Analysis of xx-top500-411-base.sdk
Contents
Original Sudoku
level: medium
position: 71..2...8.......6.4..........65...1..35............4..2.....9.....6.3......1..... initial
Autosolve
position: 719.26..835.....6.46........465...1..352..6...27.6.4..2.1...9365.46.3...6.31.2... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # H9: 4,5 => SOL * DIS # H9: 7,8 => CTR => H9: 4,5 * DIS # I4: 7,9 => CTR => I4: 2,3 * DIS # I2: 7,9 => CTR => I2: 1,2,4 * DIS # E7: 7,8 => CTR => E7: 4,5 * DIS # F7: 7,8 => CTR => F7: 4,5 * CNT 6 HDP CHAINS / 21 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # H9: 4,5 => SOL * STA H9: 4,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 71..2...8.......6.4..........65...1..35............4..2.....9.....6.3......1..... | initial |
| 719.26..835.....6.46........465...1..352..6...27.6.4..2.1...9365.46.3...6.31.2... | autosolve |
| 719426358352918764468735192946587213835241679127369485271854936594673821683192547 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) C2: 2,8 C3: 2,8 D1: 3,4 G1: 3,5 H1: 4,5 A4: 8,9 I5: 7,9 B7: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A5,A6: 1.. / A5 = 1 => 9 pairs (_) / A6 = 1 => 12 pairs (_) G8,I8: 1.. / G8 = 1 => 10 pairs (_) / I8 = 1 => 8 pairs (_) A6,F6: 1.. / A6 = 1 => 12 pairs (_) / F6 = 1 => 9 pairs (_) C2,C3: 2.. / C2 = 2 => 7 pairs (_) / C3 = 2 => 8 pairs (_) G4,I4: 2.. / G4 = 2 => 10 pairs (_) / I4 = 2 => 9 pairs (_) H3,H8: 2.. / H3 = 2 => 14 pairs (_) / H8 = 2 => 10 pairs (_) E4,D6: 3.. / E4 = 3 => 0 pairs (X) / D6 = 3 => 0 pairs (_) D1,G1: 3.. / D1 = 3 => 0 pairs (X) / G1 = 3 => 0 pairs (_) D6,I6: 3.. / D6 = 3 => 0 pairs (*) / I6 = 3 => 0 pairs (X) E3,E4: 3.. / E3 = 3 => 0 pairs (*) / E4 = 3 => 0 pairs (X) H1,I2: 4.. / H1 = 4 => 0 pairs (X) / I2 = 4 => 0 pairs (_) E5,F5: 4.. / E5 = 4 => 8 pairs (_) / F5 = 4 => 8 pairs (_) H9,I9: 4.. / H9 = 4 => 0 pairs (*) / I9 = 4 => 0 pairs (X) D1,H1: 4.. / D1 = 4 => 0 pairs (*) / H1 = 4 => 0 pairs (X) H1,H9: 4.. / H1 = 4 => 0 pairs (X) / H9 = 4 => 0 pairs (_) I2,I9: 4.. / I2 = 4 => 0 pairs (*) / I9 = 4 => 0 pairs (X) E3,F3: 5.. / E3 = 5 => 0 pairs (X) / F3 = 5 => 8 pairs (_) G1,H1: 5.. / G1 = 5 => 0 pairs (X) / H1 = 5 => 0 pairs (_) H6,I6: 5.. / H6 = 5 => 0 pairs (X) / I6 = 5 => 0 pairs (_) E7,F7: 5.. / E7 = 5 => 8 pairs (_) / F7 = 5 => 0 pairs (X) E3,E7: 5.. / E3 = 5 => 0 pairs (X) / E7 = 5 => 8 pairs (_) F3,F7: 5.. / F3 = 5 => 8 pairs (_) / F7 = 5 => 0 pairs (X) G1,G9: 5.. / G1 = 5 => 0 pairs (X) / G9 = 5 => 0 pairs (_) I6,I9: 5.. / I6 = 5 => 0 pairs (*) / I9 = 5 => 0 pairs (X) C2,C3: 8.. / C2 = 8 => 8 pairs (_) / C3 = 8 => 7 pairs (_) B8,B9: 9.. / B8 = 9 => 10 pairs (_) / B9 = 9 => 10 pairs (_) E8,E9: 9.. / E8 = 9 => 10 pairs (_) / E9 = 9 => 10 pairs (_) B8,E8: 9.. / B8 = 9 => 10 pairs (_) / E8 = 9 => 10 pairs (_) B9,E9: 9.. / B9 = 9 => 10 pairs (_) / E9 = 9 => 10 pairs (_) * DURATION: 0:00:42.468013 START: 16:51:44.939980 END: 16:52:27.407993 2017-05-04 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B7,C2,C3,D1,G1,H1,I5) * 719.26..835.....6.46........465...1..352..6...27.6.4..2.1...9365.46.3...6.31.2... * PAIR H1: 4,5 COL H H9: 4,5,7,8 # reduction candidate for 4,5 H9: 4,5 => SOLVED * 719426358352918764468735192946587213835241679127369485271854936594673821683192547 H9: 7,8 => CTR * 719.26.4835.....6.46........465...1..352..6...27.6.45.2.1...9365.46.3...6.31.2... * PAIR A4: 8,9 BLK 4 A5: 8,9,1 # reduction candidate for 8,9 A5: 8,9 # 12 pairs A6: 8,9,1 # reduction candidate for 8,9 A6: 8,9 # 9 pairs * PAIR A4: 8,9 ROW 4 F4: 8,9,7 # reduction candidate for 8,9 F4: 8,9 # 11 pairs F4: 7 # 9 pairs * PAIR I5: 7,9 BLK 6 I4: 7,9,2,3 # reduction candidate for 7,9 I4: 7,9 => CTR * 719.2654835.....6.46....3...4653.21..352..6...27.6.4532.1...9365.46.3...6.31.2..5 I4: 2,3 # 9 pairs H5: 7,9,8 # reduction candidate for 7,9 H5: 7,9 # 13 pairs * PAIR I5: 7,9 ROW 5 F5: 7,9,1,4,8 # reduction candidate for 7,9 F5: 7,9 # 12 pairs F5: 1,4,8 # 8 pairs * PAIR I5: 7,9 COL I I2: 7,9,1,2,4 # reduction candidate for 7,9 I2: 7,9 => CTR * 71932654835.....6.46........4653..1..352..6...27.6.4..2.1...9365.46.3...6.31.2..4 I2: 1,2,4 # 8 pairs I3: 7,9,1,2,3 # reduction candidate for 7,9 I3: 7,9 # 13 pairs * PAIR B7: 7,8 BLK 7 B8: 7,8,9 # reduction candidate for 7,8 B8: 7,8 # 10 pairs B9: 7,8,9 # reduction candidate for 7,8 B9: 7,8 # 10 pairs * PAIR B7: 7,8 ROW 7 D7: 7,8,4 # reduction candidate for 7,8 D7: 7,8 # 11 pairs E7: 7,8,4,5 # reduction candidate for 7,8 E7: 7,8 => CTR * 719.2654835.....6.46..5.3...4653..1..352..6...27.6.4532.14.59365.46.3...6.31.2..5 E7: 4,5 # 9 pairs F7: 7,8,4,5 # reduction candidate for 7,8 F7: 7,8 => CTR * 71932654835.....6.46...5....4653..1..352..6...27.6.4.32.145.9365.46.3...6.31.2... F7: 4,5 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-411-base-pr-000.dot * REASONING * PRF # H9: 4,5 => SOL * DIS # H9: 7,8 => CTR => H9: 4,5 * DIS # I4: 7,9 => CTR => I4: 2,3 * DIS # I2: 7,9 => CTR => I2: 1,2,4 * DIS # E7: 7,8 => CTR => E7: 4,5 * DIS # F7: 7,8 => CTR => F7: 4,5 * CNT 6 HDP CHAINS / 21 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B7,C2,C3,D1,G1,H1,I5) * 719.26..835.....6.46........465...1..352..6...27.6.4..2.1...9365.46.3...6.31.2... * PAIR H1: 4,5 COL H H9: 4,5,7,8 # reduction candidate for 4,5 H9: 4,5 => SOLVED * 719426358352918764468735192946587213835241679127369485271854936594673821683192547 * DURATION: 0:00:02.575119 START: 16:52:43.533035 END: 16:52:46.108154 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-411-base-pr-001.dot * REASONING * PRF # H9: 4,5 => SOL * STA H9: 4,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 411 solution: 719426358352918764468735192946587213835241679127369485271854936594673821683192547 info: 95022 FNBXYK S8.f 37504 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 719426358352918764468735192946587213835241679127369485271854936594673821683192547 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:
* PRF # H9: 4,5 => SOL * DIS # H9: 7,8 => CTR => H9: 4,5 * INC # A5: 8,9 => UNS * INC # A6: 8,9 => UNS * INC # F4: 8,9 => UNS * INC # F4: 7 => UNS * DIS # I4: 7,9 => CTR => I4: 2,3 * INC # I4: 2,3 => UNS * INC # H5: 7,9 => UNS * INC # F5: 7,9 => UNS * INC # F5: 1,4,8 => UNS * DIS # I2: 7,9 => CTR => I2: 1,2,4 * INC # I2: 1,2,4 => UNS * INC # I3: 7,9 => UNS * INC # B8: 7,8 => UNS * INC # B9: 7,8 => UNS * INC # D7: 7,8 => UNS * DIS # E7: 7,8 => CTR => E7: 4,5 * INC # E7: 4,5 => UNS * DIS # F7: 7,8 => CTR => F7: 4,5 * INC # F7: 4,5 => UNS * CNT 21 HDP CHAINS / 21 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # H9: 4,5 => SOL * STA H9: 4,5 * CNT 1 HDP CHAINS / 1 HYP OPENED