Analysis of xx-top500-214-base.sdk
Contents
Original Sudoku
level: medium
position: .2.6.74..8......9....2.....5...3..8..6....7............7....6..3...8............1 initial
Autosolve
position: .2.6.74388.....29..3.2.8...5...3..8..638..7...8....3...78...6.33...8..........8.1 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A6: 1,9 => CTR => A6: 2,4,7 * PRF # C3: 6,7 => SOL * PRF # A3: 4,9 => SOL * PRF # H3: 6,7 => SOL * DIS # H3: 1,5 => CTR => H3: 6,7 * DIS # I3: 6,7 => CTR => I3: 5 * PRF # I3: 5 => SOL * DIS # H3: 1,5 => CTR => H3: 6,7 * PRF # H3: 6,7 => SOL * DIS # C4: 1,9 => CTR => C4: 2,4,7 * DIS # D4: 1,9 => CTR => D4: 4,7 * DIS # F4: 1,9 => CTR => F4: 2,4,6 * DIS # I8: 2,4,7 => CTR => I8: 5,9 * CNT 13 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A6: 1,9 => CTR => A6: 2,4,7 * PRF A6: 2,4,7 # C3: 6,7 => SOL * STA A6: 2,4,7 + C3: 6,7 * CNT 2 HDP CHAINS / 15 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2.6.74..8......9....2.....5...3..8..6....7............7....6..3...8............1 | initial |
| .2.6.74388.....29..3.2.8...5...3..8..638..7...8....3...78...6.33...8..........8.1 | autosolve |
| 921657438856341297437298165514732986263819754789564312178925643342186579695473821 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) A1: 1,9 C2: 6,7 E3: 4,9 I2: 6,7 G3: 1,5 E6: 6,7 G4: 1,9 E9: 6,7 G8: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G3,H3: 1.. / G3 = 1 => 15 pairs (_) / H3 = 1 => 0 pairs (X) G3,G4: 1.. / G3 = 1 => 15 pairs (_) / G4 = 1 => 0 pairs (X) E5,E7: 2.. / E5 = 2 => 9 pairs (_) / E7 = 2 => 10 pairs (_) D2,F2: 3.. / D2 = 3 => 9 pairs (_) / F2 = 3 => 9 pairs (_) D9,F9: 3.. / D9 = 3 => 9 pairs (_) / F9 = 3 => 9 pairs (_) D2,D9: 3.. / D2 = 3 => 9 pairs (_) / D9 = 3 => 9 pairs (_) F2,F9: 3.. / F2 = 3 => 9 pairs (_) / F9 = 3 => 9 pairs (_) C1,B2: 5.. / C1 = 5 => 11 pairs (_) / B2 = 5 => 12 pairs (_) C1,E1: 5.. / C1 = 5 => 11 pairs (_) / E1 = 5 => 12 pairs (_) G3,G8: 5.. / G3 = 5 => 0 pairs (X) / G8 = 5 => 15 pairs (_) C2,I2: 6.. / C2 = 6 => 0 pairs (*) / I2 = 6 => 0 pairs (X) F4,I4: 6.. / F4 = 6 => 0 pairs (X) / I4 = 6 => 0 pairs (_) C8,F8: 6.. / C8 = 6 => 0 pairs (X) / F8 = 6 => 0 pairs (_) A3,A9: 6.. / A3 = 6 => 0 pairs (X) / A9 = 6 => 0 pairs (_) E6,E9: 6.. / E6 = 6 => 0 pairs (*) / E9 = 6 => 0 pairs (X) H3,H6: 6.. / H3 = 6 => 0 pairs (*) / H6 = 6 => 0 pairs (X) C2,I2: 7.. / C2 = 7 => 0 pairs (X) / I2 = 7 => 0 pairs (_) C4,D4: 7.. / C4 = 7 => 0 pairs (X) / D4 = 7 => 0 pairs (_) A3,A6: 7.. / A3 = 7 => 0 pairs (X) / A6 = 7 => 0 pairs (_) E6,E9: 7.. / E6 = 7 => 0 pairs (X) / E9 = 7 => 0 pairs (_) E1,E3: 9.. / E1 = 9 => 12 pairs (_) / E3 = 9 => 10 pairs (_) G8,I8: 9.. / G8 = 9 => 0 pairs (X) / I8 = 9 => 15 pairs (_) B4,B9: 9.. / B4 = 9 => 0 pairs (X) / B9 = 9 => 10 pairs (_) G4,G8: 9.. / G4 = 9 => 15 pairs (_) / G8 = 9 => 0 pairs (X) * DURATION: 0:00:45.662720 START: 10:07:23.276689 END: 10:08:08.939409 2017-05-04 * CP COUNT: (24) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,C2,E3,E6,E9,G3,G4,G8,I2) * .2.6.74388.....29..3.2.8...5...3..8..638..7...8....3...78...6.33...8..........8.1 * PAIR A1: 1,9 BLK 1 C1: 1,9,5 # reduction candidate for 1,9 C1: 1,9 # 12 pairs C1: 5 # 11 pairs * PAIR A1: 1,9 ROW 1 E1: 1,9,5 # reduction candidate for 1,9 E1: 5 # 12 pairs E1: 1,9 # 11 pairs * PAIR A1: 1,9 COL A A5: 1,9,2,4 # reduction candidate for 1,9 A5: 1,9 # 11 pairs A6: 1,9,2,4,7 # reduction candidate for 1,9 A6: 1,9 => CTR * .2.657438856...2977342981655...329862638.9754.8..6.31247892.6.33.2.86579695.7.8.1 A6: 2,4,7 # 9 pairs A7: 1,9,2,4 # reduction candidate for 1,9 A7: 1,9 # 11 pairs * PAIR C2: 6,7 BLK 1 A3: 6,7,4,9 # reduction candidate for 6,7 A3: 6,7 # 11 pairs C3: 6,7,4,9 # reduction candidate for 6,7 C3: 6,7 => SOLVED * 921657438856341297437298165514732986263819754789564312178925643342186579695473821 C3: 4,9 # 11 pairs * PAIR E3: 4,9 ROW 3 A3: 4,9,6,7 # reduction candidate for 4,9 A3: 4,9 => SOLVED * 921657438856341297437298165514732986263819754789564312178925643342186579695473821 A3: 6,7 # 11 pairs C3: 4,9,6,7 # reduction candidate for 4,9 C3: 4,9 # 11 pairs * PAIR I2: 6,7 BLK 3 H3: 6,7,1,5 # reduction candidate for 6,7 H3: 6,7 => SOLVED * 921657438856341297437298165514732986263819754789564312178925643342186579695473821 H3: 1,5 => CTR * .2.6.74388.....29.63.2.8...5...36.8..638..7..78....36..78...6.33...8........6.8.1 I3: 6,7,5 # reduction candidate for 6,7 I3: 6,7 => CTR * .2.6.74388.....29..3.2.8...5...36.8..638..7...8..7.36..78...6.33.6.8........6.8.1 I3: 5 => SOLVED * 921657438856341297437298165514732986263819754789564312178925643342186579695473821 * PAIR G3: 1,5 BLK 3 H3: 1,5,6,7 # reduction candidate for 1,5 H3: 1,5 => CTR * .2.6.74388.....29.63.2.8...5...36.8..638..7..78....36..78...6.33...8........6.8.1 H3: 6,7 => SOLVED * 921657438856341297437298165514732986263819754789564312178925643342186579695473821 * PAIR G4: 1,9 ROW 4 B4: 1,9,4 # reduction candidate for 1,9 B4: 1,9 # 11 pairs C4: 1,9,2,4,7 # reduction candidate for 1,9 C4: 1,9 => CTR * .2.657438856...297.3.298165541732986.638..7...8..6.3...78.2.64331..86579695.7.821 C4: 2,4,7 # 9 pairs D4: 1,9,4,7 # reduction candidate for 1,9 D4: 1,9 => CTR * .2.6.74388.6...29773.2.8165547132986.638..7...8.76.3..478.2.6.33...865796...7.821 D4: 4,7 # 10 pairs F4: 1,9,2,4,6 # reduction candidate for 1,9 F4: 1,9 => CTR * .2.6.74388.6...297.3.2.8.655.273..86.638..7...8..6.3...78...6.33...8657.......8.1 F4: 2,4,6 # 9 pairs * PAIR G8: 5,9 BLK 9 I8: 5,9,2,4,7 # reduction candidate for 5,9 I8: 2,4,7 => CTR * .2.6.74388.....29.63.2.85175...3618..638..7..78....36..78...6.33...8.9......6.8.1 I8: 5,9 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-214-base-pr-000.dot * REASONING * DIS # A6: 1,9 => CTR => A6: 2,4,7 * PRF # C3: 6,7 => SOL * PRF # A3: 4,9 => SOL * PRF # H3: 6,7 => SOL * DIS # H3: 1,5 => CTR => H3: 6,7 * DIS # I3: 6,7 => CTR => I3: 5 * PRF # I3: 5 => SOL * DIS # H3: 1,5 => CTR => H3: 6,7 * PRF # H3: 6,7 => SOL * DIS # C4: 1,9 => CTR => C4: 2,4,7 * DIS # D4: 1,9 => CTR => D4: 4,7 * DIS # F4: 1,9 => CTR => F4: 2,4,6 * DIS # I8: 2,4,7 => CTR => I8: 5,9 * CNT 13 HDP CHAINS / 29 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,C2,E3,E6,E9,G3,G4,G8,I2) * .2.6.74388.....29..3.2.8...5...3..8..638..7...8....3...78...6.33...8..........8.1 * PAIR A1: 1,9 BLK 1 C1: 1,9,5 # reduction candidate for 1,9 C1: 1,9 # 12 pairs C1: 5 # 11 pairs * PAIR A1: 1,9 ROW 1 E1: 1,9,5 # reduction candidate for 1,9 E1: 5 # 12 pairs E1: 1,9 # 11 pairs * PAIR A1: 1,9 COL A A5: 1,9,2,4 # reduction candidate for 1,9 A5: 1,9 # 11 pairs A6: 1,9,2,4,7 # reduction candidate for 1,9 A6: 1,9 => CTR * .2.657438856...2977342981655...329862638.9754.8..6.31247892.6.33.2.86579695.7.8.1 A7: 1,9,2,4 # reduction candidate for 1,9 A7: 1,9 # 11 pairs * PAIR RESTART * PAIR A1: 1,9 BLK 1 C1: 1,9,5 # reduction candidate for 1,9 C1: 1,9 # 12 pairs C1: 5 # 11 pairs * PAIR A1: 1,9 ROW 1 E1: 1,9,5 # reduction candidate for 1,9 E1: 5 # 12 pairs E1: 1,9 # 11 pairs * PAIR A1: 1,9 COL A A5: 1,9,2,4 # reduction candidate for 1,9 A5: 1,9 # 11 pairs A7: 1,9,2,4 # reduction candidate for 1,9 A7: 1,9 # 11 pairs * PAIR C2: 6,7 BLK 1 A3: 6,7,4,9 # reduction candidate for 6,7 A3: 6,7 # 11 pairs C3: 6,7,4,9 # reduction candidate for 6,7 C3: 6,7 => SOLVED * 921657438856341297437298165514732986263819754789564312178925643342186579695473821 * DURATION: 0:00:14.533358 START: 10:08:38.507190 END: 10:08:53.040548 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-214-base-pr-001.dot * REASONING * DIS # A6: 1,9 => CTR => A6: 2,4,7 * PRF A6: 2,4,7 # C3: 6,7 => SOL * STA A6: 2,4,7 + C3: 6,7 * CNT 2 HDP CHAINS / 15 HYP OPENED
Header Info
Top 500 Minimum 17 214 solution: 921657438856341297437298165514732986263819754789564312178925643342186579695473821 info: 1948 FNBHWY S8.f 16882 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 921657438856341297437298165514732986263819754789564312178925643342186579695473821 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:
* INC # C1: 1,9 => UNS * INC # C1: 5 => UNS * INC # E1: 1,9 => UNS * INC # E1: 5 => UNS * INC # A5: 1,9 => UNS * DIS # A6: 1,9 => CTR => A6: 2,4,7 * INC # A6: 2,4,7 => UNS * INC # A7: 1,9 => UNS * INC # A3: 6,7 => UNS * PRF # C3: 6,7 => SOL * INC # C3: 4,9 => UNS * PRF # A3: 4,9 => SOL * INC # A3: 6,7 => UNS * INC # C3: 4,9 => UNS * PRF # H3: 6,7 => SOL * DIS # H3: 1,5 => CTR => H3: 6,7 * DIS # I3: 6,7 => CTR => I3: 5 * PRF # I3: 5 => SOL * DIS # H3: 1,5 => CTR => H3: 6,7 * PRF # H3: 6,7 => SOL * INC # B4: 1,9 => UNS * DIS # C4: 1,9 => CTR => C4: 2,4,7 * INC # C4: 2,4,7 => UNS * DIS # D4: 1,9 => CTR => D4: 4,7 * INC # D4: 4,7 => UNS * DIS # F4: 1,9 => CTR => F4: 2,4,6 * INC # F4: 2,4,6 => UNS * INC # I8: 5,9 => UNS * DIS # I8: 2,4,7 => CTR => I8: 5,9 * CNT 29 HDP CHAINS / 29 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 1,9 => UNS * INC # C1: 5 => UNS * INC # E1: 1,9 => UNS * INC # E1: 5 => UNS * INC # A5: 1,9 => UNS * DIS # A6: 1,9 => CTR => A6: 2,4,7 * INC A6: 2,4,7 # A7: 1,9 => UNS * INC A6: 2,4,7 # C1: 1,9 => UNS * INC A6: 2,4,7 # C1: 5 => UNS * INC A6: 2,4,7 # E1: 1,9 => UNS * INC A6: 2,4,7 # E1: 5 => UNS * INC A6: 2,4,7 # A5: 1,9 => UNS * INC A6: 2,4,7 # A7: 1,9 => UNS * INC A6: 2,4,7 # A3: 6,7 => UNS * PRF A6: 2,4,7 # C3: 6,7 => SOL * STA A6: 2,4,7 + C3: 6,7 * CNT 15 HDP CHAINS / 15 HYP OPENED