Analysis of xx-top95-008-base.sdk
Contents
Original Sudoku
level: medium
position: .524.........7.1..............8.2...3.....6...9.5.....1.6.3...........897........ initial
Autosolve
position: .52481.......7.1.....32.......8.2...3.....6...9.5.3...1.6.3...........897.925.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 6,9 => CTR => A2: 4,8 * PRF # A3: 6,9 => SOL * DIS # H1: 6,9 => CTR => H1: 3,7 * DIS # B4: 1,7 => CTR => B4: 4,6 * PRF # B4: 4,6 => SOL * PRF # F2: 6,9 => SOL * DIS # A2: 6,9 => CTR => A2: 4,8 * DIS # H2: 6,9 => CTR => H2: 2,4,5 * DIS # H1: 7,9 => CTR => H1: 3,6 * DIS # G4: 7,9 => CTR => G4: 4,5 * PRF # D8: 1,7 => SOL * DIS # D8: 6 => CTR => D8: 1,7 * PRF # F7: 4,7 => SOL * DIS # F8: 4,7 => CTR => F8: 6 * PRF # F8: 6 => SOL * PRF # F7: 7,9 => SOL * DIS # F7: 4,8 => CTR => F7: 7,9 * DIS # E5: 1,4 => CTR => E5: 9 * DIS # E6: 1,4 => CTR => E6: 6 * DIS # F7: 4,8 => CTR => F7: 7,9 * PRF # F7: 7,9 => SOL * DIS # B9: 3 => CTR => B9: 4,8 * DIS # G8: 3,4 => CTR => G8: 2,7 * DIS # B9: 8 => CTR => B9: 3,4 * CNT 24 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 6,9 => CTR => A2: 4,8 * PRF A2: 4,8 # A3: 6,9 => SOL * STA A2: 4,8 + A3: 6,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .524.........7.1..............8.2...3.....6...9.5.....1.6.3...........897........ | initial |
| .52481.......7.1.....32.......8.2...3.....6...9.5.3...1.6.3...........897.925.... | autosolve |
| 652481937834679152971325864467812593315794628298563471186937245523146789749258316 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A1: 6,9 B3: 1,7 C3: 1,7 D2: 6,9 G1: 7,9 D5: 1,7 F5: 4,7 D7: 7,9 E8: 1,4 F9: 4,8 G9: 3,4 H9: 1,6 I9: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B3,C3: 1.. / B3 = 1 => 0 pairs (X) / C3 = 1 => 11 pairs (_) D8,E8: 1.. / D8 = 1 => 0 pairs (*) / E8 = 1 => 0 pairs (X) H9,I9: 1.. / H9 = 1 => 12 pairs (_) / I9 = 1 => 11 pairs (_) D5,D8: 1.. / D5 = 1 => 0 pairs (X) / D8 = 1 => 0 pairs (_) H2,I2: 2.. / H2 = 2 => 13 pairs (_) / I2 = 2 => 13 pairs (_) B5,A6: 2.. / B5 = 2 => 0 pairs (X) / A6 = 2 => 19 pairs (_) A6,A8: 2.. / A6 = 2 => 19 pairs (_) / A8 = 2 => 0 pairs (X) B2,C2: 3.. / B2 = 3 => 0 pairs (*) / C2 = 3 => 0 pairs (X) H1,I1: 3.. / H1 = 3 => 14 pairs (_) / I1 = 3 => 13 pairs (_) H4,I4: 3.. / H4 = 3 => 13 pairs (_) / I4 = 3 => 14 pairs (_) G8,G9: 3.. / G8 = 3 => 0 pairs (X) / G9 = 3 => 13 pairs (_) B9,G9: 3.. / B9 = 3 => 0 pairs (X) / G9 = 3 => 13 pairs (_) C2,C8: 3.. / C2 = 3 => 15 pairs (_) / C8 = 3 => 0 pairs (*) H1,H4: 3.. / H1 = 3 => 14 pairs (_) / H4 = 3 => 13 pairs (_) I1,I4: 3.. / I1 = 3 => 13 pairs (_) / I4 = 3 => 14 pairs (_) F2,F3: 5.. / F2 = 5 => 14 pairs (_) / F3 = 5 => 0 pairs (*) A8,C8: 5.. / A8 = 5 => 20 pairs (_) / C8 = 5 => 17 pairs (_) A4,A8: 5.. / A4 = 5 => 17 pairs (_) / A8 = 5 => 20 pairs (_) E4,E6: 6.. / E4 = 6 => 0 pairs (X) / E6 = 6 => 13 pairs (_) D8,F8: 6.. / D8 = 6 => 0 pairs (X) / F8 = 6 => 0 pairs (_) H9,I9: 6.. / H9 = 6 => 11 pairs (_) / I9 = 6 => 12 pairs (_) A6,E6: 6.. / A6 = 6 => 0 pairs (X) / E6 = 6 => 13 pairs (_) B2,B4: 6.. / B2 = 6 => 0 pairs (X) / B4 = 6 => 0 pairs (_) D2,D8: 6.. / D2 = 6 => 0 pairs (*) / D8 = 6 => 0 pairs (X) B3,C3: 7.. / B3 = 7 => 11 pairs (_) / C3 = 7 => 0 pairs (X) D5,F5: 7.. / D5 = 7 => 0 pairs (*) / F5 = 7 => 0 pairs (X) B3,B4: 7.. / B3 = 7 => 11 pairs (_) / B4 = 7 => 0 pairs (X) B7,B9: 8.. / B7 = 8 => 13 pairs (_) / B9 = 8 => 0 pairs (X) F7,F9: 8.. / F7 = 8 => 0 pairs (X) / F9 = 8 => 13 pairs (_) C5,I5: 8.. / C5 = 8 => 14 pairs (_) / I5 = 8 => 13 pairs (_) B7,F7: 8.. / B7 = 8 => 13 pairs (_) / F7 = 8 => 0 pairs (X) B9,F9: 8.. / B9 = 8 => 0 pairs (X) / F9 = 8 => 13 pairs (_) G3,G6: 8.. / G3 = 8 => 13 pairs (_) / G6 = 8 => 14 pairs (_) E4,E5: 9.. / E4 = 9 => 0 pairs (X) / E5 = 9 => 13 pairs (_) D7,F7: 9.. / D7 = 9 => 0 pairs (*) / F7 = 9 => 0 pairs (X) E5,H5: 9.. / E5 = 9 => 13 pairs (_) / H5 = 9 => 0 pairs (X) D2,D7: 9.. / D2 = 9 => 0 pairs (X) / D7 = 9 => 0 pairs (_) * DURATION: 0:01:06.730972 START: 22:58:10.774520 END: 22:59:17.505492 2017-05-03 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B3,C3,D2,D5,D7,E8,F5,F9,G1,G9,H9,I9) * .52481.......7.1.....32.......8.2...3.....6...9.5.3...1.6.3...........897.925.... * PAIR A1: 6,9 BLK 1 A2: 6,9,4,8 # reduction candidate for 6,9 A2: 6,9 => CTR * .524819..9..6751..871329...46.81259331579462829.563...1.693.......1467897.92583.. A2: 4,8 # 14 pairs A3: 6,9,4,8 # reduction candidate for 6,9 A3: 6,9 => SOLVED * 652481937834679152971325864467812593315794628298563471186937245523146789749258316 A3: 4,8 # 14 pairs * PAIR A1: 6,9 ROW 1 H1: 6,9,3,7 # reduction candidate for 6,9 H1: 6,9 => CTR * .524817.3...67.1...7132.....6.8.2.3.31.7..6...9.563...1.693.........6.897.925.... H1: 3,7 # 14 pairs * PAIR B3: 1,7 COL B B4: 1,7,4,6 # reduction candidate for 1,7 B4: 1,7 => CTR * .52481....639751.....326......8.2...3.....6...9.5.3...1.6739......6147897.92583.. B4: 4,6 => SOLVED * 652481937834679152971325864467812593315794628298563471186937245523146789749258316 * PAIR C3: 1,7 COL C C4: 1,7,4,5 # reduction candidate for 1,7 C4: 1,7 # 15 pairs C6: 1,7,4,8 # reduction candidate for 1,7 C6: 1,7 # 15 pairs * PAIR D2: 6,9 BLK 2 F2: 6,9,5 # reduction candidate for 6,9 F2: 6,9 => SOLVED * 652481937834679152971325864467812593315794628298563471186937245523146789749258316 F2: 5 # 14 pairs F3: 6,9,5 # reduction candidate for 6,9 F3: 6,9 # 14 pairs * PAIR D2: 6,9 ROW 2 A2: 6,9,4,8 # reduction candidate for 6,9 A2: 6,9 => CTR * .524819..9..6751..871329...46.81259331579462829.563...1.693.......1467897.92583.. A2: 4,8 # 14 pairs H2: 6,9,2,4,5 # reduction candidate for 6,9 H2: 6,9 => CTR * .524819..8...751.2.7132.....6.8.2...31.7.462.29.563...1.693.......1467897.92583.. H2: 2,4,5 # 13 pairs * PAIR G1: 7,9 BLK 3 H1: 7,9,3,6 # reduction candidate for 7,9 H1: 7,9 => CTR * 652481973...67.1...7132.....6.8.2.3.31.7.46..29.563...1.693.......1467897.92583.. H1: 3,6 # 14 pairs * PAIR G1: 7,9 COL G G4: 7,9,4,5 # reduction candidate for 7,9 G4: 7,9 => CTR * .52481......67.1...7132.....6.8.2...31.7..6...9.563...1.693.........6.897.925.... G4: 4,5 # 14 pairs * PAIR D5: 1,7 COL D D8: 1,7,6 # reduction candidate for 1,7 D8: 1,7 => SOLVED * 652481937834679152971325864467812593315794628298563471186937245523146789749258316 D8: 6 => CTR * 6524819...3.97.1..9..32.....6.8.2...32.1.76...9.5.3...186739......6147897492583.. * PAIR F5: 4,7 COL F F7: 4,7,8,9 # reduction candidate for 4,7 F7: 4,7 => SOLVED * 652481937834679152971325864467812593315794628298563471186937245523146789749258316 F7: 8,9 # 14 pairs F8: 4,7,6 # reduction candidate for 4,7 F8: 4,7 => CTR * 6524819...3.97.1..9..32.....6.8.2...32.1.76...9.5.3...186739......6147897492583.. F8: 6 => SOLVED * 652481937834679152971325864467812593315794628298563471186937245523146789749258316 * PAIR D7: 7,9 BLK 8 F7: 7,9,4,8 # reduction candidate for 7,9 F7: 7,9 => SOLVED * 652481937834679152971325864467812593315794628298563471186937245523146789749258316 F7: 4,8 => CTR * .52481......67.1...7132.....6.8.2...31.7..6...9.563...1.693.........6.897.925.... * PAIR E8: 1,4 COL E E4: 1,4,6,9 # reduction candidate for 1,4 E4: 1,4 # 14 pairs E5: 1,4,9 # reduction candidate for 1,4 E5: 1,4 => CTR * .52481.....3.7.1.....32....56.892...328...69549.563...1.6.3....2.5....897.925.... E5: 9 # 13 pairs E6: 1,4,6 # reduction candidate for 1,4 E6: 1,4 => CTR * 9524817...639751.....326...5..862...32..9.6..69.5.3...1.6739...2.56143897.925.... E6: 6 # 13 pairs * PAIR F9: 4,8 BLK 8 F7: 4,8,7,9 # reduction candidate for 4,8 F7: 4,8 => CTR * .52481......67.1...7132.....6.8.2...31.7..6...9.563...1.693.........6.897.925.... F7: 7,9 => SOLVED * 652481937834679152971325864467812593315794628298563471186937245523146789749258316 * PAIR F9: 4,8 ROW 9 B9: 4,8,3 # reduction candidate for 4,8 B9: 3 => CTR * .52481.....367.1.....32.....6.8.2...3..1.76...9.563...186934......7163897392584.. B9: 4,8 # 13 pairs * PAIR G9: 3,4 BLK 9 G8: 3,4,2,7 # reduction candidate for 3,4 G8: 3,4 => CTR * .52481......67.1...7132.....6.8.2...31.7..6...9.563...1.693.........6.897.925.... G8: 2,7 # 15 pairs * PAIR G9: 3,4 ROW 9 B9: 3,4,8 # reduction candidate for 3,4 B9: 8 => CTR * .52481......67.1.....32.....6.8.2...3..1.76...9.563...1.6938......716.897892543.. B9: 3,4 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-008-base-pr-000.dot * REASONING * DIS # A2: 6,9 => CTR => A2: 4,8 * PRF # A3: 6,9 => SOL * DIS # H1: 6,9 => CTR => H1: 3,7 * DIS # B4: 1,7 => CTR => B4: 4,6 * PRF # B4: 4,6 => SOL * PRF # F2: 6,9 => SOL * DIS # A2: 6,9 => CTR => A2: 4,8 * DIS # H2: 6,9 => CTR => H2: 2,4,5 * DIS # H1: 7,9 => CTR => H1: 3,6 * DIS # G4: 7,9 => CTR => G4: 4,5 * PRF # D8: 1,7 => SOL * DIS # D8: 6 => CTR => D8: 1,7 * PRF # F7: 4,7 => SOL * DIS # F8: 4,7 => CTR => F8: 6 * PRF # F8: 6 => SOL * PRF # F7: 7,9 => SOL * DIS # F7: 4,8 => CTR => F7: 7,9 * DIS # E5: 1,4 => CTR => E5: 9 * DIS # E6: 1,4 => CTR => E6: 6 * DIS # F7: 4,8 => CTR => F7: 7,9 * PRF # F7: 7,9 => SOL * DIS # B9: 3 => CTR => B9: 4,8 * DIS # G8: 3,4 => CTR => G8: 2,7 * DIS # B9: 8 => CTR => B9: 3,4 * CNT 24 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B3,C3,D2,D5,D7,E8,F5,F9,G1,G9,H9,I9) * .52481.......7.1.....32.......8.2...3.....6...9.5.3...1.6.3...........897.925.... * PAIR A1: 6,9 BLK 1 A2: 6,9,4,8 # reduction candidate for 6,9 A2: 6,9 => CTR * .524819..9..6751..871329...46.81259331579462829.563...1.693.......1467897.92583.. A3: 6,9,4,8 # reduction candidate for 6,9 A3: 6,9 => SOLVED * 652481937834679152971325864467812593315794628298563471186937245523146789749258316 * DURATION: 0:00:04.187939 START: 23:00:02.753060 END: 23:00:06.940999 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-008-base-pr-001.dot * REASONING * DIS # A2: 6,9 => CTR => A2: 4,8 * PRF A2: 4,8 # A3: 6,9 => SOL * STA A2: 4,8 + A3: 6,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
Top 95 Sudokus 008 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 652481937834679152971325864467812593315794628298563471186937245523146789749258316 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 # A2: 6,9 => CTR => A2: 4,8 * INC # A2: 4,8 => UNS * PRF # A3: 6,9 => SOL * INC # A3: 4,8 => UNS * DIS # H1: 6,9 => CTR => H1: 3,7 * INC # H1: 3,7 => UNS * DIS # B4: 1,7 => CTR => B4: 4,6 * PRF # B4: 4,6 => SOL * INC # C4: 1,7 => UNS * INC # C6: 1,7 => UNS * PRF # F2: 6,9 => SOL * INC # F2: 5 => UNS * INC # F3: 6,9 => UNS * DIS # A2: 6,9 => CTR => A2: 4,8 * INC # A2: 4,8 => UNS * DIS # H2: 6,9 => CTR => H2: 2,4,5 * INC # H2: 2,4,5 => UNS * DIS # H1: 7,9 => CTR => H1: 3,6 * INC # H1: 3,6 => UNS * DIS # G4: 7,9 => CTR => G4: 4,5 * INC # G4: 4,5 => UNS * PRF # D8: 1,7 => SOL * DIS # D8: 6 => CTR => D8: 1,7 * PRF # F7: 4,7 => SOL * INC # F7: 8,9 => UNS * DIS # F8: 4,7 => CTR => F8: 6 * PRF # F8: 6 => SOL * PRF # F7: 7,9 => SOL * DIS # F7: 4,8 => CTR => F7: 7,9 * INC # E4: 1,4 => UNS * DIS # E5: 1,4 => CTR => E5: 9 * INC # E5: 9 => UNS * DIS # E6: 1,4 => CTR => E6: 6 * INC # E6: 6 => UNS * DIS # F7: 4,8 => CTR => F7: 7,9 * PRF # F7: 7,9 => SOL * INC # B9: 4,8 => UNS * DIS # B9: 3 => CTR => B9: 4,8 * DIS # G8: 3,4 => CTR => G8: 2,7 * INC # G8: 2,7 => UNS * INC # B9: 3,4 => UNS * DIS # B9: 8 => CTR => B9: 3,4 * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A2: 6,9 => CTR => A2: 4,8 * PRF A2: 4,8 # A3: 6,9 => SOL * STA A2: 4,8 + A3: 6,9 * CNT 2 HDP CHAINS / 2 HYP OPENED