Analysis of xx-top500-415-base.sdk
Contents
Original Sudoku
level: medium
position: ......6.23..8........2..5..2..3...4..67.......1...........761..8......3.......... initial
Autosolve
position: 1..7..6.232.86....67.2..5.32..3...46.67...3...136..8...324761.88.61...3.7.1...26. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 5,9 => CTR => C1: 4,8 * DIS # F2: 5,9 => CTR => F2: 1 * PRF # F2: 1 => SOL * DIS # C4: 8 => CTR => C4: 5,9 * DIS # H3: 8,9 => CTR => H3: 1 * PRF # H3: 1 => SOL * DIS # C1: 8,9 => CTR => C1: 4,5 * DIS # E4: 5,9 => CTR => E4: 1 * DIS # E5: 5,9 => CTR => E5: 2,4,8 * DIS # F5: 5,9 => CTR => F5: 2,4,8 * DIS # E6: 5,9 => CTR => E6: 2,4 * DIS # F6: 5,9 => CTR => F6: 2,4,7 * DIS # H5: 5,9 => CTR => H5: 1,2 * DIS # I5: 5,9 => CTR => I5: 1 * PRF # H6: 7,9 => SOL * DIS # F4: 7,9 => CTR => F4: 1,5 * DIS # I8: 5,9 => CTR => I8: 4,7 * DIS # H5: 5,9 => CTR => H5: 1,2 * PRF # H6: 5,9 => SOL * CNT 19 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 5,9 => CTR => C1: 4,8 * DIS C1: 4,8 # B1: 8 => CTR => B1: 5,9 * DIS C1: 4,8 + B1: 5,9 # F2: 5,9 => CTR => F2: 1 * PRF C1: 4,8 + B1: 5,9 + F2: 1 => SOL * STA C1: 4,8 + B1: 5,9 + F2: 1 * CNT 4 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ......6.23..8........2..5..2..3...4..67.......1...........761..8......3.......... | initial |
| 1..7..6.232.86....67.2..5.32..3...46.67...3...136..8...324761.88.61...3.7.1...26. | autosolve |
| 194753682325861974678249513289315746567984321413627895932476158856192437741538269 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) C2: 5,9 H1: 8,9 D5: 5,9 G4: 7,9 A7: 5,9 D9: 5,9 E9: 3,8 F9: 3,8 H7: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E4,F4: 1.. / E4 = 1 => 10 pairs (_) / F4 = 1 => 0 pairs (X) H5,I5: 1.. / H5 = 1 => 0 pairs (X) / I5 = 1 => 9 pairs (_) E3,E4: 1.. / E3 = 1 => 0 pairs (X) / E4 = 1 => 10 pairs (_) I2,I5: 1.. / I2 = 1 => 0 pairs (X) / I5 = 1 => 9 pairs (_) H5,H6: 2.. / H5 = 2 => 10 pairs (_) / H6 = 2 => 13 pairs (_) E8,F8: 2.. / E8 = 2 => 10 pairs (_) / F8 = 2 => 10 pairs (_) E1,F1: 3.. / E1 = 3 => 8 pairs (_) / F1 = 3 => 7 pairs (_) E9,F9: 3.. / E9 = 3 => 7 pairs (_) / F9 = 3 => 8 pairs (_) E1,E9: 3.. / E1 = 3 => 8 pairs (_) / E9 = 3 => 7 pairs (_) F1,F9: 3.. / F1 = 3 => 7 pairs (_) / F9 = 3 => 8 pairs (_) C1,C3: 4.. / C1 = 4 => 10 pairs (_) / C3 = 4 => 0 pairs (X) G2,I2: 4.. / G2 = 4 => 10 pairs (_) / I2 = 4 => 13 pairs (_) A5,A6: 4.. / A5 = 4 => 10 pairs (_) / A6 = 4 => 13 pairs (_) B8,B9: 4.. / B8 = 4 => 11 pairs (_) / B9 = 4 => 13 pairs (_) B9,I9: 4.. / B9 = 4 => 13 pairs (_) / I9 = 4 => 11 pairs (_) G2,G8: 4.. / G2 = 4 => 10 pairs (_) / G8 = 4 => 13 pairs (_) C2,F2: 5.. / C2 = 5 => 14 pairs (_) / F2 = 5 => 0 pairs (X) A7,H7: 5.. / A7 = 5 => 0 pairs (X) / H7 = 5 => 0 pairs (_) D5,D9: 5.. / D5 = 5 => 0 pairs (X) / D9 = 5 => 16 pairs (_) F4,F6: 7.. / F4 = 7 => 0 pairs (X) / F6 = 7 => 12 pairs (_) G8,I8: 7.. / G8 = 7 => 0 pairs (X) / I8 = 7 => 11 pairs (_) F4,G4: 7.. / F4 = 7 => 0 pairs (X) / G4 = 7 => 12 pairs (_) H2,H6: 7.. / H2 = 7 => 10 pairs (_) / H6 = 7 => 0 pairs (X) H1,H3: 8.. / H1 = 8 => 11 pairs (_) / H3 = 8 => 0 pairs (X) B4,C4: 8.. / B4 = 8 => 13 pairs (_) / C4 = 8 => 0 pairs (X) E5,F5: 8.. / E5 = 8 => 7 pairs (_) / F5 = 8 => 8 pairs (_) E9,F9: 8.. / E9 = 8 => 8 pairs (_) / F9 = 8 => 7 pairs (_) C3,H3: 8.. / C3 = 8 => 11 pairs (_) / H3 = 8 => 0 pairs (X) B1,B4: 8.. / B1 = 8 => 0 pairs (X) / B4 = 8 => 13 pairs (_) E5,E9: 8.. / E5 = 8 => 7 pairs (_) / E9 = 8 => 8 pairs (_) F5,F9: 8.. / F5 = 8 => 8 pairs (_) / F9 = 8 => 7 pairs (_) A7,H7: 9.. / A7 = 9 => 0 pairs (*) / H7 = 9 => 0 pairs (X) D5,D9: 9.. / D5 = 9 => 16 pairs (_) / D9 = 9 => 0 pairs (X) * DURATION: 0:00:59.467965 START: 17:00:39.243309 END: 17:01:38.711274 2017-05-04 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,C2,D5,D9,E9,F9,G4,H1,H7) * 1..7..6.232.86....67.2..5.32..3...46.67...3...136..8...324761.88.61...3.7.1...26. * PAIR C2: 5,9 BLK 1 B1: 5,9,8 # reduction candidate for 5,9 B1: 5,9 # 13 pairs C1: 5,9,4,8 # reduction candidate for 5,9 C1: 5,9 => CTR * 1857..692329865...6742..583298351746.679..3...136.78299324761588561..93.7.1...26. C1: 4,8 # 10 pairs * PAIR C2: 5,9 ROW 2 F2: 5,9,1 # reduction candidate for 5,9 F2: 5,9 => CTR * 1..7..6.232.86.47167.2..5.32..3..746.675..3195136.782.9324761588.61..9377.19..264 F2: 1 => SOLVED * 194753682325861974678249513289315746567984321413627895932476158856192437741538269 * PAIR C2: 5,9 COL C C4: 5,9,8 # reduction candidate for 5,9 C4: 8 => CTR * 18.7..69232.86.47167.2..5832983..746.675..3195136.782.9324761588.61..9377.19..264 C4: 5,9 # 13 pairs * PAIR H1: 8,9 BLK 3 H3: 8,9,1 # reduction candidate for 8,9 H3: 8,9 => CTR * 1..7..6.232.86.47167.2..5.32..3..746.675..3195136.782.9324761588.61..9377.19..264 H3: 1 => SOLVED * 194753682325861974678249513289315746567984321413627895932476158856192437741538269 * PAIR H1: 8,9 ROW 1 B1: 8,9,5 # reduction candidate for 8,9 B1: 8,9 # 12 pairs C1: 8,9,4,5 # reduction candidate for 8,9 C1: 8,9 => CTR * 1..7..692329865...6742..5832.53...46.67...3...136..8...324761.88.61...3.7.1...26. C1: 4,5 # 10 pairs * PAIR D5: 5,9 BLK 5 E4: 5,9,1 # reduction candidate for 5,9 E4: 5,9 => CTR * 1..7..6.232.86.47167.21.5.32..3.1746.675..3195136.782.9324761588461..9377519..264 E4: 1 # 10 pairs F4: 5,9,1,7 # reduction candidate for 5,9 F4: 5,9 # 14 pairs E5: 5,9,2,4,8 # reduction candidate for 5,9 E5: 5,9 => CTR * 1..73.68232.86...96782..5132853...46467..83219136..8..5324761988.61...3.7.1.8326. E5: 2,4,8 # 9 pairs F5: 5,9,2,4,8 # reduction candidate for 5,9 F5: 5,9 => CTR * 1..7.368232.86...96782..5132853...46467.8.3219136..8..5324761988.61...3.7.1.3826. F5: 2,4,8 # 9 pairs E6: 5,9,2,4 # reduction candidate for 5,9 E6: 5,9 => CTR * 1..7..68232.86...96782..513285317946.67...3...136..8..5324761988.61...3.7.1...26. E6: 2,4 # 10 pairs F6: 5,9,2,4,7 # reduction candidate for 5,9 F6: 5,9 => CTR * 1..7..68232.86...96782..513285317946.67...3...136..8..5324761988.61...3.7.1...26. F6: 2,4,7 # 9 pairs * PAIR D5: 5,9 ROW 5 A5: 5,9,4 # reduction candidate for 5,9 A5: 5,9 # 13 pairs H5: 5,9,1,2 # reduction candidate for 5,9 H5: 5,9 => CTR * 1.47..682325861.7.6782..513289315746.679..3515136..82..324761.88.61...3.7.1...26. H5: 1,2 # 10 pairs I5: 5,9,1 # reduction candidate for 5,9 I5: 5,9 => CTR * 1..7..6.232.86.47167.2..5.32..3..746.675..3195136.782.9324761588.61..9377.19..264 I5: 1 # 9 pairs * PAIR G4: 7,9 BLK 6 H6: 7,9,2,5 # reduction candidate for 7,9 H6: 7,9 => SOLVED * 194753682325861974678249513289315746567984321413627895932476158856192437741538269 H6: 2,5 # 11 pairs I6: 7,9,5 # reduction candidate for 7,9 I6: 7,9 # 13 pairs * PAIR G4: 7,9 ROW 4 F4: 7,9,1,5 # reduction candidate for 7,9 F4: 7,9 => CTR * 1..7..68232.86....6782..51328531..46.67...3.1.136..8..5324761988.61...3.7.1...26. F4: 1,5 # 13 pairs * PAIR G4: 7,9 COL G G2: 7,9,4 # reduction candidate for 7,9 G2: 7,9 # 13 pairs G8: 7,9,4 # reduction candidate for 7,9 G8: 7,9 # 10 pairs * PAIR A7: 5,9 BLK 7 B8: 5,9,4 # reduction candidate for 5,9 B8: 5,9 # 13 pairs B9: 5,9,4 # reduction candidate for 5,9 B9: 5,9 # 11 pairs * PAIR A7: 5,9 COL A A5: 5,9,4 # reduction candidate for 5,9 A5: 5,9 # 13 pairs A6: 5,9,4 # reduction candidate for 5,9 A6: 5,9 # 10 pairs * PAIR D9: 5,9 BLK 8 E8: 5,9,2 # reduction candidate for 5,9 E8: 5,9 # 10 pairs F8: 5,9,2 # reduction candidate for 5,9 F8: 5,9 # 10 pairs * PAIR D9: 5,9 ROW 9 B9: 5,9,4 # reduction candidate for 5,9 B9: 5,9 # 11 pairs I9: 5,9,4 # reduction candidate for 5,9 I9: 5,9 # 13 pairs * PAIR H7: 5,9 BLK 9 I8: 5,9,4,7 # reduction candidate for 5,9 I8: 5,9 => CTR * 1..7..68232.86.4.96782..513285317946.67...3...136..8..5324761988461..7357915..264 I8: 4,7 # 10 pairs I9: 5,9,4 # reduction candidate for 5,9 I9: 5,9 # 13 pairs * PAIR H7: 5,9 COL H H5: 5,9,1,2 # reduction candidate for 5,9 H5: 5,9 => CTR * 1.47..682325861.7.6782..513289315746.679..3515136..82..324761.88.61...3.7.1...26. H5: 1,2 # 10 pairs H6: 5,9,2,7 # reduction candidate for 5,9 H6: 5,9 => SOLVED * 194753682325861974678249513289315746567984321413627895932476158856192437741538269 H6: 2,7 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-415-base-pr-000.dot * REASONING * DIS # C1: 5,9 => CTR => C1: 4,8 * DIS # F2: 5,9 => CTR => F2: 1 * PRF # F2: 1 => SOL * DIS # C4: 8 => CTR => C4: 5,9 * DIS # H3: 8,9 => CTR => H3: 1 * PRF # H3: 1 => SOL * DIS # C1: 8,9 => CTR => C1: 4,5 * DIS # E4: 5,9 => CTR => E4: 1 * DIS # E5: 5,9 => CTR => E5: 2,4,8 * DIS # F5: 5,9 => CTR => F5: 2,4,8 * DIS # E6: 5,9 => CTR => E6: 2,4 * DIS # F6: 5,9 => CTR => F6: 2,4,7 * DIS # H5: 5,9 => CTR => H5: 1,2 * DIS # I5: 5,9 => CTR => I5: 1 * PRF # H6: 7,9 => SOL * DIS # F4: 7,9 => CTR => F4: 1,5 * DIS # I8: 5,9 => CTR => I8: 4,7 * DIS # H5: 5,9 => CTR => H5: 1,2 * PRF # H6: 5,9 => SOL * CNT 19 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,C2,D5,D9,E9,F9,G4,H1,H7) * 1..7..6.232.86....67.2..5.32..3...46.67...3...136..8...324761.88.61...3.7.1...26. * PAIR C2: 5,9 BLK 1 B1: 5,9,8 # reduction candidate for 5,9 B1: 5,9 # 13 pairs C1: 5,9,4,8 # reduction candidate for 5,9 C1: 5,9 => CTR * 1857..692329865...6742..583298351746.679..3...136.78299324761588561..93.7.1...26. * RESTART * PAIR C2: 5,9 BLK 1 B1: 5,9,8 # reduction candidate for 5,9 B1: 8 => CTR * 1847..6923258694716792..5832983..746.675..3195136.782.9324761588.61..9377.19..264 * PAIR C2: 5,9 ROW 2 F2: 5,9,1 # reduction candidate for 5,9 F2: 5,9 => CTR * 1947..6823258694716782..5932893..746.675..3195136.782.9324761588.61..9377.19..264 F2: 1 => SOLVED * 194753682325861974678249513289315746567984321413627895932476158856192437741538269 * DURATION: 0:00:07.960204 START: 17:02:28.824258 END: 17:02:36.784462 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-415-base-pr-001.dot * REASONING * DIS # C1: 5,9 => CTR => C1: 4,8 * DIS C1: 4,8 # B1: 8 => CTR => B1: 5,9 * DIS C1: 4,8 + B1: 5,9 # F2: 5,9 => CTR => F2: 1 * PRF C1: 4,8 + B1: 5,9 + F2: 1 => SOL * STA C1: 4,8 + B1: 5,9 + F2: 1 * CNT 4 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 415 solution: 194753682325861974678249513289315746567984321413627895932476158856192437741538269 info: 95067 FNBHYK S8.f 1458 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 194753682325861974678249513289315746567984321413627895932476158856192437741538269 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 # B1: 5,9 => UNS * DIS # C1: 5,9 => CTR => C1: 4,8 * INC # C1: 4,8 => UNS * DIS # F2: 5,9 => CTR => F2: 1 * PRF # F2: 1 => SOL * INC # C4: 5,9 => UNS * DIS # C4: 8 => CTR => C4: 5,9 * DIS # H3: 8,9 => CTR => H3: 1 * PRF # H3: 1 => SOL * INC # B1: 8,9 => UNS * DIS # C1: 8,9 => CTR => C1: 4,5 * INC # C1: 4,5 => UNS * DIS # E4: 5,9 => CTR => E4: 1 * INC # E4: 1 => UNS * INC # F4: 5,9 => UNS * DIS # E5: 5,9 => CTR => E5: 2,4,8 * INC # E5: 2,4,8 => UNS * DIS # F5: 5,9 => CTR => F5: 2,4,8 * INC # F5: 2,4,8 => UNS * DIS # E6: 5,9 => CTR => E6: 2,4 * INC # E6: 2,4 => UNS * DIS # F6: 5,9 => CTR => F6: 2,4,7 * INC # F6: 2,4,7 => UNS * INC # A5: 5,9 => UNS * DIS # H5: 5,9 => CTR => H5: 1,2 * INC # H5: 1,2 => UNS * DIS # I5: 5,9 => CTR => I5: 1 * INC # I5: 1 => UNS * PRF # H6: 7,9 => SOL * INC # H6: 2,5 => UNS * INC # I6: 7,9 => UNS * DIS # F4: 7,9 => CTR => F4: 1,5 * INC # F4: 1,5 => UNS * INC # G2: 7,9 => UNS * INC # G8: 7,9 => UNS * INC # B8: 5,9 => UNS * INC # B9: 5,9 => UNS * INC # A5: 5,9 => UNS * INC # A6: 5,9 => UNS * INC # E8: 5,9 => UNS * INC # F8: 5,9 => UNS * INC # B9: 5,9 => UNS * INC # I9: 5,9 => UNS * DIS # I8: 5,9 => CTR => I8: 4,7 * INC # I8: 4,7 => UNS * INC # I9: 5,9 => UNS * DIS # H5: 5,9 => CTR => H5: 1,2 * INC # H5: 1,2 => UNS * PRF # H6: 5,9 => SOL * INC # H6: 2,7 => UNS * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 5,9 => UNS * DIS # C1: 5,9 => CTR => C1: 4,8 * INC C1: 4,8 # B1: 5,9 => UNS * DIS C1: 4,8 # B1: 8 => CTR => B1: 5,9 * DIS C1: 4,8 + B1: 5,9 # F2: 5,9 => CTR => F2: 1 * PRF C1: 4,8 + B1: 5,9 + F2: 1 => SOL * STA C1: 4,8 + B1: 5,9 + F2: 1 * CNT 6 HDP CHAINS / 5 HYP OPENED