate for 2,7 I4: 2,7 => CTR * 1..2798655.846391.963518..4619354.8.85.9..3.13..18.596.8673145..956.2138.318956.. I4: 4,9 # 9 pairs H5: 2,7,4 # reduction candidate for 2,7 H5: 2,7 # 11 pairs H6: 2,7,4,9 # reduction candidate for 2,7 H6: 2,7 => CTR * 1..2..8655284..91376.518...61.35..898..9..3413..18.5.6986731452...6..138.318.5697 H6: 4,9 # 9 pairs * PAIR G4: 2,7 ROW 4 C4: 2,7,4,9 # reduction candidate for 2,7 C4: 2,7 => CTR * 1..2..8655284..91376.518...61.35..898..9..3.13..18.5.6986731452...6..138.318.5697 C4: 4,9 # 9 pairs F4: 2,7,4 # reduction candidate for 2,7 F4: 2,7 # 11 pairs * PAIR A7: 2,9 BLK 7 A8: 2,9,4,7 # reduction candidate for 2,9 A8: 2,9 => CTR * 1..2..8655.84..91.76951824361.35..8.8..9..3.13..18.5.6.8673145....6..138.318.56.. A8: 4,7 # 9 pairs B8: 2,9,5,7 # reduction candidate for 2,9 B8: 2,9 # 11 pairs C8: 2,9,5,7 # reduction candidate for 2,9 C8: 2,9 => CTR * 1..2..8655284..91..6.518...61.35..898.59..3.139.18.5.69867314527526..138431825697 C8: 5,7 # 9 pairs A9: 2,9,4 # reduction candidate for 2,9 A9: 2,9 => CTR * 1..2..8655.84..91.76951824361.35..8.8..9..3.13..18.5.6.8673145.4..6..138.318456.. A9: 4 # 9 pairs * PAIR A7: 2,9 COL A A3: 2,9,7 # reduction candidate for 2,9 A3: 7 => CTR * 1..2..8655.84..91.76951824361.35..8.8..9..3.13..18.5.6.8673145....6..138.318.56.. A3: 2,9 # 10 pairs * PAIR I7: 2,9 BLK 9 H9: 2,9,7 # reduction candidate for 2,9 H9: 2,9 # 12 pairs I9: 2,9,7 # reduction candidate for 2,9 I9: 2,9 => CTR * 1..27986552846391796751824361935278485.94.3.13..18.596.8673145..956..138.31895672 I9: 7 # 12 pairs * PAIR I7: 2,9 COL I I4: 2,9,4,7 # reduction candidate for 2,9 I4: 2,9 => CTR * 1..2.38655284..913963518..461.35..8.8..9..3.13..18.5.62867314597..6.91384318256.7 I4: 4,7 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-291-base-pr-000.dot * REASONING * DIS # C1: 4,7 => CTR => C1: 3 * DIS # B5: 4,7 => CTR => B5: 2,5 * DIS # B6: 4,7 => CTR => B6: 2,9 * DIS # A3: 2,7 => CTR => A3: 9 * DIS # I2: 3 => CTR => I2: 2,7 * DIS # B5: 2,7 => CTR => B5: 4,5 * DIS # B8: 2,7 => CTR => B8: 5,9 * DIS # F1: 3 => CTR => F1: 7,9 * DIS # F2: 6,7 => CTR => F2: 3 * DIS # E5: 6,7 => CTR => E5: 2,4 * DIS # H3: 2,7 => CTR => H3: 4 * DIS # I3: 2,7 => CTR => I3: 3,4 * DIS # A3: 2,7 => CTR => A3: 9 * DIS # I4: 2,7 => CTR => I4: 4,9 * DIS # H6: 2,7 => CTR => H6: 4,9 * DIS # C4: 2,7 => CTR => C4: 4,9 * DIS # A8: 2,9 => CTR => A8: 4,7 * DIS # C8: 2,9 => CTR => C8: 5,7 * DIS # A9: 2,9 => CTR => A9: 4 * DIS # A3: 7 => CTR => A3: 2,9 * DIS # I9: 2,9 => CTR => I9: 7 * DIS # I4: 2,9 => CTR => I4: 4,7 * CNT 22 HDP CHAINS / 52 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B1,B2,E1,E2,G3,G4,I7) * 1..2..8655.84..91..6.518...61.35..8.8..9..3.13..18.5.6.8673145....6..138.318.56.. * PAIR B1: 4,7 BLK 1 C1: 4,7,3 # reduction candidate for 4,7 C1: 4,7 => CTR * 1..2938655284..913963518...61.35..8.8..9..3.139.18.5.628673145975.6.9138.318.56.. * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (B2,B6,C3,E5,E8,F4,F8,G3,G4,H5,H9,I2,I9) * 1432798655.846391.96.518.4361935..8485.9.63.13..18.5962867314597956..1384318956.. * PAIR C3: 2,7 COL C C5: 2,7,4 # reduction candidate for 2,7 C5: 2,7 # 12 pairs C6: 2,7,4 # reduction candidate for 2,7 C6: 2,7 => SOLVED * 143279865578463912962518743619357284854926371327184596286731459795642138431895627 * DURATION: 0:00:06.330085 START: 12:55:36.928642 END: 12:55:43.258727 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-291-base-pr-001.dot * REASONING * DIS # C1: 4,7 => CTR => C1: 3 * PRF C1: 3 # C6: 2,7 => SOL * STA C1: 3 + C6: 2,7 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 291 solution: 143279865578463912962518743619357284854926371327184596286731459795642138431895627 info: 2404 FNBTHWXY S8.f 47450 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 143279865578463912962518743619357284854926371327184596286731459795642138431895627 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 # C1: 4,7 => CTR => C1: 3 * INC # C1: 3 => UNS * DIS # B5: 4,7 => CTR => B5: 2,5 * INC # B5: 2,5 => UNS * DIS # B6: 4,7 => CTR => B6: 2,9 * INC # B6: 2,9 => UNS * DIS # A3: 2,7 => CTR => A3: 9 * INC # A3: 9 => UNS * INC # C3: 2,7 => UNS * INC # I2: 2,7 => UNS * DIS # I2: 3 => CTR => I2: 2,7 * DIS # B5: 2,7 => CTR => B5: 4,5 * INC # B5: 4,5 => UNS * INC # B6: 2,7 => UNS * DIS # B8: 2,7 => CTR => B8: 5,9 * INC # B8: 5,9 => UNS * INC # F1: 7,9 => UNS * DIS # F1: 3 => CTR => F1: 7,9 * DIS # F2: 6,7 => CTR => F2: 3 * INC # F2: 3 => UNS * DIS # E5: 6,7 => CTR => E5: 2,4 * INC # E5: 2,4 => UNS * INC # I2: 2,7 => UNS * DIS # H3: 2,7 => CTR => H3: 4 * INC # H3: 4 => UNS * DIS # I3: 2,7 => CTR => I3: 3,4 * INC # I3: 3,4 => UNS * DIS # A3: 2,7 => CTR => A3: 9 * INC # A3: 9 => UNS * INC # C3: 2,7 => UNS * DIS # I4: 2,7 => CTR => I4: 4,9 * INC # I4: 4,9 => UNS * INC # H5: 2,7 => UNS * DIS # H6: 2,7 => CTR => H6: 4,9 * INC # H6: 4,9 => UNS * DIS # C4: 2,7 => CTR => C4: 4,9 * INC # C4: 4,9 => UNS * INC # F4: 2,7 => UNS * DIS # A8: 2,9 => CTR => A8: 4,7 * INC # A8: 4,7 => UNS * INC # B8: 2,9 => UNS * DIS # C8: 2,9 => CTR => C8: 5,7 * INC # C8: 5,7 => UNS * DIS # A9: 2,9 => CTR => A9: 4 * INC # A9: 4 => UNS * INC # A3: 2,9 => UNS * DIS # A3: 7 => CTR => A3: 2,9 * INC # H9: 2,9 => UNS * DIS # I9: 2,9 => CTR => I9: 7 * INC # I9: 7 => UNS * DIS # I4: 2,9 => CTR => I4: 4,7 * INC # I4: 4,7 => UNS * CNT 52 HDP CHAINS / 52 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C1: 4,7 => CTR => C1: 3 * INC C1: 3 # C5: 2,7 => UNS * PRF C1: 3 # C6: 2,7 => SOL * STA C1: 3 + C6: 2,7 * CNT 3 HDP CHAINS / 3 HYP OPENED