Analysis of xx-top500-092-base.sdk
Contents
Original Sudoku
level: medium
position: .325........6...1..............8.2.361..4..........5..4.7....8....3.....8........ initial
Autosolve
position: .325.46.8.8.63..1...68...3....1852636152438..3287..5414579..3862.13.8.548.345.12. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G2: 7 => CTR => G2: 4,9 * DIS # G3: 9 => CTR => G3: 4,7 * CNT 2 HDP CHAINS / 17 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G2: 7 => CTR => G2: 4,9 * DIS G2: 4,9 # G3: 9 => CTR => G3: 4,7 * PRF G2: 4,9 + G3: 4,7 # A1: 7,9 => SOL * STA G2: 4,9 + G3: 4,7 + A1: 7,9 * CNT 3 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .325........6...1..............8.2.361..4..........5..4.7....8....3.....8........ | initial |
| .325.46.8.8.63..1...68...3....1852636152438..3287..5414579..3862.13.8.548.345.12. | autosolve |
| 732514698589637412146892735974185263615243879328769541457921386261378954893456127 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) C2: 4,9 B3: 4,7 H1: 7,9 I2: 2,5 I3: 2,5 A4: 7,9 B4: 4,7 C4: 4,9 E6: 6,9 F6: 6,9 H5: 7,9 I5: 7,9 B8: 6,9 B9: 6,9 E7: 1,2 F7: 1,2 E8: 6,7 F9: 6,7 G8: 7,9 I9: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A3: 1.. / A1 = 1 => 22 pairs (_) / A3 = 1 => 19 pairs (_) E7,F7: 1.. / E7 = 1 => 20 pairs (_) / F7 = 1 => 18 pairs (_) A1,E1: 1.. / A1 = 1 => 22 pairs (_) / E1 = 1 => 19 pairs (_) F3,F7: 1.. / F3 = 1 => 20 pairs (_) / F7 = 1 => 18 pairs (_) I2,I3: 2.. / I2 = 2 => 20 pairs (_) / I3 = 2 => 20 pairs (_) E7,F7: 2.. / E7 = 2 => 18 pairs (_) / F7 = 2 => 20 pairs (_) F2,I2: 2.. / F2 = 2 => 20 pairs (_) / I2 = 2 => 20 pairs (_) E3,E7: 2.. / E3 = 2 => 20 pairs (_) / E7 = 2 => 18 pairs (_) C2,B3: 4.. / C2 = 4 => 18 pairs (_) / B3 = 4 => 19 pairs (_) G2,G3: 4.. / G2 = 4 => 19 pairs (_) / G3 = 4 => 18 pairs (_) B4,C4: 4.. / B4 = 4 => 18 pairs (_) / C4 = 4 => 19 pairs (_) C2,G2: 4.. / C2 = 4 => 18 pairs (_) / G2 = 4 => 19 pairs (_) B3,G3: 4.. / B3 = 4 => 19 pairs (_) / G3 = 4 => 18 pairs (_) B3,B4: 4.. / B3 = 4 => 19 pairs (_) / B4 = 4 => 18 pairs (_) C2,C4: 4.. / C2 = 4 => 18 pairs (_) / C4 = 4 => 19 pairs (_) A2,A3: 5.. / A2 = 5 => 20 pairs (_) / A3 = 5 => 20 pairs (_) I2,I3: 5.. / I2 = 5 => 20 pairs (_) / I3 = 5 => 20 pairs (_) A2,I2: 5.. / A2 = 5 => 20 pairs (_) / I2 = 5 => 20 pairs (_) A3,I3: 5.. / A3 = 5 => 20 pairs (_) / I3 = 5 => 20 pairs (_) E6,F6: 6.. / E6 = 6 => 0 pairs (*) / F6 = 6 => 0 pairs (X) B8,B9: 6.. / B8 = 6 => 0 pairs (*) / B9 = 6 => 0 pairs (X) E8,F9: 6.. / E8 = 6 => 0 pairs (X) / F9 = 6 => 0 pairs (_) B8,E8: 6.. / B8 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) B9,F9: 6.. / B9 = 6 => 0 pairs (X) / F9 = 6 => 0 pairs (_) E6,E8: 6.. / E6 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) F6,F9: 6.. / F6 = 6 => 0 pairs (X) / F9 = 6 => 0 pairs (_) A4,B4: 7.. / A4 = 7 => 18 pairs (_) / B4 = 7 => 19 pairs (_) H5,I5: 7.. / H5 = 7 => 0 pairs (*) / I5 = 7 => 0 pairs (X) E8,F9: 7.. / E8 = 7 => 0 pairs (*) / F9 = 7 => 0 pairs (X) G8,I9: 7.. / G8 = 7 => 0 pairs (X) / I9 = 7 => 0 pairs (_) E8,G8: 7.. / E8 = 7 => 0 pairs (*) / G8 = 7 => 0 pairs (X) F9,I9: 7.. / F9 = 7 => 0 pairs (X) / I9 = 7 => 0 pairs (_) B3,B4: 7.. / B3 = 7 => 18 pairs (_) / B4 = 7 => 19 pairs (_) H1,H5: 7.. / H1 = 7 => 0 pairs (X) / H5 = 7 => 0 pairs (_) I5,I9: 7.. / I5 = 7 => 0 pairs (X) / I9 = 7 => 0 pairs (_) A4,C4: 9.. / A4 = 9 => 19 pairs (_) / C4 = 9 => 18 pairs (_) E6,F6: 9.. / E6 = 9 => 0 pairs (X) / F6 = 9 => 0 pairs (_) H5,I5: 9.. / H5 = 9 => 0 pairs (X) / I5 = 9 => 0 pairs (_) B8,B9: 9.. / B8 = 9 => 0 pairs (X) / B9 = 9 => 0 pairs (_) G8,I9: 9.. / G8 = 9 => 0 pairs (*) / I9 = 9 => 0 pairs (X) B8,G8: 9.. / B8 = 9 => 0 pairs (X) / G8 = 9 => 0 pairs (_) B9,I9: 9.. / B9 = 9 => 0 pairs (*) / I9 = 9 => 0 pairs (X) C2,C4: 9.. / C2 = 9 => 19 pairs (_) / C4 = 9 => 18 pairs (_) H1,H5: 9.. / H1 = 9 => 0 pairs (*) / H5 = 9 => 0 pairs (X) I5,I9: 9.. / I5 = 9 => 0 pairs (*) / I9 = 9 => 0 pairs (X) * DURATION: 0:01:23.796610 START: 05:55:19.701791 END: 05:56:43.498401 2017-05-04 * CP COUNT: (45) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B3,B4,B8,B9,C2,C4,E6,E7,E8,F6,F7,F9,G8,H1,H5,I2,I3,I5,I9) * .325.46.8.8.63..1...68...3....1852636152438..3287..5414579..3862.13.8.548.345.12. * PAIR C2: 4,9 ROW 2 G2: 4,9,7 # reduction candidate for 4,9 G2: 7 => CTR * .325.46.8.8463.71..768..43.7491852636152438793287..5414579..3862.1378954893456127 G2: 4,9 # 23 pairs * PAIR B3: 4,7 ROW 3 G3: 4,7,9 # reduction candidate for 4,7 G3: 9 => CTR * .325.467878963241..468..93..741852636152438973287..5414579..386291368754863457129 G3: 4,7 # 21 pairs * PAIR H1: 7,9 BLK 3 G2: 7,9,4 # reduction candidate for 7,9 G2: 7,9 # 18 pairs G3: 7,9,4 # reduction candidate for 7,9 G3: 7,9 # 19 pairs * PAIR H1: 7,9 ROW 1 A1: 7,9,1 # reduction candidate for 7,9 A1: 7,9 # 19 pairs E1: 7,9,1 # reduction candidate for 7,9 E1: 7,9 # 22 pairs * PAIR A4: 7,9 COL A A1: 7,9,1 # reduction candidate for 7,9 A1: 7,9 # 19 pairs A2: 7,9,5 # reduction candidate for 7,9 A2: 7,9 # 20 pairs A3: 7,9,1,5 # reduction candidate for 7,9 A3: 7,9 # 24 pairs * PAIR E7: 1,2 COL E E3: 1,2,7,9 # reduction candidate for 1,2 E3: 1,2 # 22 pairs E3: 7,9 # 19 pairs * PAIR F7: 1,2 COL F F3: 1,2,7,9 # reduction candidate for 1,2 F3: 7,9 # 20 pairs F3: 1,2 # 20 pairs * PAIR G8: 7,9 COL G G2: 7,9,4 # reduction candidate for 7,9 G2: 7,9 # 18 pairs G3: 7,9,4 # reduction candidate for 7,9 G3: 7,9 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-092-base-pr-000.dot * REASONING * DIS # G2: 7 => CTR => G2: 4,9 * DIS # G3: 9 => CTR => G3: 4,7 * CNT 2 HDP CHAINS / 17 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B3,B4,B8,B9,C2,C4,E6,E7,E8,F6,F7,F9,G8,H1,H5,I2,I3,I5,I9) * .325.46.8.8.63..1...68...3....1852636152438..3287..5414579..3862.13.8.548.345.12. * PAIR C2: 4,9 ROW 2 G2: 4,9,7 # reduction candidate for 4,9 G2: 7 => CTR * .325.46.8.8463.71..768..43.7491852636152438793287..5414579..3862.1378954893456127 * PAIR RESTART * PAIR B3: 4,7 ROW 3 G3: 4,7,9 # reduction candidate for 4,7 G3: 9 => CTR * .325.4678.8.63.41..468..93..741852636152438973287.95414579..386291368.548.345.12. * PAIR RESTART * PAIR H1: 7,9 ROW 1 A1: 7,9,1 # reduction candidate for 7,9 A1: 7,9 => SOLVED * 732514698589637412146892735974185263615243879328769541457921386261378954893456127 * DURATION: 0:00:06.401703 START: 05:57:01.679147 END: 05:57:08.080850 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-092-base-pr-001.dot * REASONING * DIS # G2: 7 => CTR => G2: 4,9 * DIS G2: 4,9 # G3: 9 => CTR => G3: 4,7 * PRF G2: 4,9 + G3: 4,7 # A1: 7,9 => SOL * STA G2: 4,9 + G3: 4,7 + A1: 7,9 * CNT 3 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 092 solution: 732514698589637412146892735974185263615243879328769541457921386261378954893456127 info: 1567 FNBTWXY S8.f 18308 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 732514698589637412146892735974185263615243879328769541457921386261378954893456127 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 # G2: 4,9 => UNS * DIS # G2: 7 => CTR => G2: 4,9 * INC # G3: 4,7 => UNS * DIS # G3: 9 => CTR => G3: 4,7 * INC # G2: 7,9 => UNS * INC # G3: 7,9 => UNS * INC # A1: 7,9 => UNS * INC # E1: 7,9 => UNS * INC # A1: 7,9 => UNS * INC # A2: 7,9 => UNS * INC # A3: 7,9 => UNS * INC # E3: 1,2 => UNS * INC # E3: 7,9 => UNS * INC # F3: 1,2 => UNS * INC # F3: 7,9 => UNS * INC # G2: 7,9 => UNS * INC # G3: 7,9 => UNS * CNT 17 HDP CHAINS / 17 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G2: 4,9 => UNS * DIS # G2: 7 => CTR => G2: 4,9 * INC G2: 4,9 # G3: 4,7 => UNS * DIS G2: 4,9 # G3: 9 => CTR => G3: 4,7 * PRF G2: 4,9 + G3: 4,7 # A1: 7,9 => SOL * STA G2: 4,9 + G3: 4,7 + A1: 7,9 * CNT 5 HDP CHAINS / 5 HYP OPENED