Analysis of xx-top500-370-base.sdk
Contents
Original Sudoku
level: medium
position: .41..........23.......9....6......54...8...1.3........2.....9.....1..3...7.5..... initial
Autosolve
position: 941....325...231...32.915..618937254.298...1335.21.8..2.53..9.1.9.1.23.51735.942. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # I3: 6 => SOL * DIS # D3: 4 => CTR => D3: 6,7 * PRF # D3: 4,7 => SOL * DIS # D3: 6 => CTR => D3: 4,7 * DIS # I3: 8 => CTR => I3: 6,7 * DIS # F5: 4,6 => CTR => F5: 5 * DIS # F7: 8 => CTR => F7: 4,6 * DIS # I6: 9 => CTR => I6: 6,7 * DIS # I6: 6,9 => CTR => I6: 7 * PRF # I6: 7 => SOL * DIS # E7: 6,8 => CTR => E7: 4,7 * PRF # H7: 6,8 => SOL * DIS # E7: 6,8 => CTR => E7: 4,7 * PRF # E8: 6,8 => SOL * PRF # H7: 6,8 => SOL * DIS # I3: 7 => CTR => I3: 6,8 * CNT 16 HDP CHAINS / 32 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # I3: 6 => SOL * STA I3: 6 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .41..........23.......9....6......54...8...1.3........2.....9.....1..3...7.5..... | initial |
| 941....325...231...32.915..618937254.298...1335.21.8..2.53..9.1.9.1.23.51735.942. | autosolve |
| 941658732567423189832791546618937254729845613354216897285374961496182375173569428 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) B2: 6,8 C2: 6,7 A3: 7,8 D1: 6,7 E1: 5,8 F1: 5,8 D2: 4,7 G1: 6,7 A5: 4,7 C6: 4,7 F6: 4,6 G5: 6,7 H6: 6,9 B7: 6,8 A8: 4,8 C8: 4,6 E9: 6,8 I9: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,D3: 4.. / D2 = 4 => 19 pairs (_) / D3 = 4 => 0 pairs (X) H2,H3: 4.. / H2 = 4 => 0 pairs (X) / H3 = 4 => 19 pairs (_) A5,C6: 4.. / A5 = 4 => 0 pairs (X) / C6 = 4 => 0 pairs (_) A8,C8: 4.. / A8 = 4 => 0 pairs (*) / C8 = 4 => 0 pairs (X) E7,F7: 4.. / E7 = 4 => 21 pairs (_) / F7 = 4 => 0 pairs (*) D2,H2: 4.. / D2 = 4 => 19 pairs (_) / H2 = 4 => 0 pairs (X) D3,H3: 4.. / D3 = 4 => 0 pairs (X) / H3 = 4 => 19 pairs (_) C6,F6: 4.. / C6 = 4 => 0 pairs (*) / F6 = 4 => 0 pairs (X) A5,A8: 4.. / A5 = 4 => 0 pairs (X) / A8 = 4 => 0 pairs (_) C6,C8: 4.. / C6 = 4 => 0 pairs (*) / C8 = 4 => 0 pairs (X) E5,E7: 4.. / E5 = 4 => 0 pairs (*) / E7 = 4 => 0 pairs (X) E1,F1: 5.. / E1 = 5 => 18 pairs (_) / F1 = 5 => 0 pairs (X) E5,F5: 5.. / E5 = 5 => 0 pairs (X) / F5 = 5 => 18 pairs (_) E1,E5: 5.. / E1 = 5 => 18 pairs (_) / E5 = 5 => 0 pairs (X) F1,F5: 5.. / F1 = 5 => 0 pairs (X) / F5 = 5 => 18 pairs (_) B2,C2: 6.. / B2 = 6 => 0 pairs (*) / C2 = 6 => 0 pairs (X) D1,D3: 6.. / D1 = 6 => 0 pairs (*) / D3 = 6 => 0 pairs (X) B7,C8: 6.. / B7 = 6 => 0 pairs (X) / C8 = 6 => 0 pairs (_) D1,G1: 6.. / D1 = 6 => 0 pairs (*) / G1 = 6 => 0 pairs (X) E9,I9: 6.. / E9 = 6 => 24 pairs (_) / I9 = 6 => 24 pairs (_) B2,B7: 6.. / B2 = 6 => 0 pairs (*) / B7 = 6 => 0 pairs (X) C2,C8: 6.. / C2 = 6 => 0 pairs (X) / C8 = 6 => 0 pairs (_) G1,G5: 6.. / G1 = 6 => 0 pairs (X) / G5 = 6 => 0 pairs (_) C2,A3: 7.. / C2 = 7 => 0 pairs (*) / A3 = 7 => 0 pairs (X) A5,C6: 7.. / A5 = 7 => 0 pairs (*) / C6 = 7 => 0 pairs (X) G5,I6: 7.. / G5 = 7 => 0 pairs (X) / I6 = 7 => 0 pairs (_) E7,E8: 7.. / E7 = 7 => 0 pairs (*) / E8 = 7 => 0 pairs (X) H7,H8: 7.. / H7 = 7 => 19 pairs (_) / H8 = 7 => 0 pairs (*) D1,G1: 7.. / D1 = 7 => 0 pairs (X) / G1 = 7 => 0 pairs (_) A5,G5: 7.. / A5 = 7 => 0 pairs (*) / G5 = 7 => 0 pairs (X) C6,I6: 7.. / C6 = 7 => 0 pairs (X) / I6 = 7 => 0 pairs (_) E7,H7: 7.. / E7 = 7 => 0 pairs (*) / H7 = 7 => 0 pairs (X) E8,H8: 7.. / E8 = 7 => 19 pairs (_) / H8 = 7 => 0 pairs (*) A3,A5: 7.. / A3 = 7 => 0 pairs (X) / A5 = 7 => 0 pairs (_) C2,C6: 7.. / C2 = 7 => 0 pairs (*) / C6 = 7 => 0 pairs (X) G1,G5: 7.. / G1 = 7 => 0 pairs (*) / G5 = 7 => 0 pairs (X) B2,A3: 8.. / B2 = 8 => 0 pairs (X) / A3 = 8 => 0 pairs (_) E1,F1: 8.. / E1 = 8 => 0 pairs (X) / F1 = 8 => 18 pairs (_) B7,A8: 8.. / B7 = 8 => 0 pairs (*) / A8 = 8 => 0 pairs (X) E9,I9: 8.. / E9 = 8 => 24 pairs (_) / I9 = 8 => 24 pairs (_) A3,A8: 8.. / A3 = 8 => 0 pairs (*) / A8 = 8 => 0 pairs (X) B2,B7: 8.. / B2 = 8 => 0 pairs (X) / B7 = 8 => 0 pairs (_) F1,F7: 8.. / F1 = 8 => 18 pairs (_) / F7 = 8 => 0 pairs (X) H2,I2: 9.. / H2 = 9 => 0 pairs (X) / I2 = 9 => 19 pairs (_) H6,I6: 9.. / H6 = 9 => 19 pairs (_) / I6 = 9 => 0 pairs (X) H2,H6: 9.. / H2 = 9 => 0 pairs (X) / H6 = 9 => 19 pairs (_) I2,I6: 9.. / I2 = 9 => 19 pairs (_) / I6 = 9 => 0 pairs (X) * DURATION: 0:01:41.347122 START: 15:29:31.459242 END: 15:31:12.806364 2017-05-04 * CP COUNT: (47) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,A8,B2,B7,C2,C6,C8,D1,D2,E1,E9,F1,F6,G1,G5,H6,I9) * 941....325...231...32.915..618937254.298...1335.21.8..2.53..9.1.9.1.23.51735.942. * PAIR A3: 7,8 ROW 3 I3: 7,8,6 # reduction candidate for 7,8 I3: 6 => SOLVED * 941658732567423189832791546618937254729845613354216897285374961496182375173569428 I3: 7,8 # 21 pairs * PAIR D1: 6,7 BLK 2 D3: 6,7,4 # reduction candidate for 6,7 D3: 4 => CTR * 9416..7325..7231497324915..6189372544298..61335721.8..2.53..9.1.9.1.23.51735.942. D3: 6,7 # 19 pairs * PAIR D2: 4,7 BLK 2 D3: 4,7,6 # reduction candidate for 4,7 D3: 4,7 => SOLVED * 941658732567423189832791546618937254729845613354216897285374961496182375173569428 D3: 6 => CTR * 9417..6325..4231...3269154.618937254.298..7133572148..2.534.971.94172365173569428 * PAIR G1: 6,7 BLK 3 I3: 6,7,8 # reduction candidate for 6,7 I3: 8 => CTR * 941.58.32586.231..732.915.86189372544298657133572148692653..9.18941.23.5173589426 I3: 6,7 # 21 pairs * PAIR F6: 4,6 BLK 5 E5: 4,6,5 # reduction candidate for 4,6 E5: 4,6 # 18 pairs F5: 4,6,5 # reduction candidate for 4,6 F5: 4,6 => CTR * 941.85.32586.231..732.9158661893725442985..1335.21.8..2.5348971894172365173569428 F5: 5 # 18 pairs * PAIR F6: 4,6 COL F F7: 4,6,8 # reduction candidate for 4,6 F7: 8 => CTR * 941.85.32586.231..732.915866189372544298...1335.21.8..2.5348971894172365173569428 F7: 4,6 # 18 pairs * PAIR G5: 6,7 BLK 6 I6: 6,7,9 # reduction candidate for 6,7 I6: 9 => CTR * 941....325...231...32.915..618937254.298..7133572148692.534.971.941.23.51735.942. I6: 6,7 # 19 pairs * PAIR H6: 6,9 BLK 6 I6: 6,9,7 # reduction candidate for 6,9 I6: 6,9 => CTR * 9417856325.64231.7.32.915..618937254.298..7133572148..2.534.971.94172365173569428 I6: 7 => SOLVED * 941658732567423189832791546618937254729845613354216897285374961496182375173569428 * PAIR B7: 6,8 ROW 7 E7: 6,8,4,7 # reduction candidate for 6,8 E7: 6,8 => CTR * 941658732567.231...32.915..618937254.298456133542168972.53.4971496172385173589426 E7: 4,7 # 19 pairs F7: 6,8,4 # reduction candidate for 6,8 F7: 6,8 # 21 pairs H7: 6,8,7 # reduction candidate for 6,8 H7: 6,8 => SOLVED * 941658732567423189832791546618937254729845613354216897285374961496182375173569428 H7: 7 # 19 pairs * PAIR E9: 6,8 BLK 8 E7: 6,8,4,7 # reduction candidate for 6,8 E7: 6,8 => CTR * 941658732567.231...32.915..618937254.298456133542168972.53.4971496172385173589426 E7: 4,7 # 19 pairs F7: 6,8,4 # reduction candidate for 6,8 F7: 6,8 # 21 pairs E8: 6,8,7 # reduction candidate for 6,8 E8: 6,8 => SOLVED * 941658732567423189832791546618937254729845613354216897285374961496182375173569428 E8: 7 # 19 pairs * PAIR I9: 6,8 BLK 9 H7: 6,8,7 # reduction candidate for 6,8 H7: 6,8 => SOLVED * 941658732567423189832791546618937254729845613354216897285374961496182375173569428 H7: 7 # 19 pairs H8: 6,8,7 # reduction candidate for 6,8 H8: 6,8 # 19 pairs * PAIR I9: 6,8 COL I I3: 6,8,7 # reduction candidate for 6,8 I3: 7 => CTR * 941....325...231...32.915.76189372547298..61335.21.8..2.53..9.1.9.1.23.51735.942. I3: 6,8 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-370-base-pr-000.dot * REASONING * PRF # I3: 6 => SOL * DIS # D3: 4 => CTR => D3: 6,7 * PRF # D3: 4,7 => SOL * DIS # D3: 6 => CTR => D3: 4,7 * DIS # I3: 8 => CTR => I3: 6,7 * DIS # F5: 4,6 => CTR => F5: 5 * DIS # F7: 8 => CTR => F7: 4,6 * DIS # I6: 9 => CTR => I6: 6,7 * DIS # I6: 6,9 => CTR => I6: 7 * PRF # I6: 7 => SOL * DIS # E7: 6,8 => CTR => E7: 4,7 * PRF # H7: 6,8 => SOL * DIS # E7: 6,8 => CTR => E7: 4,7 * PRF # E8: 6,8 => SOL * PRF # H7: 6,8 => SOL * DIS # I3: 7 => CTR => I3: 6,8 * CNT 16 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,A8,B2,B7,C2,C6,C8,D1,D2,E1,E9,F1,F6,G1,G5,H6,I9) * 941....325...231...32.915..618937254.298...1335.21.8..2.53..9.1.9.1.23.51735.942. * PAIR A3: 7,8 ROW 3 I3: 7,8,6 # reduction candidate for 7,8 I3: 6 => SOLVED * 941658732567423189832791546618937254729845613354216897285374961496182375173569428 * DURATION: 0:00:03.499575 START: 15:31:53.710878 END: 15:31:57.210453 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-370-base-pr-001.dot * REASONING * PRF # I3: 6 => SOL * STA I3: 6 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 370 solution: 941658732567423189832791546618937254729845613354216897285374961496182375173569428 info: 5414 FNBTWXY S8.f 19270 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 941658732567423189832791546618937254729845613354216897285374961496182375173569428 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 # I3: 7,8 => UNS * PRF # I3: 6 => SOL * INC # D3: 6,7 => UNS * DIS # D3: 4 => CTR => D3: 6,7 * PRF # D3: 4,7 => SOL * DIS # D3: 6 => CTR => D3: 4,7 * INC # I3: 6,7 => UNS * DIS # I3: 8 => CTR => I3: 6,7 * INC # E5: 4,6 => UNS * DIS # F5: 4,6 => CTR => F5: 5 * INC # F5: 5 => UNS * INC # F7: 4,6 => UNS * DIS # F7: 8 => CTR => F7: 4,6 * INC # I6: 6,7 => UNS * DIS # I6: 9 => CTR => I6: 6,7 * DIS # I6: 6,9 => CTR => I6: 7 * PRF # I6: 7 => SOL * DIS # E7: 6,8 => CTR => E7: 4,7 * INC # E7: 4,7 => UNS * INC # F7: 6,8 => UNS * PRF # H7: 6,8 => SOL * INC # H7: 7 => UNS * DIS # E7: 6,8 => CTR => E7: 4,7 * INC # E7: 4,7 => UNS * INC # F7: 6,8 => UNS * PRF # E8: 6,8 => SOL * INC # E8: 7 => UNS * PRF # H7: 6,8 => SOL * INC # H7: 7 => UNS * INC # H8: 6,8 => UNS * INC # I3: 6,8 => UNS * DIS # I3: 7 => CTR => I3: 6,8 * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # I3: 7,8 => UNS * PRF # I3: 6 => SOL * STA I3: 6 * CNT 2 HDP CHAINS / 2 HYP OPENED