Analysis of xx-top500-322-base.sdk
Contents
Original Sudoku
level: medium
position: .7.....164...3..............68....9.2.1..........4.3.....8.6...5.....2.....1..... initial
Autosolve
position: .73....164...3.............368....9.241..........4.3.....8.6...5.....2.....1..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 8,9 => CTR => B2: 1,2,5 * DIS # A3: 8,9 => CTR => A3: 1,6 * DIS # F1: 8,9 => CTR => F1: 2,4,5 * PRF # G1: 8,9 => SOL * DIS # A9: 8,9 => CTR => A9: 6,7 * PRF # A7: 7,9 => SOL * DIS # A7: 1 => CTR => A7: 7,9 * DIS # A9: 7,9 => CTR => A9: 6,8 * DIS # C6: 7 => CTR => C6: 5,9 * PRF # B2: 5,9 => SOL * PRF # H6: 8 => SOL * PRF # C8: 7,9 => SOL * DIS # I8: 7,9 => CTR => I8: 1,3,4,8 * DIS # E3: 7,9 => CTR => E3: 1,5,6,8 * DIS # E5: 7,9 => CTR => E5: 5,6,8 * CNT 15 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 8,9 => CTR => B2: 1,2,5 * DIS B2: 1,2,5 # A3: 8,9 => CTR => A3: 1,6 * PRF B2: 1,2,5 + A3: 1,6 # B3: 1,2,5 => SOL * STA B2: 1,2,5 + A3: 1,6 + B3: 1,2,5 * CNT 3 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .7.....164...3..............68....9.2.1..........4.3.....8.6...5.....2.....1..... | initial |
| .73....164...3.............368....9.241..........4.3.....8.6...5.....2.....1..... | autosolve |
| 873254916456931827129768543368517492241389675795642381932876154517493268684125739 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) A1: 8,9 A6: 7,9 B6: 5,9 D6: 2,6 E8: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,F2: 1.. / B2 = 1 => 0 pairs (X) / F2 = 1 => 0 pairs (_) F6,I6: 1.. / F6 = 1 => 0 pairs (X) / I6 = 1 => 0 pairs (_) B8,I8: 1.. / B8 = 1 => 0 pairs (*) / I8 = 1 => 0 pairs (X) A3,A7: 1.. / A3 = 1 => 0 pairs (*) / A7 = 1 => 0 pairs (X) E3,E4: 1.. / E3 = 1 => 0 pairs (X) / E4 = 1 => 0 pairs (_) G4,G7: 1.. / G4 = 1 => 0 pairs (X) / G7 = 1 => 0 pairs (_) H3,I3: 3.. / H3 = 3 => 5 pairs (_) / I3 = 3 => 5 pairs (_) D5,F5: 3.. / D5 = 3 => 5 pairs (_) / F5 = 3 => 5 pairs (_) D5,D8: 3.. / D5 = 3 => 5 pairs (_) / D8 = 3 => 5 pairs (_) G4,I4: 4.. / G4 = 4 => 0 pairs (*) / I4 = 4 => 0 pairs (X) B6,C6: 5.. / B6 = 5 => 5 pairs (_) / C6 = 5 => 4 pairs (_) C2,D2: 6.. / C2 = 6 => 0 pairs (*) / D2 = 6 => 0 pairs (X) D6,H6: 6.. / D6 = 6 => 0 pairs (*) / H6 = 6 => 0 pairs (X) C8,H8: 6.. / C8 = 6 => 0 pairs (X) / H8 = 6 => 0 pairs (_) A3,A9: 6.. / A3 = 6 => 0 pairs (X) / A9 = 6 => 0 pairs (_) E3,E5: 6.. / E3 = 6 => 0 pairs (*) / E5 = 6 => 0 pairs (X) G5,G9: 6.. / G5 = 6 => 0 pairs (*) / G9 = 6 => 0 pairs (X) A6,C6: 7.. / A6 = 7 => 6 pairs (_) / C6 = 7 => 0 pairs (X) * DURATION: 0:00:27.904797 START: 13:55:26.254585 END: 13:55:54.159382 2017-05-04 * CP COUNT: (18) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B6,D6,E8) * .73....164...3.............368....9.241..........4.3.....8.6...5.....2.....1..... * PAIR A1: 8,9 BLK 1 B2: 8,9,1,2,5 # reduction candidate for 8,9 B2: 8,9 => CTR * 8732549164967318251259687..368517492241389657.5.642381.3.8.61..51.4.326868.1.5... B2: 1,2,5 # 5 pairs A3: 8,9,1,6 # reduction candidate for 8,9 A3: 8,9 => CTR * .73....164...3.............368...194241...6..7..6413..1..8.6...5.....2616..1..... A3: 1,6 # 6 pairs B3: 8,9,1,2,5 # reduction candidate for 8,9 B3: 8,9 # 7 pairs * PAIR A1: 8,9 ROW 1 E1: 8,9,2,5 # reduction candidate for 8,9 E1: 8,9 # 7 pairs F1: 8,9,2,4,5 # reduction candidate for 8,9 F1: 8,9 => CTR * 8732594164.67318..1..468...36851..9.2419836.....642381.3.8.61..51.3..26868.1..... F1: 2,4,5 # 5 pairs G1: 8,9,4,5 # reduction candidate for 8,9 G1: 8,9 => SOLVED * 873254916456931827129768543368517492241389675795642381932876154517493268684125739 G1: 4,5 # 6 pairs * PAIR A1: 8,9 COL A A9: 8,9,6,7 # reduction candidate for 8,9 A9: 8,9 => CTR * .73....164..63....6........368...19.241.6.......24.36.1..8.6...5.6...2.1...1..6.. A9: 6,7 # 6 pairs * PAIR A6: 7,9 BLK 4 C6: 7,9,5 # reduction candidate for 7,9 C6: 7,9 # 5 pairs C6: 5 # 4 pairs * PAIR A6: 7,9 COL A A7: 7,9,1 # reduction candidate for 7,9 A7: 7,9 => SOLVED * 873254916456931827129768543368517492241389675795642381932876154517493268684125739 A7: 1 => CTR * .73....1641..3........1....368...194241.68......2413..1..8.6...5.....2.1...1..... A9: 7,9,6,8 # reduction candidate for 7,9 A9: 7,9 => CTR * 873....164..63....6...8....368.1..92241.6.......24836.1..8.6...5.6...2.1...1..6.. A9: 6,8 # 6 pairs * PAIR B6: 5,9 BLK 4 C6: 5,9,7 # reduction candidate for 5,9 C6: 7 => CTR * 8732549164.6.318..1.5.687..368.1.4922413896..95764238173.8.61..51947326868.1.5... C6: 5,9 # 6 pairs * PAIR B6: 5,9 COL B B2: 5,9,1,2,8 # reduction candidate for 5,9 B2: 5,9 => SOLVED * 873254916456931827129768543368517492241389675795642381932876154517493268684125739 B2: 1,2,8 # 5 pairs B3: 5,9,1,2,8 # reduction candidate for 5,9 B3: 5,9 # 6 pairs * PAIR D6: 2,6 ROW 6 H6: 2,6,8 # reduction candidate for 2,6 H6: 8 => SOLVED * 873254916456931827129768543368517492241389675795642381932876154517493268684125739 H6: 2,6 # 8 pairs * PAIR E8: 7,9 BLK 8 E7: 7,9,2,5 # reduction candidate for 7,9 E7: 7,9 # 12 pairs D8: 7,9,3,4 # reduction candidate for 7,9 D8: 7,9 # 15 pairs F8: 7,9,3,4 # reduction candidate for 7,9 F8: 7,9 # 14 pairs E9: 7,9,2,5 # reduction candidate for 7,9 E9: 7,9 # 12 pairs F9: 7,9,2,3,4,5 # reduction candidate for 7,9 F9: 7,9 # 13 pairs * PAIR E8: 7,9 ROW 8 C8: 7,9,4,6 # reduction candidate for 7,9 C8: 7,9 => SOLVED * 873254916456931827129768543368517492241389675795642381932876154517493268684125739 C8: 4,6 # 6 pairs I8: 7,9,1,3,4,8 # reduction candidate for 7,9 I8: 7,9 => CTR * .73....164...31...1........368.1..9.241..........4.3.1...8.61..516...28....1..... I8: 1,3,4,8 # 5 pairs * PAIR E8: 7,9 COL E E3: 7,9,1,5,6,8 # reduction candidate for 7,9 E3: 7,9 => CTR * .73....164...3.............368.1..9.241.6.......248361...8.61..516...2.....1..6.. E3: 1,5,6,8 # 5 pairs E5: 7,9,5,6,8 # reduction candidate for 7,9 E5: 7,9 => CTR * .73.8..164.6.3........6....368.1..9.241..........4.3.1...8.61..51....2..68.1..... E5: 5,6,8 # 7 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-322-base-pr-000.dot * REASONING * DIS # B2: 8,9 => CTR => B2: 1,2,5 * DIS # A3: 8,9 => CTR => A3: 1,6 * DIS # F1: 8,9 => CTR => F1: 2,4,5 * PRF # G1: 8,9 => SOL * DIS # A9: 8,9 => CTR => A9: 6,7 * PRF # A7: 7,9 => SOL * DIS # A7: 1 => CTR => A7: 7,9 * DIS # A9: 7,9 => CTR => A9: 6,8 * DIS # C6: 7 => CTR => C6: 5,9 * PRF # B2: 5,9 => SOL * PRF # H6: 8 => SOL * PRF # C8: 7,9 => SOL * DIS # I8: 7,9 => CTR => I8: 1,3,4,8 * DIS # E3: 7,9 => CTR => E3: 1,5,6,8 * DIS # E5: 7,9 => CTR => E5: 5,6,8 * CNT 15 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B6,D6,E8) * .73....164...3.............368....9.241..........4.3.....8.6...5.....2.....1..... * PAIR A1: 8,9 BLK 1 B2: 8,9,1,2,5 # reduction candidate for 8,9 B2: 8,9 => CTR * 8732549164967318251259687..368517492241389657.5.642381.3.8.61..51.4.326868.1.5... A3: 8,9,1,6 # reduction candidate for 8,9 A3: 8,9 => CTR * .73....164...3.............368...194241...6..7..6413..1..8.6...5.....2616..1..... B3: 8,9,1,2,5 # reduction candidate for 8,9 B3: 8,9 # 7 pairs * RESTART * PAIR A1: 8,9 BLK 1 B3: 8,9,1,2,5 # reduction candidate for 8,9 B3: 1,2,5 => SOLVED * 873254916456931827129768543368517492241389675795642381932876154517493268684125739 * DURATION: 0:00:05.840821 START: 13:56:22.126668 END: 13:56:27.967489 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-322-base-pr-001.dot * REASONING * DIS # B2: 8,9 => CTR => B2: 1,2,5 * DIS B2: 1,2,5 # A3: 8,9 => CTR => A3: 1,6 * PRF B2: 1,2,5 + A3: 1,6 # B3: 1,2,5 => SOL * STA B2: 1,2,5 + A3: 1,6 + B3: 1,2,5 * CNT 3 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 322 solution: 873254916456931827129768543368517492241389675795642381932876154517493268684125739 info: 2931 FNBTHWY S8.f 22050 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 873254916456931827129768543368517492241389675795642381932876154517493268684125739 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 # B2: 8,9 => CTR => B2: 1,2,5 * INC # B2: 1,2,5 => UNS * DIS # A3: 8,9 => CTR => A3: 1,6 * INC # A3: 1,6 => UNS * INC # B3: 8,9 => UNS * INC # E1: 8,9 => UNS * DIS # F1: 8,9 => CTR => F1: 2,4,5 * INC # F1: 2,4,5 => UNS * PRF # G1: 8,9 => SOL * INC # G1: 4,5 => UNS * DIS # A9: 8,9 => CTR => A9: 6,7 * INC # A9: 6,7 => UNS * INC # C6: 7,9 => UNS * INC # C6: 5 => UNS * PRF # A7: 7,9 => SOL * DIS # A7: 1 => CTR => A7: 7,9 * DIS # A9: 7,9 => CTR => A9: 6,8 * INC # A9: 6,8 => UNS * INC # C6: 5,9 => UNS * DIS # C6: 7 => CTR => C6: 5,9 * PRF # B2: 5,9 => SOL * INC # B2: 1,2,8 => UNS * INC # B3: 5,9 => UNS * INC # H6: 2,6 => UNS * PRF # H6: 8 => SOL * INC # E7: 7,9 => UNS * INC # D8: 7,9 => UNS * INC # F8: 7,9 => UNS * INC # E9: 7,9 => UNS * INC # F9: 7,9 => UNS * PRF # C8: 7,9 => SOL * INC # C8: 4,6 => UNS * DIS # I8: 7,9 => CTR => I8: 1,3,4,8 * INC # I8: 1,3,4,8 => UNS * DIS # E3: 7,9 => CTR => E3: 1,5,6,8 * INC # E3: 1,5,6,8 => UNS * DIS # E5: 7,9 => CTR => E5: 5,6,8 * INC # E5: 5,6,8 => UNS * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B2: 8,9 => CTR => B2: 1,2,5 * DIS B2: 1,2,5 # A3: 8,9 => CTR => A3: 1,6 * INC B2: 1,2,5 + A3: 1,6 # B3: 8,9 => UNS * INC B2: 1,2,5 + A3: 1,6 # B3: 8,9 => UNS * PRF B2: 1,2,5 + A3: 1,6 # B3: 1,2,5 => SOL * STA B2: 1,2,5 + A3: 1,6 + B3: 1,2,5 * CNT 5 HDP CHAINS / 5 HYP OPENED