Analysis of xx-top500-321-base.sdk
Contents
Original Sudoku
level: medium
position: .5.....614...3..............67....8.2.1..........4.3.....7.6...5.....2.....1..... initial
Autosolve
position: .53....614...3.............367....8.241........5.4.3.....7.6...5.....2.....1..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 8,9 => CTR => A1: 7 * PRF # A1: 7 => SOL * DIS # A3: 8,9 => CTR => A3: 1,6,7 * PRF # A7: 8,9 => SOL * DIS # A7: 1 => CTR => A7: 8,9 * DIS # A9: 8,9 => CTR => A9: 6,7 * PRF # B2: 8,9 => SOL * DIS # B8: 8,9 => CTR => B8: 1,3,7 * PRF # I6: 7 => SOL * DIS # B8: 8,9 => CTR => B8: 1,3,7 * PRF # C8: 8,9 => SOL * DIS # I8: 8,9 => CTR => I8: 3,4,6,7 * PRF # E1: 8,9 => SOL * DIS # E3: 8,9 => CTR => E3: 1,5,6,7 * DIS # E5: 8,9 => CTR => E5: 5,6,7 * CNT 15 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 8,9 => CTR => A1: 7 * PRF A1: 7 => SOL * STA A1: 7 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .5.....614...3..............67....8.2.1..........4.3.....7.6...5.....2.....1..... | initial |
| .53....614...3.............367....8.241........5.4.3.....7.6...5.....2.....1..... | autosolve |
| 753294861496831725128567943367915482241378659985642317832756194519483276674129538 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) A6: 8,9 B6: 8,9 D6: 2,6 E8: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G4,H6: 1.. / G4 = 1 => 0 pairs (X) / H6 = 1 => 0 pairs (_) B2,F2: 1.. / B2 = 1 => 0 pairs (X) / F2 = 1 => 0 pairs (_) F6,H6: 1.. / F6 = 1 => 0 pairs (X) / H6 = 1 => 0 pairs (_) B8,H8: 1.. / B8 = 1 => 0 pairs (*) / H8 = 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 => 4 pairs (_) / I3 = 3 => 4 pairs (_) D5,F5: 3.. / D5 = 3 => 4 pairs (_) / F5 = 3 => 4 pairs (_) D5,D8: 3.. / D5 = 3 => 4 pairs (_) / D8 = 3 => 4 pairs (_) G4,I4: 4.. / G4 = 4 => 0 pairs (*) / I4 = 4 => 0 pairs (X) C2,D2: 6.. / C2 = 6 => 0 pairs (*) / D2 = 6 => 0 pairs (X) D6,I6: 6.. / D6 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) C8,I8: 6.. / C8 = 6 => 0 pairs (X) / I8 = 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,B6: 8.. / A6 = 8 => 4 pairs (_) / B6 = 8 => 4 pairs (_) A6,B6: 9.. / A6 = 9 => 4 pairs (_) / B6 = 9 => 4 pairs (_) * DURATION: 0:00:28.668495 START: 13:54:16.051675 END: 13:54:44.720170 2017-05-04 * CP COUNT: (19) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B6,D6,E8) * .53....614...3.............367....8.241........5.4.3.....7.6...5.....2.....1..... * PAIR A6: 8,9 COL A A1: 8,9,7 # reduction candidate for 8,9 A1: 8,9 => CTR * .53....6141..3........1....367...184241.67.....52413..1..7.6...5.....21....1..... A1: 7 => SOLVED * 753294861496831725128567943367915482241378659985642317832756194519483276674129538 A3: 8,9,1,6,7 # reduction candidate for 8,9 A3: 8,9 => CTR * 753....614...3.............367...184241...6....56413..1..7.6...5.....2166..1..... A3: 1,6,7 # 4 pairs A7: 8,9,1 # reduction candidate for 8,9 A7: 8,9 => SOLVED * 753294861496831725128567943367915482241378659985642317832756194519483276674129538 A7: 1 => CTR * .53....6141..3........1....367...184241.67.....52413..1..7.6...5.....21....1..... A9: 8,9,6,7 # reduction candidate for 8,9 A9: 8,9 => CTR * 753....614..63....6...7....367.1..82241.6......52473.61..7.6...5.6...21....1..6.. A9: 6,7 # 5 pairs * PAIR B6: 8,9 COL B B2: 8,9,1,2,7 # reduction candidate for 8,9 B2: 8,9 => SOLVED * 753294861496831725128567943367915482241378659985642317832756194519483276674129538 B2: 1,2,7 # 4 pairs B3: 8,9,1,2,7 # reduction candidate for 8,9 B3: 8,9 # 5 pairs B7: 8,9,1,2,3 # reduction candidate for 8,9 B7: 8,9 # 5 pairs B8: 8,9,1,3,7 # reduction candidate for 8,9 B8: 8,9 => CTR * .53....6141.63.............367...184241........5.41372...7.6...5.6...217...1..... B8: 1,3,7 # 4 pairs B9: 8,9,2,3,7 # reduction candidate for 8,9 B9: 8,9 # 5 pairs * PAIR D6: 2,6 ROW 6 I6: 2,6,7 # reduction candidate for 2,6 I6: 7 => SOLVED * 753294861496831725128567943367915482241378659985642317832756194519483276674129538 I6: 2,6 # 7 pairs * PAIR E8: 8,9 BLK 8 E7: 8,9,2,5 # reduction candidate for 8,9 E7: 8,9 # 12 pairs D8: 8,9,3,4 # reduction candidate for 8,9 D8: 8,9 # 11 pairs F8: 8,9,3,4 # reduction candidate for 8,9 F8: 8,9 # 11 pairs E9: 8,9,2,5 # reduction candidate for 8,9 E9: 8,9 # 12 pairs F9: 8,9,2,3,4,5 # reduction candidate for 8,9 F9: 8,9 # 10 pairs * PAIR E8: 8,9 ROW 8 B8: 8,9,1,3,7 # reduction candidate for 8,9 B8: 8,9 => CTR * .53....6141.63.............367...184241........5.41372...7.6...5.6...217...1..... B8: 1,3,7 # 4 pairs C8: 8,9,4,6 # reduction candidate for 8,9 C8: 8,9 => SOLVED * 753294861496831725128567943367915482241378659985642317832756194519483276674129538 C8: 4,6 # 5 pairs I8: 8,9,3,4,6,7 # reduction candidate for 8,9 I8: 8,9 => CTR * .53....614..63....6........367...18.241.6......524.3.61..7.6...5.6...21....1..6.. I8: 3,4,6,7 # 4 pairs * PAIR E8: 8,9 COL E E1: 8,9,2,7 # reduction candidate for 8,9 E1: 8,9 => SOLVED * 753294861496831725128567943367915482241378659985642317832756194519483276674129538 E1: 2,7 # 5 pairs E3: 8,9,1,5,6,7 # reduction candidate for 8,9 E3: 8,9 => CTR * .53....614...3.............367.1..8.241.6......5247316...7.61..516...2.....1..6.. E3: 1,5,6,7 # 4 pairs E5: 8,9,5,6,7 # reduction candidate for 8,9 E5: 8,9 => CTR * .53.7..614.6.3........6....367.1..8.241........5.4.31....7.61..51....2..67.1..... E5: 5,6,7 # 6 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-321-base-pr-000.dot * REASONING * DIS # A1: 8,9 => CTR => A1: 7 * PRF # A1: 7 => SOL * DIS # A3: 8,9 => CTR => A3: 1,6,7 * PRF # A7: 8,9 => SOL * DIS # A7: 1 => CTR => A7: 8,9 * DIS # A9: 8,9 => CTR => A9: 6,7 * PRF # B2: 8,9 => SOL * DIS # B8: 8,9 => CTR => B8: 1,3,7 * PRF # I6: 7 => SOL * DIS # B8: 8,9 => CTR => B8: 1,3,7 * PRF # C8: 8,9 => SOL * DIS # I8: 8,9 => CTR => I8: 3,4,6,7 * PRF # E1: 8,9 => SOL * DIS # E3: 8,9 => CTR => E3: 1,5,6,7 * DIS # E5: 8,9 => CTR => E5: 5,6,7 * CNT 15 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B6,D6,E8) * .53....614...3.............367....8.241........5.4.3.....7.6...5.....2.....1..... * PAIR A6: 8,9 COL A A1: 8,9,7 # reduction candidate for 8,9 A1: 8,9 => CTR * .53....6141..3........1....367...184241.67.....52413..1..7.6...5.....21....1..... A1: 7 => SOLVED * 753294861496831725128567943367915482241378659985642317832756194519483276674129538 * DURATION: 0:00:01.891457 START: 13:55:09.467909 END: 13:55:11.359366 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-321-base-pr-001.dot * REASONING * DIS # A1: 8,9 => CTR => A1: 7 * PRF A1: 7 => SOL * STA A1: 7 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 321 solution: 753294861496831725128567943367915482241378659985642317832756194519483276674129538 info: 2931 FNBTHWY S8.f 19683 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 753294861496831725128567943367915482241378659985642317832756194519483276674129538 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 # A1: 8,9 => CTR => A1: 7 * PRF # A1: 7 => SOL * DIS # A3: 8,9 => CTR => A3: 1,6,7 * INC # A3: 1,6,7 => UNS * PRF # A7: 8,9 => SOL * DIS # A7: 1 => CTR => A7: 8,9 * DIS # A9: 8,9 => CTR => A9: 6,7 * INC # A9: 6,7 => UNS * PRF # B2: 8,9 => SOL * INC # B2: 1,2,7 => UNS * INC # B3: 8,9 => UNS * INC # B7: 8,9 => UNS * DIS # B8: 8,9 => CTR => B8: 1,3,7 * INC # B8: 1,3,7 => UNS * INC # B9: 8,9 => UNS * INC # I6: 2,6 => UNS * PRF # I6: 7 => SOL * INC # E7: 8,9 => UNS * INC # D8: 8,9 => UNS * INC # F8: 8,9 => UNS * INC # E9: 8,9 => UNS * INC # F9: 8,9 => UNS * DIS # B8: 8,9 => CTR => B8: 1,3,7 * INC # B8: 1,3,7 => UNS * PRF # C8: 8,9 => SOL * INC # C8: 4,6 => UNS * DIS # I8: 8,9 => CTR => I8: 3,4,6,7 * INC # I8: 3,4,6,7 => UNS * PRF # E1: 8,9 => SOL * INC # E1: 2,7 => UNS * DIS # E3: 8,9 => CTR => E3: 1,5,6,7 * INC # E3: 1,5,6,7 => UNS * DIS # E5: 8,9 => CTR => E5: 5,6,7 * INC # E5: 5,6,7 => UNS * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 8,9 => CTR => A1: 7 * PRF A1: 7 => SOL * STA A1: 7 * CNT 2 HDP CHAINS / 1 HYP OPENED