Analysis of xx-top500-314-base.sdk
Contents
Original Sudoku
level: medium
position: 2......4....6..3.....1......3.....7.....7..2...1......78..2.........56.....3..1.. initial
Autosolve
position: 21..3.746..76.231.36.1.725..32.16.7.6...73.21.712...63786921.3.143785692.2.364187 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A4: 4,8 => CTR => A4: 5,9 * PRF # E2: 4 => SOL * PRF # D4: 5,8 => SOL * PRF # E2: 4,9 => SOL * DIS # E2: 5 => CTR => E2: 4,9 * DIS # A4: 4,8 => CTR => A4: 5,9 * DIS # G5: 4,8 => CTR => G5: 5,9 * DIS # A4: 4,8 => CTR => A4: 5,9 * DIS # G5: 4,8 => CTR => G5: 5,9 * PRF # E2: 4 => SOL * DIS # G4: 4,5 => CTR => G4: 8,9 * PRF # G5: 4,5 => SOL * PRF # A4: 4,5 => SOL * DIS # A4: 4,8 => CTR => A4: 5,9 * DIS # G4: 4,5 => CTR => G4: 8,9 * PRF # G5: 4,5 => SOL * CNT 16 HDP CHAINS / 37 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A4: 4,8 => CTR => A4: 5,9 * DIS A4: 5,9 # E2: 5,9 => CTR => E2: 4 * PRF A4: 5,9 + E2: 4 => SOL * STA A4: 5,9 + E2: 4 * CNT 3 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2......4....6..3.....1......3.....7.....7..2...1......78..2.........56.....3..1.. | initial |
| 21..3.746..76.231.36.1.725..32.16.7.6...73.21.712...63786921.3.143785692.2.364187 | autosolve |
| 219538746857642319364197258532816974698473521471259863786921435143785692925364187 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) C1: 5,9 A2: 4,8 B2: 5,9 C3: 4,8 D1: 5,8 F1: 8,9 E3: 4,9 I2: 8,9 I3: 8,9 B5: 5,9 C5: 4,8 E6: 5,9 F6: 8,9 I4: 4,5 A9: 5,9 C9: 5,9 G7: 4,5 I7: 4,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,C3: 4.. / A2 = 4 => 15 pairs (_) / C3 = 4 => 0 pairs (*) E2,E3: 4.. / E2 = 4 => 0 pairs (*) / E3 = 4 => 0 pairs (X) D4,D5: 4.. / D4 = 4 => 19 pairs (_) / D5 = 4 => 0 pairs (*) G7,I7: 4.. / G7 = 4 => 0 pairs (*) / I7 = 4 => 0 pairs (X) A2,E2: 4.. / A2 = 4 => 15 pairs (_) / E2 = 4 => 0 pairs (*) C3,E3: 4.. / C3 = 4 => 0 pairs (*) / E3 = 4 => 0 pairs (X) A6,G6: 4.. / A6 = 4 => 0 pairs (*) / G6 = 4 => 0 pairs (X) C3,C5: 4.. / C3 = 4 => 0 pairs (*) / C5 = 4 => 0 pairs (X) I4,I7: 4.. / I4 = 4 => 0 pairs (*) / I7 = 4 => 0 pairs (X) C1,B2: 5.. / C1 = 5 => 0 pairs (X) / B2 = 5 => 0 pairs (_) D1,E2: 5.. / D1 = 5 => 0 pairs (*) / E2 = 5 => 0 pairs (X) A9,C9: 5.. / A9 = 5 => 0 pairs (X) / C9 = 5 => 0 pairs (_) G7,I7: 5.. / G7 = 5 => 17 pairs (_) / I7 = 5 => 0 pairs (*) C1,D1: 5.. / C1 = 5 => 0 pairs (X) / D1 = 5 => 0 pairs (_) B2,E2: 5.. / B2 = 5 => 0 pairs (*) / E2 = 5 => 0 pairs (X) B2,B5: 5.. / B2 = 5 => 0 pairs (*) / B5 = 5 => 0 pairs (X) C1,C9: 5.. / C1 = 5 => 0 pairs (X) / C9 = 5 => 0 pairs (_) E2,E6: 5.. / E2 = 5 => 0 pairs (X) / E6 = 5 => 0 pairs (_) I4,I7: 5.. / I4 = 5 => 17 pairs (_) / I7 = 5 => 0 pairs (*) A2,C3: 8.. / A2 = 8 => 0 pairs (*) / C3 = 8 => 0 pairs (X) D1,F1: 8.. / D1 = 8 => 0 pairs (X) / F1 = 8 => 0 pairs (_) I2,I3: 8.. / I2 = 8 => 15 pairs (_) / I3 = 8 => 0 pairs (*) A2,I2: 8.. / A2 = 8 => 0 pairs (*) / I2 = 8 => 0 pairs (X) C3,I3: 8.. / C3 = 8 => 15 pairs (_) / I3 = 8 => 0 pairs (*) C3,C5: 8.. / C3 = 8 => 15 pairs (_) / C5 = 8 => 0 pairs (*) F1,F6: 8.. / F1 = 8 => 0 pairs (*) / F6 = 8 => 0 pairs (X) C1,B2: 9.. / C1 = 9 => 0 pairs (*) / B2 = 9 => 0 pairs (X) I2,I3: 9.. / I2 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) A4,B5: 9.. / A4 = 9 => 0 pairs (X) / B5 = 9 => 0 pairs (_) E6,F6: 9.. / E6 = 9 => 0 pairs (X) / F6 = 9 => 0 pairs (_) G4,G5: 9.. / G4 = 9 => 0 pairs (*) / G5 = 9 => 0 pairs (X) A9,C9: 9.. / A9 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) C1,F1: 9.. / C1 = 9 => 0 pairs (*) / F1 = 9 => 0 pairs (X) E3,I3: 9.. / E3 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) A4,G4: 9.. / A4 = 9 => 0 pairs (X) / G4 = 9 => 0 pairs (_) B5,G5: 9.. / B5 = 9 => 0 pairs (*) / G5 = 9 => 0 pairs (X) A4,A9: 9.. / A4 = 9 => 0 pairs (X) / A9 = 9 => 0 pairs (_) B2,B5: 9.. / B2 = 9 => 0 pairs (X) / B5 = 9 => 0 pairs (_) C1,C9: 9.. / C1 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) F1,F6: 9.. / F1 = 9 => 0 pairs (X) / F6 = 9 => 0 pairs (_) * DURATION: 0:01:19.328732 START: 13:43:07.701551 END: 13:44:27.030283 2017-05-04 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A9,B2,B5,C1,C3,C5,C9,D1,E3,E6,F1,F6,G7,I2,I3,I4,I7) * 21..3.746..76.231.36.1.725..32.16.7.6...73.21.712...63786921.3.143785692.2.364187 * PAIR A2: 4,8 COL A A4: 4,8,5,9 # reduction candidate for 4,8 A4: 4,8 => CTR * 21..3.746..76.231.36.1.725..32.1697.69..73.21571298463786921534143785692925364187 A4: 5,9 # 20 pairs A6: 4,8,5 # reduction candidate for 4,8 A6: 4,8 # 20 pairs * PAIR B2: 5,9 ROW 2 E2: 5,9,4 # reduction candidate for 5,9 E2: 4 => SOLVED * 219538746857642319364197258532816974698473521471259863786921435143785692925364187 E2: 5,9 # 15 pairs * PAIR D1: 5,8 COL D D4: 5,8,4 # reduction candidate for 5,8 D4: 5,8 => SOLVED * 219538746857642319364197258532816974698473521471259863786921435143785692925364187 D4: 4 # 19 pairs D5: 5,8,4 # reduction candidate for 5,8 D5: 5,8 # 19 pairs * PAIR E3: 4,9 BLK 2 E2: 4,9,5 # reduction candidate for 4,9 E2: 4,9 => SOLVED * 219538746857642319364197258532816974698473521471259863786921435143785692925364187 E2: 5 => CTR * 21..3.7464.7652318368147259.32.16.7.654873.21.712...63786921.3.143785692.2.364187 * PAIR B5: 5,9 BLK 4 A4: 5,9,4,8 # reduction candidate for 5,9 A4: 4,8 => CTR * 21..3.746..76.231.36.1.725..32.1697.69..73.21571298463786921534143785692925364187 A4: 5,9 # 20 pairs * PAIR B5: 5,9 ROW 5 G5: 5,9,4,8 # reduction candidate for 5,9 G5: 4,8 => CTR * 21..3.746..76.231.36.1.725..32.1697.69.573.21.71298.63786921.3.143785692925364187 G5: 5,9 # 20 pairs * PAIR C5: 4,8 BLK 4 A4: 4,8,5,9 # reduction candidate for 4,8 A4: 4,8 => CTR * 21..3.746..76.231.36.1.725..32.1697.69..73.21571298463786921534143785692925364187 A4: 5,9 # 20 pairs A6: 4,8,5 # reduction candidate for 4,8 A6: 4,8 # 20 pairs * PAIR C5: 4,8 ROW 5 D5: 4,8,5 # reduction candidate for 4,8 D5: 4,8 # 20 pairs G5: 4,8,5,9 # reduction candidate for 4,8 G5: 4,8 => CTR * 21..3.746..76.231.36.1.725..32.1697.69.573.21.71298.63786921.3.143785692925364187 G5: 5,9 # 20 pairs * PAIR E6: 5,9 COL E E2: 5,9,4 # reduction candidate for 5,9 E2: 4 => SOLVED * 219538746857642319364197258532816974698473521471259863786921435143785692925364187 E2: 5,9 # 15 pairs * PAIR I4: 4,5 BLK 6 G4: 4,5,8,9 # reduction candidate for 4,5 G4: 4,5 => CTR * 21..3.746..76.231.36.1.725.932816.7.65.47392147125..63786921.3.143785692.2.364187 G4: 8,9 # 19 pairs G5: 4,5,8,9 # reduction candidate for 4,5 G5: 4,5 => SOLVED * 219538746857642319364197258532816974698473521471259863786921435143785692925364187 G5: 8,9 # 19 pairs G6: 4,5,8 # reduction candidate for 4,5 G6: 4,5 # 21 pairs * PAIR I4: 4,5 ROW 4 A4: 4,5,8,9 # reduction candidate for 4,5 A4: 4,5 => SOLVED * 219538746857642319364197258532816974698473521471259863786921435143785692925364187 A4: 8,9 # 19 pairs D4: 4,5,8 # reduction candidate for 4,5 D4: 4,5 # 21 pairs * PAIR A9: 5,9 COL A A4: 5,9,4,8 # reduction candidate for 5,9 A4: 4,8 => CTR * 21..3.746..76.231.36.1.725..32.1697.69..73.21571298463786921534143785692925364187 A4: 5,9 # 20 pairs * PAIR G7: 4,5 COL G G4: 4,5,8,9 # reduction candidate for 4,5 G4: 4,5 => CTR * 21..3.746..76.231.36.1.725.932816.7.65.47392147125..63786921.3.143785692.2.364187 G4: 8,9 # 19 pairs G5: 4,5,8,9 # reduction candidate for 4,5 G5: 4,5 => SOLVED * 219538746857642319364197258532816974698473521471259863786921435143785692925364187 G5: 8,9 # 19 pairs G6: 4,5,8 # reduction candidate for 4,5 G6: 4,5 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-314-base-pr-000.dot * REASONING * DIS # A4: 4,8 => CTR => A4: 5,9 * PRF # E2: 4 => SOL * PRF # D4: 5,8 => SOL * PRF # E2: 4,9 => SOL * DIS # E2: 5 => CTR => E2: 4,9 * DIS # A4: 4,8 => CTR => A4: 5,9 * DIS # G5: 4,8 => CTR => G5: 5,9 * DIS # A4: 4,8 => CTR => A4: 5,9 * DIS # G5: 4,8 => CTR => G5: 5,9 * PRF # E2: 4 => SOL * DIS # G4: 4,5 => CTR => G4: 8,9 * PRF # G5: 4,5 => SOL * PRF # A4: 4,5 => SOL * DIS # A4: 4,8 => CTR => A4: 5,9 * DIS # G4: 4,5 => CTR => G4: 8,9 * PRF # G5: 4,5 => SOL * CNT 16 HDP CHAINS / 37 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A9,B2,B5,C1,C3,C5,C9,D1,E3,E6,F1,F6,G7,I2,I3,I4,I7) * 21..3.746..76.231.36.1.725..32.16.7.6...73.21.712...63786921.3.143785692.2.364187 * PAIR A2: 4,8 COL A A4: 4,8,5,9 # reduction candidate for 4,8 A4: 4,8 => CTR * 21..3.746..76.231.36.1.725..32.1697.69..73.21571298463786921534143785692925364187 * RESTART * PAIR RESTART * PAIR B2: 5,9 ROW 2 E2: 5,9,4 # reduction candidate for 5,9 E2: 5,9 => CTR * 2195387464576.2318368147259.32.16.7.6.4.73.218712.9463786921534143785692.2.364187 E2: 4 => SOLVED * 219538746857642319364197258532816974698473521471259863786921435143785692925364187 * DURATION: 0:00:04.808610 START: 13:45:11.069625 END: 13:45:15.878235 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-314-base-pr-001.dot * REASONING * DIS # A4: 4,8 => CTR => A4: 5,9 * DIS A4: 5,9 # E2: 5,9 => CTR => E2: 4 * PRF A4: 5,9 + E2: 4 => SOL * STA A4: 5,9 + E2: 4 * CNT 3 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 314 solution: 219538746857642319364197258532816974698473521471259863786921435143785692925364187 info: 2869 FNBTWX S8.f 26752 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 219538746857642319364197258532816974698473521471259863786921435143785692925364187 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 # A4: 4,8 => CTR => A4: 5,9 * INC # A4: 5,9 => UNS * INC # A6: 4,8 => UNS * INC # E2: 5,9 => UNS * PRF # E2: 4 => SOL * PRF # D4: 5,8 => SOL * INC # D4: 4 => UNS * INC # D5: 5,8 => UNS * PRF # E2: 4,9 => SOL * DIS # E2: 5 => CTR => E2: 4,9 * INC # A4: 5,9 => UNS * DIS # A4: 4,8 => CTR => A4: 5,9 * INC # G5: 5,9 => UNS * DIS # G5: 4,8 => CTR => G5: 5,9 * DIS # A4: 4,8 => CTR => A4: 5,9 * INC # A4: 5,9 => UNS * INC # A6: 4,8 => UNS * INC # D5: 4,8 => UNS * DIS # G5: 4,8 => CTR => G5: 5,9 * INC # G5: 5,9 => UNS * INC # E2: 5,9 => UNS * PRF # E2: 4 => SOL * DIS # G4: 4,5 => CTR => G4: 8,9 * INC # G4: 8,9 => UNS * PRF # G5: 4,5 => SOL * INC # G5: 8,9 => UNS * INC # G6: 4,5 => UNS * PRF # A4: 4,5 => SOL * INC # A4: 8,9 => UNS * INC # D4: 4,5 => UNS * INC # A4: 5,9 => UNS * DIS # A4: 4,8 => CTR => A4: 5,9 * DIS # G4: 4,5 => CTR => G4: 8,9 * INC # G4: 8,9 => UNS * PRF # G5: 4,5 => SOL * INC # G5: 8,9 => UNS * INC # G6: 4,5 => UNS * CNT 37 HDP CHAINS / 37 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A4: 4,8 => CTR => A4: 5,9 * DIS A4: 5,9 # E2: 5,9 => CTR => E2: 4 * PRF A4: 5,9 + E2: 4 => SOL * STA A4: 5,9 + E2: 4 * CNT 3 HDP CHAINS / 2 HYP OPENED