Analysis of xx-top95-093-base.sdk
Contents
Original Sudoku
level: medium
position: .5..9....1.....6.....3.8.....8.4...9514.......3....2..........4.8...6..77..15..6. initial
Autosolve
position: 85..9....1.....6.....3.8.....8.4...9514.......3....24.........4.8...6..77..15..6. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D1: 2,7 => CTR => D1: 4,6 * DIS # D2: 2,7 => CTR => D2: 4,5 * PRF # F2: 2,7 => SOL * DIS # E3: 2,7 => CTR => E3: 1,6 * DIS # E7: 2,7 => CTR => E7: 3,8 * PRF # A3: 6,9 => SOL * DIS # E7: 2,3 => CTR => E7: 7,8 * CNT 7 HDP CHAINS / 44 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D1: 2,7 => CTR => D1: 4,6 * DIS D1: 4,6 # D2: 2,7 => CTR => D2: 4,5 * PRF D1: 4,6 + D2: 4,5 # F2: 2,7 => SOL * STA D1: 4,6 + D2: 4,5 + F2: 2,7 * CNT 3 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .5..9....1.....6.....3.8.....8.4...9514.......3....2..........4.8...6..77..15..6. | initial |
| 85..9....1.....6.....3.8.....8.4...9514.......3....24.........4.8...6..77..15..6. | autosolve |
| 856491372143572698927368451278645139514923786639817245361789524485236917792154863 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) E2: 2,7 A4: 2,6 A6: 6,9 C7: 1,5 C8: 1,5 C9: 2,9 E8: 2,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F1,E3: 1.. / F1 = 1 => 21 pairs (_) / E3 = 1 => 14 pairs (_) C7,C8: 1.. / C7 = 1 => 5 pairs (_) / C8 = 1 => 5 pairs (_) E3,E6: 1.. / E3 = 1 => 14 pairs (_) / E6 = 1 => 21 pairs (_) A4,B4: 2.. / A4 = 2 => 7 pairs (_) / B4 = 2 => 11 pairs (_) C1,C2: 3.. / C1 = 3 => 15 pairs (_) / C2 = 3 => 8 pairs (_) A7,A8: 3.. / A7 = 3 => 8 pairs (_) / A8 = 3 => 16 pairs (_) G1,G3: 4.. / G1 = 4 => 9 pairs (_) / G3 = 4 => 0 pairs (*) A8,B9: 4.. / A8 = 4 => 11 pairs (_) / B9 = 4 => 8 pairs (_) D8,F9: 4.. / D8 = 4 => 8 pairs (_) / F9 = 4 => 11 pairs (_) A8,D8: 4.. / A8 = 4 => 11 pairs (_) / D8 = 4 => 8 pairs (_) B9,F9: 4.. / B9 = 4 => 8 pairs (_) / F9 = 4 => 11 pairs (_) A3,A8: 4.. / A3 = 4 => 8 pairs (_) / A8 = 4 => 11 pairs (_) D2,F2: 5.. / D2 = 5 => 8 pairs (_) / F2 = 5 => 8 pairs (_) C7,C8: 5.. / C7 = 5 => 5 pairs (_) / C8 = 5 => 5 pairs (_) I3,I6: 5.. / I3 = 5 => 9 pairs (_) / I6 = 5 => 11 pairs (_) D1,E3: 6.. / D1 = 6 => 12 pairs (_) / E3 = 6 => 21 pairs (_) I5,I6: 6.. / I5 = 6 => 9 pairs (_) / I6 = 6 => 0 pairs (X) A7,B7: 6.. / A7 = 6 => 18 pairs (_) / B7 = 6 => 8 pairs (_) C1,D1: 6.. / C1 = 6 => 21 pairs (_) / D1 = 6 => 12 pairs (_) B4,C6: 7.. / B4 = 7 => 21 pairs (_) / C6 = 7 => 10 pairs (_) H2,I2: 8.. / H2 = 8 => 9 pairs (_) / I2 = 8 => 10 pairs (_) D7,E7: 8.. / D7 = 8 => 0 pairs (X) / E7 = 8 => 7 pairs (_) G9,I9: 8.. / G9 = 8 => 9 pairs (_) / I9 = 8 => 11 pairs (_) G5,G9: 8.. / G5 = 8 => 11 pairs (_) / G9 = 8 => 9 pairs (_) H2,H5: 8.. / H2 = 8 => 9 pairs (_) / H5 = 8 => 10 pairs (_) A6,C6: 9.. / A6 = 9 => 7 pairs (_) / C6 = 9 => 21 pairs (_) D5,F5: 9.. / D5 = 9 => 8 pairs (_) / F5 = 9 => 7 pairs (_) * DURATION: 0:00:35.175395 START: 01:11:22.711752 END: 01:11:57.887147 2017-05-04 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,C7,C8,C9,E2,E8) * 85..9....1.....6.....3.8.....8.4...9514.......3....24.........4.8...6..77..15..6. * PAIR E2: 2,7 BLK 2 D1: 2,7,4,6 # reduction candidate for 2,7 D1: 2,7 => CTR * 856.914..1.3.7.6....7368..1.78645..9514...786639817245.6.78...4.8...6..77.215.863 D1: 4,6 # 8 pairs F1: 2,7,1,4 # reduction candidate for 2,7 F1: 2,7 # 17 pairs D2: 2,7,4,5 # reduction candidate for 2,7 D2: 2,7 => CTR * 856491...143..5698..73684.1.78.43..9514....8..3981724536..8...448..36..7792154863 D2: 4,5 # 8 pairs F2: 2,7,4,5 # reduction candidate for 2,7 F2: 2,7 => SOLVED * 856491372143572698927368451278645139514923786639817245361789524485236917792154863 F2: 4,5 # 8 pairs E3: 2,7,1,6 # reduction candidate for 2,7 E3: 2,7 => CTR * 85.6914..1.....6.....3.8..1..8.4...9514.6.....3..1.24.........4.8...6..77..15..6. E3: 1,6 # 8 pairs * PAIR E2: 2,7 ROW 2 B2: 2,7,4,9 # reduction candidate for 2,7 B2: 2,7 # 12 pairs C2: 2,7,3,9 # reduction candidate for 2,7 C2: 2,7 # 19 pairs H2: 2,7,3,8,9 # reduction candidate for 2,7 H2: 2,7 # 15 pairs * PAIR E2: 2,7 COL E E5: 2,7,3,6,8 # reduction candidate for 2,7 E5: 2,7 # 12 pairs E7: 2,7,3,8 # reduction candidate for 2,7 E7: 2,7 => CTR * 85.6924.11...75682...318..5628743..95142.9...9375.124.36.827..448.936.2779.15..6. E7: 3,8 # 8 pairs * PAIR A4: 2,6 BLK 4 B4: 2,6,7 # reduction candidate for 2,6 B4: 7 # 21 pairs B4: 2,6 # 10 pairs * PAIR A4: 2,6 COL A A3: 2,6,4,9 # reduction candidate for 2,6 A3: 2,6 # 12 pairs A7: 2,6,3,9 # reduction candidate for 2,6 A7: 2,6 # 17 pairs * PAIR A6: 6,9 BLK 4 C6: 6,9,7 # reduction candidate for 6,9 C6: 6,9 # 21 pairs C6: 7 # 10 pairs * PAIR A6: 6,9 COL A A3: 6,9,2,4 # reduction candidate for 6,9 A3: 6,9 => SOLVED * 856491372143572698927368451278645139514923786639817245361789524485236917792154863 A3: 2,4 # 8 pairs A7: 6,9,2,3 # reduction candidate for 6,9 A7: 6,9 # 17 pairs * PAIR C7: 1,5 ROW 7 G7: 1,5,3,9 # reduction candidate for 1,5 G7: 1,5 # 8 pairs H7: 1,5,2,3,9 # reduction candidate for 1,5 H7: 1,5 # 9 pairs * PAIR C8: 1,5 ROW 8 G8: 1,5,3,9 # reduction candidate for 1,5 G8: 1,5 # 8 pairs H8: 1,5,2,3,9 # reduction candidate for 1,5 H8: 1,5 # 9 pairs * PAIR C9: 2,9 BLK 7 A7: 2,9,3,6 # reduction candidate for 2,9 A7: 2,9 # 20 pairs B7: 2,9,6 # reduction candidate for 2,9 B7: 2,9 # 18 pairs A8: 2,9,3,4 # reduction candidate for 2,9 A8: 2,9 # 11 pairs B9: 2,9,4 # reduction candidate for 2,9 B9: 2,9 # 11 pairs * PAIR C9: 2,9 ROW 9 F9: 2,9,3,4 # reduction candidate for 2,9 F9: 2,9 # 11 pairs F9: 3,4 # 8 pairs * PAIR C9: 2,9 COL C C2: 2,9,3,7 # reduction candidate for 2,9 C2: 2,9 # 15 pairs C3: 2,9,6,7 # reduction candidate for 2,9 C3: 2,9 # 9 pairs * PAIR E8: 2,3 BLK 8 E7: 2,3,7,8 # reduction candidate for 2,3 E7: 2,3 => CTR * 85.6924.11...75682...318..5..8743..95142.9....375.124....8.7..4.8.9.6..77..154.6. E7: 7,8 # 8 pairs F7: 2,3,7,9 # reduction candidate for 2,3 F7: 2,3 # 15 pairs F9: 2,3,4,9 # reduction candidate for 2,3 F9: 2,3 # 12 pairs * PAIR E8: 2,3 ROW 8 A8: 2,3,4,9 # reduction candidate for 2,3 A8: 2,3 # 10 pairs H8: 2,3,1,5,9 # reduction candidate for 2,3 H8: 2,3 # 13 pairs * PAIR E8: 2,3 COL E E5: 2,3,6,7,8 # reduction candidate for 2,3 E5: 6,7,8 # 12 pairs E5: 2,3 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-093-base-pr-000.dot * REASONING * DIS # D1: 2,7 => CTR => D1: 4,6 * DIS # D2: 2,7 => CTR => D2: 4,5 * PRF # F2: 2,7 => SOL * DIS # E3: 2,7 => CTR => E3: 1,6 * DIS # E7: 2,7 => CTR => E7: 3,8 * PRF # A3: 6,9 => SOL * DIS # E7: 2,3 => CTR => E7: 7,8 * CNT 7 HDP CHAINS / 44 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,C7,C8,C9,E2,E8) * 85..9....1.....6.....3.8.....8.4...9514.......3....24.........4.8...6..77..15..6. * PAIR E2: 2,7 BLK 2 D1: 2,7,4,6 # reduction candidate for 2,7 D1: 2,7 => CTR * 856.914..1.3.7.6....7368..1.78645..9514...786639817245.6.78...4.8...6..77.215.863 F1: 2,7,1,4 # reduction candidate for 2,7 F1: 2,7 # 17 pairs D2: 2,7,4,5 # reduction candidate for 2,7 D2: 2,7 => CTR * 856491...143..5698..73684.1.78.43..9514....8..3981724536..8...448..36..7792154863 F2: 2,7,4,5 # reduction candidate for 2,7 F2: 2,7 => SOLVED * 856491372143572698927368451278645139514923786639817245361789524485236917792154863 * DURATION: 0:00:05.242630 START: 01:12:31.021993 END: 01:12:36.264623 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-093-base-pr-001.dot * REASONING * DIS # D1: 2,7 => CTR => D1: 4,6 * DIS D1: 4,6 # D2: 2,7 => CTR => D2: 4,5 * PRF D1: 4,6 + D2: 4,5 # F2: 2,7 => SOL * STA D1: 4,6 + D2: 4,5 + F2: 2,7 * CNT 3 HDP CHAINS / 4 HYP OPENED
Header Info
Top 95 Sudokus 093 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 856491372143572698927368451278645139514923786639817245361789524485236917792154863 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 # D1: 2,7 => CTR => D1: 4,6 * INC # D1: 4,6 => UNS * INC # F1: 2,7 => UNS * DIS # D2: 2,7 => CTR => D2: 4,5 * INC # D2: 4,5 => UNS * PRF # F2: 2,7 => SOL * INC # F2: 4,5 => UNS * DIS # E3: 2,7 => CTR => E3: 1,6 * INC # E3: 1,6 => UNS * INC # B2: 2,7 => UNS * INC # C2: 2,7 => UNS * INC # H2: 2,7 => UNS * INC # E5: 2,7 => UNS * DIS # E7: 2,7 => CTR => E7: 3,8 * INC # E7: 3,8 => UNS * INC # B4: 2,6 => UNS * INC # B4: 7 => UNS * INC # A3: 2,6 => UNS * INC # A7: 2,6 => UNS * INC # C6: 6,9 => UNS * INC # C6: 7 => UNS * PRF # A3: 6,9 => SOL * INC # A3: 2,4 => UNS * INC # A7: 6,9 => UNS * INC # G7: 1,5 => UNS * INC # H7: 1,5 => UNS * INC # G8: 1,5 => UNS * INC # H8: 1,5 => UNS * INC # A7: 2,9 => UNS * INC # B7: 2,9 => UNS * INC # A8: 2,9 => UNS * INC # B9: 2,9 => UNS * INC # F9: 2,9 => UNS * INC # F9: 3,4 => UNS * INC # C2: 2,9 => UNS * INC # C3: 2,9 => UNS * DIS # E7: 2,3 => CTR => E7: 7,8 * INC # E7: 7,8 => UNS * INC # F7: 2,3 => UNS * INC # F9: 2,3 => UNS * INC # A8: 2,3 => UNS * INC # H8: 2,3 => UNS * INC # E5: 2,3 => UNS * INC # E5: 6,7,8 => UNS * CNT 44 HDP CHAINS / 44 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D1: 2,7 => CTR => D1: 4,6 * INC D1: 4,6 # F1: 2,7 => UNS * DIS D1: 4,6 # D2: 2,7 => CTR => D2: 4,5 * PRF D1: 4,6 + D2: 4,5 # F2: 2,7 => SOL * STA D1: 4,6 + D2: 4,5 + F2: 2,7 * CNT 4 HDP CHAINS / 4 HYP OPENED