Analysis of xx-top500-125-base.sdk
Contents
Original Sudoku
level: medium
position: 64...........8.1..2...4....8.......4.....1.3....2......3.7..5.....6..2....1...... initial
Autosolve
position: 6481..32.3...8214621.346.8.823.6..14..64.18321.423865.93271456848.6.32.1.6182.4.3 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C2: 5,7 => SOL * DIS # C2: 9 => CTR => C2: 5,7 * PRF # B5: 5,7 => SOL * DIS # B5: 9 => CTR => B5: 5,7 * PRF # C2: 5,9 => SOL * DIS # C2: 7 => CTR => C2: 5,9 * PRF # I3: 5,9 => SOL * DIS # I3: 7 => CTR => I3: 5,9 * DIS # E1: 5,9 => CTR => E1: 7 * PRF # E1: 7 => SOL * PRF # F1: 5,9 => SOL * DIS # F1: 7 => CTR => F1: 5,9 * PRF # C2: 5,9 => SOL * DIS # C2: 7 => CTR => C2: 5,9 * PRF # I3: 5,9 => SOL * DIS # I3: 7 => CTR => I3: 5,9 * DIS # E1: 5,9 => CTR => E1: 7 * PRF # E1: 7 => SOL * PRF # F1: 5,9 => SOL * DIS # F1: 7 => CTR => F1: 5,9 * DIS # I3: 7,9 => CTR => I3: 5 * PRF # I3: 5 => SOL * PRF # B5: 5,7 => SOL * DIS # B5: 9 => CTR => B5: 5,7 * DIS # B5: 7,9 => CTR => B5: 5 * PRF # B5: 5 => SOL * DIS # F4: 5,9 => CTR => F4: 7 * PRF # F4: 7 => SOL * PRF # F4: 7,9 => SOL * DIS # F4: 5 => CTR => F4: 7,9 * DIS # B5: 7,9 => CTR => B5: 5 * PRF # B5: 5 => SOL * PRF # E1: 7,9 => SOL * DIS # E1: 5 => CTR => E1: 7,9 * PRF # F4: 7,9 => SOL * DIS # F4: 5 => CTR => F4: 7,9 * DIS # I3: 7,9 => CTR => I3: 5 * PRF # I3: 5 => SOL * PRF # C2: 5,7 => SOL * DIS # C2: 9 => CTR => C2: 5,7 * DIS # E1: 5,9 => CTR => E1: 7 * PRF # E1: 7 => SOL * PRF # F1: 5,9 => SOL * DIS # F1: 7 => CTR => F1: 5,9 * DIS # F4: 5,9 => CTR => F4: 7 * PRF # F4: 7 => SOL * CNT 46 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C2: 5,7 => SOL * STA C2: 5,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 64...........8.1..2...4....8.......4.....1.3....2......3.7..5.....6..2....1...... | initial |
| 6481..32.3...8214621.346.8.823.6..14..64.18321.423865.93271456848.6.32.1.6182.4.3 | autosolve |
| 648175329375982146219346785823567914756491832194238657932714568487653291561829473 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) B2: 5,7 C3: 5,9 D2: 5,9 I1: 5,9 G3: 7,9 A5: 5,7 B6: 7,9 D4: 5,9 E5: 7,9 G4: 7,9 I6: 7,9 C8: 5,7 A9: 5,7 E8: 5,9 F9: 5,9 H8: 7,9 H9: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I1,I3: 5.. / I1 = 5 => 0 pairs (X) / I3 = 5 => 0 pairs (_) A5,B5: 5.. / A5 = 5 => 0 pairs (X) / B5 = 5 => 0 pairs (_) D4,F4: 5.. / D4 = 5 => 0 pairs (*) / F4 = 5 => 0 pairs (X) C8,A9: 5.. / C8 = 5 => 0 pairs (X) / A9 = 5 => 0 pairs (_) E8,F9: 5.. / E8 = 5 => 0 pairs (*) / F9 = 5 => 0 pairs (X) C3,I3: 5.. / C3 = 5 => 0 pairs (X) / I3 = 5 => 0 pairs (_) C8,E8: 5.. / C8 = 5 => 0 pairs (X) / E8 = 5 => 0 pairs (_) A9,F9: 5.. / A9 = 5 => 0 pairs (*) / F9 = 5 => 0 pairs (X) A5,A9: 5.. / A5 = 5 => 0 pairs (X) / A9 = 5 => 0 pairs (_) B2,B5: 5.. / B2 = 5 => 0 pairs (X) / B5 = 5 => 0 pairs (_) D2,D4: 5.. / D2 = 5 => 0 pairs (X) / D4 = 5 => 0 pairs (_) E1,E8: 5.. / E1 = 5 => 0 pairs (X) / E8 = 5 => 0 pairs (_) B2,C2: 7.. / B2 = 7 => 0 pairs (*) / C2 = 7 => 0 pairs (X) E1,F1: 7.. / E1 = 7 => 0 pairs (*) / F1 = 7 => 0 pairs (X) G3,I3: 7.. / G3 = 7 => 0 pairs (*) / I3 = 7 => 0 pairs (X) F4,E5: 7.. / F4 = 7 => 0 pairs (*) / E5 = 7 => 0 pairs (X) G4,I6: 7.. / G4 = 7 => 0 pairs (X) / I6 = 7 => 0 pairs (_) C8,A9: 7.. / C8 = 7 => 0 pairs (*) / A9 = 7 => 0 pairs (X) H8,H9: 7.. / H8 = 7 => 0 pairs (X) / H9 = 7 => 0 pairs (_) F4,G4: 7.. / F4 = 7 => 0 pairs (*) / G4 = 7 => 0 pairs (X) B6,I6: 7.. / B6 = 7 => 0 pairs (X) / I6 = 7 => 0 pairs (_) C8,H8: 7.. / C8 = 7 => 0 pairs (*) / H8 = 7 => 0 pairs (X) A9,H9: 7.. / A9 = 7 => 0 pairs (X) / H9 = 7 => 0 pairs (_) A5,A9: 7.. / A5 = 7 => 0 pairs (*) / A9 = 7 => 0 pairs (X) C2,C8: 7.. / C2 = 7 => 0 pairs (X) / C8 = 7 => 0 pairs (_) E1,E5: 7.. / E1 = 7 => 0 pairs (*) / E5 = 7 => 0 pairs (X) F1,F4: 7.. / F1 = 7 => 0 pairs (X) / F4 = 7 => 0 pairs (_) G3,G4: 7.. / G3 = 7 => 0 pairs (*) / G4 = 7 => 0 pairs (X) I3,I6: 7.. / I3 = 7 => 0 pairs (X) / I6 = 7 => 0 pairs (_) C2,C3: 9.. / C2 = 9 => 0 pairs (X) / C3 = 9 => 0 pairs (_) B5,B6: 9.. / B5 = 9 => 0 pairs (X) / B6 = 9 => 0 pairs (_) G4,I6: 9.. / G4 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) E8,F9: 9.. / E8 = 9 => 0 pairs (X) / F9 = 9 => 0 pairs (_) H8,H9: 9.. / H8 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) C2,D2: 9.. / C2 = 9 => 0 pairs (X) / D2 = 9 => 0 pairs (_) B5,E5: 9.. / B5 = 9 => 0 pairs (X) / E5 = 9 => 0 pairs (_) B6,I6: 9.. / B6 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) E8,H8: 9.. / E8 = 9 => 0 pairs (X) / H8 = 9 => 0 pairs (_) F9,H9: 9.. / F9 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) D2,D4: 9.. / D2 = 9 => 0 pairs (*) / D4 = 9 => 0 pairs (X) G3,G4: 9.. / G3 = 9 => 0 pairs (X) / G4 = 9 => 0 pairs (_) * DURATION: 0:01:11.544357 START: 07:02:06.646875 END: 07:03:18.191232 2017-05-04 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A9,B2,B6,C3,C8,D2,D4,E5,E8,F9,G3,G4,H8,H9,I1,I6) * 6481..32.3...8214621.346.8.823.6..14..64.18321.423865.93271456848.6.32.1.6182.4.3 * PAIR B2: 5,7 BLK 1 C2: 5,7,9 # reduction candidate for 5,7 C2: 5,7 => SOLVED * 648175329375982146219346785823567914756491832194238657932714568487653291561829473 C2: 9 => CTR * 6481..32.379582146215346.8.823965714..64.18321.423865.93271456848.6.32.1.6182.4.3 * PAIR B2: 5,7 COL B B5: 5,7,9 # reduction candidate for 5,7 B5: 5,7 => SOLVED * 648175329375982146219346785823567914756491832194238657932714568487653291561829473 B5: 9 => CTR * 6481..32.357982146219346785823567914..64.18321.423865.93271456848.6.32.1.6182.4.3 * PAIR C3: 5,9 BLK 1 C2: 5,9,7 # reduction candidate for 5,9 C2: 5,9 => SOLVED * 648175329375982146219346785823567914756491832194238657932714568487653291561829473 C2: 7 => CTR * 6481..32.3.7982146219346785823567914..64918321942386579327145684856.32.1.6182.4.3 * PAIR C3: 5,9 ROW 3 I3: 5,9,7 # reduction candidate for 5,9 I3: 5,9 => SOLVED * 648175329375982146219346785823567914756491832194238657932714568487653291561829473 I3: 7 => CTR * 6481..3253..582146215346987823965714..64.18321.423865.93271456848.6.32.1.6182.4.3 * PAIR D2: 5,9 BLK 2 E1: 5,9,7 # reduction candidate for 5,9 E1: 5,9 => CTR * 6481.732.3...8214621.346.8.823.6.714..647183217423865993271456848.6.32.1761825493 E1: 7 => SOLVED * 648175329375982146219346785823567914756491832194238657932714568487653291561829473 F1: 5,9,7 # reduction candidate for 5,9 F1: 5,9 => SOLVED * 648175329375982146219346785823567914756491832194238657932714568487653291561829473 F1: 7 => CTR * 6481.732.3...8214621.346.8.823.6.714..647183217423865993271456848.6.32.1761825493 * PAIR D2: 5,9 ROW 2 C2: 5,9,7 # reduction candidate for 5,9 C2: 5,9 => SOLVED * 648175329375982146219346785823567914756491832194238657932714568487653291561829473 C2: 7 => CTR * 6481..32.3.7982146219346785823567914..64918321942386579327145684856.32.1.6182.4.3 * PAIR I1: 5,9 BLK 3 I3: 5,9,7 # reduction candidate for 5,9 I3: 5,9 => SOLVED * 648175329375982146219346785823567914756491832194238657932714568487653291561829473 I3: 7 => CTR * 6481..3253..582146215346987823965714..64.18321.423865.93271456848.6.32.1.6182.4.3 * PAIR I1: 5,9 ROW 1 E1: 5,9,7 # reduction candidate for 5,9 E1: 5,9 => CTR * 6481.732.3...8214621.346.8.823.6.714..647183217423865993271456848.6.32.1761825493 E1: 7 => SOLVED * 648175329375982146219346785823567914756491832194238657932714568487653291561829473 F1: 5,9,7 # reduction candidate for 5,9 F1: 5,9 => SOLVED * 648175329375982146219346785823567914756491832194238657932714568487653291561829473 F1: 7 => CTR * 6481.732.3...8214621.346.8.823.6.714..647183217423865993271456848.6.32.1761825493 * PAIR G3: 7,9 BLK 3 I3: 7,9,5 # reduction candidate for 7,9 I3: 7,9 => CTR * 6481..3253..582146215346.8.823965714..64.18321.423865.93271456848.6.32.1.6182.4.3 I3: 5 => SOLVED * 648175329375982146219346785823567914756491832194238657932714568487653291561829473 * PAIR A5: 5,7 BLK 4 B5: 5,7,9 # reduction candidate for 5,7 B5: 5,7 => SOLVED * 648175329375982146219346785823567914756491832194238657932714568487653291561829473 B5: 9 => CTR * 6481..32.357982146219346785823567914..64.18321.423865.93271456848.6.32.1.6182.4.3 * PAIR B6: 7,9 BLK 4 B5: 7,9,5 # reduction candidate for 7,9 B5: 7,9 => CTR * 6481..32.3579821462193467858235679145764918321942386579327145684856.32.1.6182.4.3 B5: 5 => SOLVED * 648175329375982146219346785823567914756491832194238657932714568487653291561829473 * PAIR D4: 5,9 BLK 5 F4: 5,9,7 # reduction candidate for 5,9 F4: 5,9 => CTR * 6481.732.3...8214621.346.8.823.6.714..647183217423865993271456848.6.32.1761825493 F4: 7 => SOLVED * 648175329375982146219346785823567914756491832194238657932714568487653291561829473 * PAIR E5: 7,9 BLK 5 F4: 7,9,5 # reduction candidate for 7,9 F4: 7,9 => SOLVED * 648175329375982146219346785823567914756491832194238657932714568487653291561829473 F4: 5 => CTR * 6481.732.3...8214621.346.8.823.65714..647183217423865993271456848.653291.6182.4.3 * PAIR E5: 7,9 ROW 5 B5: 7,9,5 # reduction candidate for 7,9 B5: 7,9 => CTR * 6481..32.3579821462193467858235679145764918321942386579327145684856.32.1.6182.4.3 B5: 5 => SOLVED * 648175329375982146219346785823567914756491832194238657932714568487653291561829473 * PAIR E5: 7,9 COL E E1: 7,9,5 # reduction candidate for 7,9 E1: 7,9 => SOLVED * 648175329375982146219346785823567914756491832194238657932714568487653291561829473 E1: 5 => CTR * 6481573293..98214621934678.823.6..14..64.18321.423865.93271456848.6.32.1.6182.4.3 * PAIR G4: 7,9 ROW 4 F4: 7,9,5 # reduction candidate for 7,9 F4: 7,9 => SOLVED * 648175329375982146219346785823567914756491832194238657932714568487653291561829473 F4: 5 => CTR * 6481.732.3...8214621.346.8.823.65714..647183217423865993271456848.653291.6182.4.3 * PAIR I6: 7,9 COL I I3: 7,9,5 # reduction candidate for 7,9 I3: 7,9 => CTR * 6481..3253..582146215346.8.823965714..64.18321.423865.93271456848.6.32.1.6182.4.3 I3: 5 => SOLVED * 648175329375982146219346785823567914756491832194238657932714568487653291561829473 * PAIR C8: 5,7 COL C C2: 5,7,9 # reduction candidate for 5,7 C2: 5,7 => SOLVED * 648175329375982146219346785823567914756491832194238657932714568487653291561829473 C2: 9 => CTR * 6481..32.379582146215346.8.823965714..64.18321.423865.93271456848.6.32.1.6182.4.3 * PAIR E8: 5,9 COL E E1: 5,9,7 # reduction candidate for 5,9 E1: 5,9 => CTR * 6481.732.3...8214621.346.8.823.6.714..647183217423865993271456848.6.32.1761825493 E1: 7 => SOLVED * 648175329375982146219346785823567914756491832194238657932714568487653291561829473 * PAIR F9: 5,9 COL F F1: 5,9,7 # reduction candidate for 5,9 F1: 5,9 => SOLVED * 648175329375982146219346785823567914756491832194238657932714568487653291561829473 F1: 7 => CTR * 6481.732.3...8214621.346.8.823.6.714..647183217423865993271456848.6.32.1761825493 F4: 5,9,7 # reduction candidate for 5,9 F4: 5,9 => CTR * 6481.732.3...8214621.346.8.823.6.714..647183217423865993271456848.6.32.1761825493 F4: 7 => SOLVED * 648175329375982146219346785823567914756491832194238657932714568487653291561829473 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-125-base-pr-000.dot * REASONING * PRF # C2: 5,7 => SOL * DIS # C2: 9 => CTR => C2: 5,7 * PRF # B5: 5,7 => SOL * DIS # B5: 9 => CTR => B5: 5,7 * PRF # C2: 5,9 => SOL * DIS # C2: 7 => CTR => C2: 5,9 * PRF # I3: 5,9 => SOL * DIS # I3: 7 => CTR => I3: 5,9 * DIS # E1: 5,9 => CTR => E1: 7 * PRF # E1: 7 => SOL * PRF # F1: 5,9 => SOL * DIS # F1: 7 => CTR => F1: 5,9 * PRF # C2: 5,9 => SOL * DIS # C2: 7 => CTR => C2: 5,9 * PRF # I3: 5,9 => SOL * DIS # I3: 7 => CTR => I3: 5,9 * DIS # E1: 5,9 => CTR => E1: 7 * PRF # E1: 7 => SOL * PRF # F1: 5,9 => SOL * DIS # F1: 7 => CTR => F1: 5,9 * DIS # I3: 7,9 => CTR => I3: 5 * PRF # I3: 5 => SOL * PRF # B5: 5,7 => SOL * DIS # B5: 9 => CTR => B5: 5,7 * DIS # B5: 7,9 => CTR => B5: 5 * PRF # B5: 5 => SOL * DIS # F4: 5,9 => CTR => F4: 7 * PRF # F4: 7 => SOL * PRF # F4: 7,9 => SOL * DIS # F4: 5 => CTR => F4: 7,9 * DIS # B5: 7,9 => CTR => B5: 5 * PRF # B5: 5 => SOL * PRF # E1: 7,9 => SOL * DIS # E1: 5 => CTR => E1: 7,9 * PRF # F4: 7,9 => SOL * DIS # F4: 5 => CTR => F4: 7,9 * DIS # I3: 7,9 => CTR => I3: 5 * PRF # I3: 5 => SOL * PRF # C2: 5,7 => SOL * DIS # C2: 9 => CTR => C2: 5,7 * DIS # E1: 5,9 => CTR => E1: 7 * PRF # E1: 7 => SOL * PRF # F1: 5,9 => SOL * DIS # F1: 7 => CTR => F1: 5,9 * DIS # F4: 5,9 => CTR => F4: 7 * PRF # F4: 7 => SOL * CNT 46 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A9,B2,B6,C3,C8,D2,D4,E5,E8,F9,G3,G4,H8,H9,I1,I6) * 6481..32.3...8214621.346.8.823.6..14..64.18321.423865.93271456848.6.32.1.6182.4.3 * PAIR B2: 5,7 BLK 1 C2: 5,7,9 # reduction candidate for 5,7 C2: 5,7 => SOLVED * 648175329375982146219346785823567914756491832194238657932714568487653291561829473 * DURATION: 0:00:01.902153 START: 07:04:10.177535 END: 07:04:12.079688 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-125-base-pr-001.dot * REASONING * PRF # C2: 5,7 => SOL * STA C2: 5,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 125 solution: 648175329375982146219346785823567914756491832194238657932714568487653291561829473 info: 1808 FNBWY S8.f 35874 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 648175329375982146219346785823567914756491832194238657932714568487653291561829473 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 # C2: 5,7 => SOL * DIS # C2: 9 => CTR => C2: 5,7 * PRF # B5: 5,7 => SOL * DIS # B5: 9 => CTR => B5: 5,7 * PRF # C2: 5,9 => SOL * DIS # C2: 7 => CTR => C2: 5,9 * PRF # I3: 5,9 => SOL * DIS # I3: 7 => CTR => I3: 5,9 * DIS # E1: 5,9 => CTR => E1: 7 * PRF # E1: 7 => SOL * PRF # F1: 5,9 => SOL * DIS # F1: 7 => CTR => F1: 5,9 * PRF # C2: 5,9 => SOL * DIS # C2: 7 => CTR => C2: 5,9 * PRF # I3: 5,9 => SOL * DIS # I3: 7 => CTR => I3: 5,9 * DIS # E1: 5,9 => CTR => E1: 7 * PRF # E1: 7 => SOL * PRF # F1: 5,9 => SOL * DIS # F1: 7 => CTR => F1: 5,9 * DIS # I3: 7,9 => CTR => I3: 5 * PRF # I3: 5 => SOL * PRF # B5: 5,7 => SOL * DIS # B5: 9 => CTR => B5: 5,7 * DIS # B5: 7,9 => CTR => B5: 5 * PRF # B5: 5 => SOL * DIS # F4: 5,9 => CTR => F4: 7 * PRF # F4: 7 => SOL * PRF # F4: 7,9 => SOL * DIS # F4: 5 => CTR => F4: 7,9 * DIS # B5: 7,9 => CTR => B5: 5 * PRF # B5: 5 => SOL * PRF # E1: 7,9 => SOL * DIS # E1: 5 => CTR => E1: 7,9 * PRF # F4: 7,9 => SOL * DIS # F4: 5 => CTR => F4: 7,9 * DIS # I3: 7,9 => CTR => I3: 5 * PRF # I3: 5 => SOL * PRF # C2: 5,7 => SOL * DIS # C2: 9 => CTR => C2: 5,7 * DIS # E1: 5,9 => CTR => E1: 7 * PRF # E1: 7 => SOL * PRF # F1: 5,9 => SOL * DIS # F1: 7 => CTR => F1: 5,9 * DIS # F4: 5,9 => CTR => F4: 7 * PRF # F4: 7 => SOL * CNT 46 HDP CHAINS / 46 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C2: 5,7 => SOL * STA C2: 5,7 * CNT 1 HDP CHAINS / 1 HYP OPENED