Analysis of xx-top500-038-base.sdk
Contents
Original Sudoku
level: medium
position: 4...1..7..2....5...........3.......1...2.6......5..6......9..4.2.5.......68...... initial
Autosolve
position: 4...1..7..2....5...........3.6.....1..42.6.....25.16......9..4.245......968...... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D1: 3,9 => CTR => D1: 6,8 * DIS # F1: 3,9 => CTR => F1: 2,5,8 * DIS # I1: 3,9 => CTR => I1: 2,6,8 * DIS # F3: 2,5 => CTR => F3: 3,4,7,8,9 * PRF # B4: 7,8 => SOL * DIS # B4: 5 => CTR => B4: 7,8 * DIS # A5: 7,8 => CTR => A5: 1,5 * DIS # B5: 7,8 => CTR => B5: 1,5,9 * DIS # B6: 7,8 => CTR => B6: 9 * DIS # I6: 7,8 => CTR => I6: 3,4,9 * PRF # A2: 7,8 => SOL * DIS # A3: 7,8 => CTR => A3: 1,5,6 * DIS # A2: 1,7 => CTR => A2: 6,8 * DIS # A3: 1,7 => CTR => A3: 5,6,8 * DIS # A5: 1,7 => CTR => A5: 5,8 * DIS # D8: 6,8 => CTR => D8: 1,3,7 * DIS # I7: 6,8 => CTR => I7: 2,5 * PRF # I7: 2,5 => SOL * DIS # D2: 6,8 => CTR => D2: 3,4,7,9 * DIS # D3: 6,8 => CTR => D3: 3,4,7,9 * DIS # F9: 2,5 => CTR => F9: 3,4,7 * PRF # I7: 2,8 => SOL * DIS # F7: 2,8 => CTR => F7: 5 * PRF # F7: 5 => SOL * DIS # G1: 2,8 => CTR => G1: 3,9 * DIS # G3: 2,8 => CTR => G3: 1,3,4,9 * CNT 26 HDP CHAINS / 59 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D1: 3,9 => CTR => D1: 6,8 * DIS D1: 6,8 # F1: 3,9 => CTR => F1: 2,5,8 * DIS D1: 6,8 + F1: 2,5,8 # I1: 3,9 => CTR => I1: 2,6,8 * DIS D1: 6,8 + F1: 2,5,8 + I1: 2,6,8 # G1: 2,8 => CTR => G1: 3,9 * DIS D1: 6,8 + F1: 2,5,8 + I1: 2,6,8 + G1: 3,9 # F3: 2,5 => CTR => F3: 3,4,7,8,9 * PRF D1: 6,8 + F1: 2,5,8 + I1: 2,6,8 + G1: 3,9 + F3: 3,4,7,8,9 # B4: 7,8 => SOL * STA D1: 6,8 + F1: 2,5,8 + I1: 2,6,8 + G1: 3,9 + F3: 3,4,7,8,9 + B4: 7,8 * CNT 6 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 4...1..7..2....5...........3.......1...2.6......5..6......9..4.2.5.......68...... | initial |
| 4...1..7..2....5...........3.6.....1..42.6.....25.16......9..4.245......968...... | autosolve |
| 453812976829467513671953428386749251514286397792531684137695842245378169968124735 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) C1: 3,9 E3: 2,5 A6: 7,8 A7: 1,7 D7: 6,8 E9: 2,5 G7: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A5,B5: 1.. / A5 = 1 => 0 pairs (X) / B5 = 1 => 9 pairs (_) D8,D9: 1.. / D8 = 1 => 7 pairs (_) / D9 = 1 => 8 pairs (_) G4,H4: 2.. / G4 = 2 => 0 pairs (*) / H4 = 2 => 0 pairs (X) E3,E9: 2.. / E3 = 2 => 0 pairs (X) / E9 = 2 => 0 pairs (_) E5,E6: 3.. / E5 = 3 => 7 pairs (_) / E6 = 3 => 10 pairs (_) B7,C7: 3.. / B7 = 3 => 9 pairs (_) / C7 = 3 => 10 pairs (_) G4,I6: 4.. / G4 = 4 => 0 pairs (X) / I6 = 4 => 7 pairs (_) D9,F9: 4.. / D9 = 4 => 7 pairs (_) / F9 = 4 => 8 pairs (_) E6,I6: 4.. / E6 = 4 => 0 pairs (X) / I6 = 4 => 7 pairs (_) G3,G4: 4.. / G3 = 4 => 7 pairs (_) / G4 = 4 => 0 pairs (X) B1,F1: 5.. / B1 = 5 => 0 pairs (*) / F1 = 5 => 0 pairs (X) B4,H4: 5.. / B4 = 5 => 0 pairs (X) / H4 = 5 => 0 pairs (_) F7,I7: 5.. / F7 = 5 => 0 pairs (*) / I7 = 5 => 0 pairs (X) A3,A5: 5.. / A3 = 5 => 0 pairs (X) / A5 = 5 => 0 pairs (_) E3,E9: 5.. / E3 = 5 => 0 pairs (*) / E9 = 5 => 0 pairs (X) A2,A3: 6.. / A2 = 6 => 0 pairs (X) / A3 = 6 => 0 pairs (_) D1,I1: 6.. / D1 = 6 => 0 pairs (X) / I1 = 6 => 0 pairs (_) D7,I7: 6.. / D7 = 6 => 0 pairs (*) / I7 = 6 => 0 pairs (X) E2,E8: 6.. / E2 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) B5,B6: 9.. / B5 = 9 => 0 pairs (X) / B6 = 9 => 8 pairs (_) D4,F4: 9.. / D4 = 9 => 7 pairs (_) / F4 = 9 => 7 pairs (_) * DURATION: 0:00:32.487113 START: 03:58:01.724787 END: 03:58:34.211900 2017-05-04 * CP COUNT: (21) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A7,C1,D7,E3,E9,G7) * 4...1..7..2....5...........3.6.....1..42.6.....25.16......9..4.245......968...... * PAIR C1: 3,9 BLK 1 C2: 3,9,1,7 # reduction candidate for 3,9 C2: 3,9 # 11 pairs C3: 3,9,1,7 # reduction candidate for 3,9 C3: 3,9 # 11 pairs * PAIR C1: 3,9 ROW 1 D1: 3,9,6,8 # reduction candidate for 3,9 D1: 3,9 => CTR * 4...12.76.2..6.5..6...5.4..3.6.4.2515142.6....925.16.4...695842245....6.968.2...5 D1: 6,8 # 8 pairs F1: 3,9,2,5,8 # reduction candidate for 3,9 F1: 3,9 => CTR * 45..1..72.2....5........4..3.6...2515142.6....925.16.4...69.84.245......968...... F1: 2,5,8 # 7 pairs G1: 3,9,2,8 # reduction candidate for 3,9 G1: 3,9 # 10 pairs I1: 3,9,2,6,8 # reduction candidate for 3,9 I1: 3,9 => CTR * 4..612.7..2....5......5...23.6....215142.6....925.16.....895246245.6....968.2..5. I1: 2,6,8 # 7 pairs * PAIR E3: 2,5 BLK 2 F1: 2,5,3,8,9 # reduction candidate for 2,5 F1: 2,5 # 8 pairs F3: 2,5,3,4,7,8,9 # reduction candidate for 2,5 F3: 2,5 => CTR * 45.61..72.2....5......25...3.6...2515142.6....925.16.4....92845245......968.5..2. F3: 3,4,7,8,9 # 8 pairs * PAIR A6: 7,8 BLK 4 B4: 7,8,5 # reduction candidate for 7,8 B4: 7,8 => SOLVED * 453812976829467513671953428386749251514286397792531684137695842245378169968124735 B4: 5 => CTR * 4...15.7.62....5..5...2....356.....1..42.6.5...25.16.....69..45245......968.5.... A5: 7,8,1,5 # reduction candidate for 7,8 A5: 7,8 => CTR * 4...15.7.62....5..5...2....356.....1.142.6.5..925.16..1...9..45245.6....968.5.... A5: 1,5 # 8 pairs B5: 7,8,1,5,9 # reduction candidate for 7,8 B5: 7,8 => CTR * 4...15.7.62....5..5...2....356.....1174236.5.8925.163.7...9..45245.6....968.5.... B5: 1,5,9 # 7 pairs B6: 7,8,9 # reduction candidate for 7,8 B6: 7,8 => CTR * 4...15.7.62....5..5...2....356.....11942.6.5.8725.16..7...9..45245.6....968.5.... B6: 9 # 8 pairs * PAIR A6: 7,8 ROW 6 E6: 7,8,3,4 # reduction candidate for 7,8 E6: 7,8 # 11 pairs I6: 7,8,3,4,9 # reduction candidate for 7,8 I6: 7,8 => CTR * 4...15.7.621...5..5...2.1..356...421..4236.5..9254163....69..452451.....968.5..1. I6: 3,4,9 # 7 pairs * PAIR A6: 7,8 COL A A2: 7,8,1,6 # reduction candidate for 7,8 A2: 7,8 => SOLVED * 453812976829467513671953428386749251514286397792531684137695842245378169968124735 A2: 1,6 # 8 pairs A3: 7,8,1,5,6 # reduction candidate for 7,8 A3: 7,8 => CTR * 4...1..7.62....5.........6.3.6....515142.6....925.16..1..89.246245.6....968.....5 A3: 1,5,6 # 7 pairs * PAIR A7: 1,7 BLK 7 B7: 1,7,3 # reduction candidate for 1,7 B7: 1,7 # 10 pairs C7: 1,7,3 # reduction candidate for 1,7 C7: 1,7 # 9 pairs * PAIR A7: 1,7 COL A A2: 1,7,6,8 # reduction candidate for 1,7 A2: 1,7 => CTR * 4...12.76.2..6.5..6...5.4..376.4.251514236...892571634.3.695842245.8..6.968.2..15 A2: 6,8 # 8 pairs A3: 1,7,5,6,8 # reduction candidate for 1,7 A3: 1,7 => CTR * 4...1..7.62....5.........6.376....51514236...892571634.3.89.246245.6....968....15 A3: 5,6,8 # 7 pairs A5: 1,7,5,8 # reduction candidate for 1,7 A5: 1,7 => CTR * 4...15.7.62....5..5...2....3.6.....1..42.6...8.25.16......9..45245.6....968.5.... A5: 5,8 # 10 pairs * PAIR D7: 6,8 BLK 8 D8: 6,8,1,3,7 # reduction candidate for 6,8 D8: 6,8 => CTR * 4...12.76.2.46.5..6...5.4..3.6.4.2515142.6...7925.16.41..695842245873169968124.35 D8: 1,3,7 # 7 pairs E8: 6,8,7 # reduction candidate for 6,8 E8: 6,8 # 10 pairs * PAIR D7: 6,8 ROW 7 I7: 6,8,2,5 # reduction candidate for 6,8 I7: 6,8 => CTR * 45..1..7..2....5......5....3.6.....1..42.6.....25.16......9524.245......968.2.... I7: 2,5 => SOLVED * 453812976829467513671953428386749251514286397792531684137695842245378169968124735 * PAIR D7: 6,8 COL D D1: 6,8,3,9 # reduction candidate for 6,8 D1: 6,8 # 8 pairs D2: 6,8,3,4,7,9 # reduction candidate for 6,8 D2: 6,8 => CTR * 48..1..76.2.86.5..6........376...251514236...892571634.3.69.84.245.8..6.968...... D2: 3,4,7,9 # 7 pairs D3: 6,8,3,4,7,9 # reduction candidate for 6,8 D3: 6,8 => CTR * 48..1..76.2..6.5..6..8.....3.6...2515142.6....925.16.4...69.84.245....6.968...... D3: 3,4,7,9 # 7 pairs * PAIR E9: 2,5 BLK 8 F7: 2,5,8 # reduction candidate for 2,5 F7: 2,5 # 8 pairs F9: 2,5,3,4,7 # reduction candidate for 2,5 F9: 2,5 => CTR * 4...1..7..2..6.5..6........3.6.....15142.6....925.16.....698245245173...9684..... F9: 3,4,7 # 8 pairs * PAIR E9: 2,5 ROW 9 H9: 2,5,1,3 # reduction candidate for 2,5 H9: 2,5 # 10 pairs I9: 2,5,3,7 # reduction candidate for 2,5 I9: 2,5 # 10 pairs * PAIR G7: 2,8 BLK 9 I7: 2,8,5,6 # reduction candidate for 2,8 I7: 2,8 => SOLVED * 453812976829467513671953428386749251514286397792531684137695842245378169968124735 I7: 5,6 # 8 pairs * PAIR G7: 2,8 ROW 7 F7: 2,8,5 # reduction candidate for 2,8 F7: 2,8 => CTR * 4...1..76.2..6.5..6........3.6...2515142.6....925.16.4...692845245....6.968.5.... F7: 5 => SOLVED * 453812976829467513671953428386749251514286397792531684137695842245378169968124735 * PAIR G7: 2,8 COL G G1: 2,8,3,9 # reduction candidate for 2,8 G1: 2,8 => CTR * 4...15.7.62....5..5...2....356....21..42.6.5...25.16.....69..45245......968.5.... G1: 3,9 # 10 pairs G3: 2,8,1,3,4,9 # reduction candidate for 2,8 G3: 2,8 => CTR * 4...15.7262....5..5...2.8..356...421..4236.5...25416.....698245245.73...968452... G3: 1,3,4,9 # 7 pairs G4: 2,8,4,7 # reduction candidate for 2,8 G4: 2,8 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-038-base-pr-000.dot * REASONING * DIS # D1: 3,9 => CTR => D1: 6,8 * DIS # F1: 3,9 => CTR => F1: 2,5,8 * DIS # I1: 3,9 => CTR => I1: 2,6,8 * DIS # F3: 2,5 => CTR => F3: 3,4,7,8,9 * PRF # B4: 7,8 => SOL * DIS # B4: 5 => CTR => B4: 7,8 * DIS # A5: 7,8 => CTR => A5: 1,5 * DIS # B5: 7,8 => CTR => B5: 1,5,9 * DIS # B6: 7,8 => CTR => B6: 9 * DIS # I6: 7,8 => CTR => I6: 3,4,9 * PRF # A2: 7,8 => SOL * DIS # A3: 7,8 => CTR => A3: 1,5,6 * DIS # A2: 1,7 => CTR => A2: 6,8 * DIS # A3: 1,7 => CTR => A3: 5,6,8 * DIS # A5: 1,7 => CTR => A5: 5,8 * DIS # D8: 6,8 => CTR => D8: 1,3,7 * DIS # I7: 6,8 => CTR => I7: 2,5 * PRF # I7: 2,5 => SOL * DIS # D2: 6,8 => CTR => D2: 3,4,7,9 * DIS # D3: 6,8 => CTR => D3: 3,4,7,9 * DIS # F9: 2,5 => CTR => F9: 3,4,7 * PRF # I7: 2,8 => SOL * DIS # F7: 2,8 => CTR => F7: 5 * PRF # F7: 5 => SOL * DIS # G1: 2,8 => CTR => G1: 3,9 * DIS # G3: 2,8 => CTR => G3: 1,3,4,9 * CNT 26 HDP CHAINS / 59 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A7,C1,D7,E3,E9,G7) * 4...1..7..2....5...........3.6.....1..42.6.....25.16......9..4.245......968...... * PAIR C1: 3,9 BLK 1 C2: 3,9,1,7 # reduction candidate for 3,9 C2: 3,9 # 11 pairs C3: 3,9,1,7 # reduction candidate for 3,9 C3: 3,9 # 11 pairs * PAIR C1: 3,9 ROW 1 D1: 3,9,6,8 # reduction candidate for 3,9 D1: 3,9 => CTR * 4...12.76.2..6.5..6...5.4..3.6.4.2515142.6....925.16.4...695842245....6.968.2...5 F1: 3,9,2,5,8 # reduction candidate for 3,9 F1: 3,9 => CTR * 45.81..7..2....5...........3.6...2515142.6....925.16.4....9.84.245......968...... G1: 3,9,2,8 # reduction candidate for 3,9 G1: 3,9 # 10 pairs I1: 3,9,2,6,8 # reduction candidate for 3,9 I1: 3,9 => CTR * 4..612.7..2....5......5...23.6....215142.6....925.16.....895246245.6....968.2..5. * RESTART * PAIR C1: 3,9 ROW 1 G1: 3,9,2,8 # reduction candidate for 3,9 G1: 2,8 => CTR * 439815276.2..6.5..65..2....3.6.....1..42.6.....25.16....369..45245......968.5.... * PAIR RESTART * PAIR C1: 3,9 BLK 1 C2: 3,9,1,7 # reduction candidate for 3,9 C2: 3,9 # 13 pairs C3: 3,9,1,7 # reduction candidate for 3,9 C3: 3,9 # 13 pairs * PAIR E3: 2,5 BLK 2 F1: 2,5,8 # reduction candidate for 2,5 F1: 2,5 # 11 pairs F3: 2,5,3,4,7,8,9 # reduction candidate for 2,5 F3: 2,5 => CTR * 45..18.72.2....5...........3.6....515142.6....925.16.....89.246245.6....968.2...5 * RESTART * PAIR A6: 7,8 BLK 4 B4: 7,8,5 # reduction candidate for 7,8 B4: 7,8 => SOLVED * 453812976829467513671953428386749251514286397792531684137695842245378169968124735 * DURATION: 0:00:12.765563 START: 03:59:20.686206 END: 03:59:33.451769 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-038-base-pr-001.dot * REASONING * DIS # D1: 3,9 => CTR => D1: 6,8 * DIS D1: 6,8 # F1: 3,9 => CTR => F1: 2,5,8 * DIS D1: 6,8 + F1: 2,5,8 # I1: 3,9 => CTR => I1: 2,6,8 * DIS D1: 6,8 + F1: 2,5,8 + I1: 2,6,8 # G1: 2,8 => CTR => G1: 3,9 * DIS D1: 6,8 + F1: 2,5,8 + I1: 2,6,8 + G1: 3,9 # F3: 2,5 => CTR => F3: 3,4,7,8,9 * PRF D1: 6,8 + F1: 2,5,8 + I1: 2,6,8 + G1: 3,9 + F3: 3,4,7,8,9 # B4: 7,8 => SOL * STA D1: 6,8 + F1: 2,5,8 + I1: 2,6,8 + G1: 3,9 + F3: 3,4,7,8,9 + B4: 7,8 * CNT 6 HDP CHAINS / 13 HYP OPENED
Header Info
Top 500 Minimum 17 038 solution: 453812976829467513671953428386749251514286397792531684137695842245378169968124735 info: 1369 FNBHWXY S8.f 44343 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 453812976829467513671953428386749251514286397792531684137695842245378169968124735 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 # C2: 3,9 => UNS * INC # C3: 3,9 => UNS * DIS # D1: 3,9 => CTR => D1: 6,8 * INC # D1: 6,8 => UNS * DIS # F1: 3,9 => CTR => F1: 2,5,8 * INC # F1: 2,5,8 => UNS * INC # G1: 3,9 => UNS * DIS # I1: 3,9 => CTR => I1: 2,6,8 * INC # I1: 2,6,8 => UNS * INC # F1: 2,5 => UNS * DIS # F3: 2,5 => CTR => F3: 3,4,7,8,9 * INC # F3: 3,4,7,8,9 => UNS * PRF # B4: 7,8 => SOL * DIS # B4: 5 => CTR => B4: 7,8 * DIS # A5: 7,8 => CTR => A5: 1,5 * INC # A5: 1,5 => UNS * DIS # B5: 7,8 => CTR => B5: 1,5,9 * INC # B5: 1,5,9 => UNS * DIS # B6: 7,8 => CTR => B6: 9 * INC # B6: 9 => UNS * INC # E6: 7,8 => UNS * DIS # I6: 7,8 => CTR => I6: 3,4,9 * INC # I6: 3,4,9 => UNS * PRF # A2: 7,8 => SOL * INC # A2: 1,6 => UNS * DIS # A3: 7,8 => CTR => A3: 1,5,6 * INC # A3: 1,5,6 => UNS * INC # B7: 1,7 => UNS * INC # C7: 1,7 => UNS * DIS # A2: 1,7 => CTR => A2: 6,8 * INC # A2: 6,8 => UNS * DIS # A3: 1,7 => CTR => A3: 5,6,8 * INC # A3: 5,6,8 => UNS * DIS # A5: 1,7 => CTR => A5: 5,8 * INC # A5: 5,8 => UNS * DIS # D8: 6,8 => CTR => D8: 1,3,7 * INC # D8: 1,3,7 => UNS * INC # E8: 6,8 => UNS * DIS # I7: 6,8 => CTR => I7: 2,5 * PRF # I7: 2,5 => SOL * INC # D1: 6,8 => UNS * DIS # D2: 6,8 => CTR => D2: 3,4,7,9 * INC # D2: 3,4,7,9 => UNS * DIS # D3: 6,8 => CTR => D3: 3,4,7,9 * INC # D3: 3,4,7,9 => UNS * INC # F7: 2,5 => UNS * DIS # F9: 2,5 => CTR => F9: 3,4,7 * INC # F9: 3,4,7 => UNS * INC # H9: 2,5 => UNS * INC # I9: 2,5 => UNS * PRF # I7: 2,8 => SOL * INC # I7: 5,6 => UNS * DIS # F7: 2,8 => CTR => F7: 5 * PRF # F7: 5 => SOL * DIS # G1: 2,8 => CTR => G1: 3,9 * INC # G1: 3,9 => UNS * DIS # G3: 2,8 => CTR => G3: 1,3,4,9 * INC # G3: 1,3,4,9 => UNS * INC # G4: 2,8 => UNS * CNT 59 HDP CHAINS / 59 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 3,9 => UNS * INC # C3: 3,9 => UNS * DIS # D1: 3,9 => CTR => D1: 6,8 * DIS D1: 6,8 # F1: 3,9 => CTR => F1: 2,5,8 * INC D1: 6,8 + F1: 2,5,8 # G1: 3,9 => UNS * DIS D1: 6,8 + F1: 2,5,8 # I1: 3,9 => CTR => I1: 2,6,8 * INC D1: 6,8 + F1: 2,5,8 + I1: 2,6,8 # G1: 3,9 => UNS * DIS D1: 6,8 + F1: 2,5,8 + I1: 2,6,8 # G1: 2,8 => CTR => G1: 3,9 * INC D1: 6,8 + F1: 2,5,8 + I1: 2,6,8 + G1: 3,9 # C2: 3,9 => UNS * INC D1: 6,8 + F1: 2,5,8 + I1: 2,6,8 + G1: 3,9 # C3: 3,9 => UNS * INC D1: 6,8 + F1: 2,5,8 + I1: 2,6,8 + G1: 3,9 # F1: 2,5 => UNS * DIS D1: 6,8 + F1: 2,5,8 + I1: 2,6,8 + G1: 3,9 # F3: 2,5 => CTR => F3: 3,4,7,8,9 * PRF D1: 6,8 + F1: 2,5,8 + I1: 2,6,8 + G1: 3,9 + F3: 3,4,7,8,9 # B4: 7,8 => SOL * STA D1: 6,8 + F1: 2,5,8 + I1: 2,6,8 + G1: 3,9 + F3: 3,4,7,8,9 + B4: 7,8 * CNT 13 HDP CHAINS / 13 HYP OPENED