Analysis of xx-top500-084-base.sdk
Contents
Original Sudoku
level: medium
position: .5....3.....1...4....2.....4..7.......2...8......5.6..56..3.........4.2.........1 initial
Autosolve
position: 257.4931....17.24.14.2..7..4857261..672391854.1.4586725619324877...14.2..24..7..1 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 3,9 => CTR => A2: 8 * DIS # C2: 3,9 => CTR => C2: 6,8 * PRF # D9: 6,8 => SOL * DIS # C3: 6,8 => CTR => C3: 3,9 * DIS # I3: 6,8 => CTR => I3: 5,9 * DIS # I2: 6,8 => CTR => I2: 5,9 * DIS # I3: 6,8 => CTR => I3: 5,9 * DIS # I2: 6,9 => CTR => I2: 5,8 * PRF # I3: 6,9 => SOL * DIS # C3: 6,9 => CTR => C3: 3,8 * DIS # A2: 3,9 => CTR => A2: 8 * DIS # C2: 3,9 => CTR => C2: 6,8 * DIS # C8: 3,9 => CTR => C8: 8 * DIS # C8: 3,9 => CTR => C8: 8 * PRF # D9: 6,8 => SOL * CNT 15 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 3,9 => CTR => A2: 8 * DIS A2: 8 # C2: 3,9 => CTR => C2: 6 * PRF A2: 8 + C2: 6 # D9: 6,8 => SOL * STA A2: 8 + C2: 6 + D9: 6,8 * CNT 3 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .5....3.....1...4....2.....4..7.......2...8......5.6..56..3.........4.2.........1 | initial |
| 257.4931....17.24.14.2..7..4857261..672391854.1.4586725619324877...14.2..24..7..1 | autosolve |
| 257649318896173245143285769485726193672391854319458672561932487738514926924867531 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) B2: 3,9 D1: 6,8 F2: 3,5 E3: 6,8 F3: 3,5 I1: 6,8 H3: 6,9 A6: 3,9 C6: 3,9 H4: 3,9 I4: 3,9 B8: 3,9 E9: 6,8 G8: 5,9 I8: 3,6 G9: 5,9 H9: 3,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F2,F3: 3.. / F2 = 3 => 0 pairs (*) / F3 = 3 => 0 pairs (X) A6,C6: 3.. / A6 = 3 => 0 pairs (*) / C6 = 3 => 0 pairs (X) H4,I4: 3.. / H4 = 3 => 0 pairs (X) / I4 = 3 => 0 pairs (_) I8,H9: 3.. / I8 = 3 => 0 pairs (X) / H9 = 3 => 0 pairs (_) C3,F3: 3.. / C3 = 3 => 0 pairs (*) / F3 = 3 => 0 pairs (X) A9,H9: 3.. / A9 = 3 => 0 pairs (X) / H9 = 3 => 0 pairs (_) B2,B8: 3.. / B2 = 3 => 15 pairs (_) / B8 = 3 => 0 pairs (*) H4,H9: 3.. / H4 = 3 => 0 pairs (X) / H9 = 3 => 0 pairs (_) I4,I8: 3.. / I4 = 3 => 0 pairs (*) / I8 = 3 => 0 pairs (X) F2,F3: 5.. / F2 = 5 => 15 pairs (_) / F3 = 5 => 0 pairs (*) I2,I3: 5.. / I2 = 5 => 0 pairs (*) / I3 = 5 => 0 pairs (X) D8,D9: 5.. / D8 = 5 => 0 pairs (*) / D9 = 5 => 0 pairs (X) G8,G9: 5.. / G8 = 5 => 17 pairs (_) / G9 = 5 => 0 pairs (*) F2,I2: 5.. / F2 = 5 => 15 pairs (_) / I2 = 5 => 0 pairs (*) F3,I3: 5.. / F3 = 5 => 0 pairs (*) / I3 = 5 => 0 pairs (X) D8,G8: 5.. / D8 = 5 => 0 pairs (*) / G8 = 5 => 0 pairs (X) D9,G9: 5.. / D9 = 5 => 17 pairs (_) / G9 = 5 => 0 pairs (*) C2,C3: 6.. / C2 = 6 => 17 pairs (_) / C3 = 6 => 0 pairs (X) D1,E3: 6.. / D1 = 6 => 0 pairs (*) / E3 = 6 => 0 pairs (X) I8,H9: 6.. / I8 = 6 => 0 pairs (*) / H9 = 6 => 0 pairs (X) D1,I1: 6.. / D1 = 6 => 0 pairs (*) / I1 = 6 => 0 pairs (X) C2,I2: 6.. / C2 = 6 => 17 pairs (_) / I2 = 6 => 0 pairs (X) D8,I8: 6.. / D8 = 6 => 0 pairs (X) / I8 = 6 => 0 pairs (_) E3,E9: 6.. / E3 = 6 => 0 pairs (X) / E9 = 6 => 0 pairs (_) H3,H9: 6.. / H3 = 6 => 0 pairs (*) / H9 = 6 => 0 pairs (X) D1,E3: 8.. / D1 = 8 => 0 pairs (X) / E3 = 8 => 0 pairs (_) C8,A9: 8.. / C8 = 8 => 19 pairs (_) / A9 = 8 => 0 pairs (X) D1,I1: 8.. / D1 = 8 => 0 pairs (X) / I1 = 8 => 0 pairs (_) C8,D8: 8.. / C8 = 8 => 19 pairs (_) / D8 = 8 => 0 pairs (X) A2,A9: 8.. / A2 = 8 => 19 pairs (_) / A9 = 8 => 0 pairs (X) E3,E9: 8.. / E3 = 8 => 0 pairs (*) / E9 = 8 => 0 pairs (X) A6,C6: 9.. / A6 = 9 => 15 pairs (_) / C6 = 9 => 0 pairs (*) H4,I4: 9.. / H4 = 9 => 0 pairs (*) / I4 = 9 => 0 pairs (X) G8,G9: 9.. / G8 = 9 => 0 pairs (*) / G9 = 9 => 0 pairs (X) A9,G9: 9.. / A9 = 9 => 0 pairs (*) / G9 = 9 => 0 pairs (X) B2,B8: 9.. / B2 = 9 => 0 pairs (*) / B8 = 9 => 0 pairs (X) H3,H4: 9.. / H3 = 9 => 0 pairs (X) / H4 = 9 => 0 pairs (_) * DURATION: 0:01:03.643866 START: 05:39:17.008982 END: 05:40:20.652848 2017-05-04 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B2,B8,C6,D1,E3,E9,F2,F3,G8,G9,H3,H4,H9,I1,I4,I8) * 257.4931....17.24.14.2..7..4857261..672391854.1.4586725619324877...14.2..24..7..1 * PAIR B2: 3,9 BLK 1 A2: 3,9,8 # reduction candidate for 3,9 A2: 3,9 => CTR * 257649318..817.24614.2..7..4857261..672391854.1.4586725619324877...14.2.824.67931 A2: 8 # 19 pairs C2: 3,9,6,8 # reduction candidate for 3,9 C2: 3,9 => CTR * 257.4931....17.246146283795485726139672391854.1.4586725619324877.8614.2..24..7..1 C2: 6,8 # 18 pairs C3: 3,9,6,8 # reduction candidate for 3,9 C3: 3,9 # 21 pairs * PAIR D1: 6,8 COL D D8: 6,8,5 # reduction candidate for 6,8 D8: 6,8 # 17 pairs D9: 6,8,5 # reduction candidate for 6,8 D9: 6,8 => SOLVED * 257649318896173245143285769485726193672391854319458672561932487738514926924867531 D9: 5 # 17 pairs * PAIR E3: 6,8 ROW 3 C3: 6,8,3,9 # reduction candidate for 6,8 C3: 6,8 => CTR * 257.4931.8391752461462.3795485726139672391854.1.4586725619324877...14.23324..7961 C3: 3,9 # 21 pairs I3: 6,8,5,9 # reduction candidate for 6,8 I3: 6,8 => CTR * 257.4931.83.17.24514.2.579.485726139672391854.1.4586725619324877...14.23324..7961 I3: 5,9 # 18 pairs * PAIR I1: 6,8 BLK 3 I2: 6,8,5,9 # reduction candidate for 6,8 I2: 6,8 => CTR * 257.4931.8391752461462.37.54857261.9672391854.1.4586725619324877...14.23324..7961 I2: 5,9 # 21 pairs I3: 6,8,5,9 # reduction candidate for 6,8 I3: 6,8 => CTR * 257.4931.83.17.24514.2.579.485726139672391854.1.4586725619324877...14.23324..7961 I3: 5,9 # 18 pairs * PAIR H3: 6,9 BLK 3 I2: 6,9,5,8 # reduction candidate for 6,9 I2: 6,9 => CTR * 257649318..61752491492837654857261936723918549134586725619324877...14.26.24.67.31 I2: 5,8 # 19 pairs I3: 6,9,5,8 # reduction candidate for 6,9 I3: 6,9 => SOLVED * 257649318896173245143285769485726193672391854319458672561932487738514926924867531 I3: 5,8 # 18 pairs * PAIR H3: 6,9 ROW 3 C3: 6,9,3,8 # reduction candidate for 6,9 C3: 6,9 => CTR * 257649318..61752491492837654857261936723918549134586725619324877...14.26.24.67.31 C3: 3,8 # 19 pairs * PAIR A6: 3,9 COL A A2: 3,9,8 # reduction candidate for 3,9 A2: 3,9 => CTR * 257649318..817.24614.2..7..4857261..672391854.1.4586725619324877...14.2.824.67931 A2: 8 # 19 pairs A9: 3,9,8 # reduction candidate for 3,9 A9: 3,9 # 19 pairs * PAIR C6: 3,9 COL C C2: 3,9,6,8 # reduction candidate for 3,9 C2: 3,9 => CTR * 257.4931....17.246146283795485726139672391854.1.4586725619324877.8614.2..24..7..1 C2: 6,8 # 18 pairs C3: 3,9,6,8 # reduction candidate for 3,9 C3: 3,9 # 21 pairs C8: 3,9,8 # reduction candidate for 3,9 C8: 3,9 => CTR * 257649318...17.24.14.2..7..4857261..672391854.1.4586725619324877..814526824567931 C8: 8 # 19 pairs * PAIR B8: 3,9 BLK 7 C8: 3,9,8 # reduction candidate for 3,9 C8: 3,9 => CTR * 257649318...17.24.14.2..7..4857261..672391854.1.4586725619324877..814526824567931 C8: 8 # 19 pairs A9: 3,9,8 # reduction candidate for 3,9 A9: 3,9 # 19 pairs * PAIR E9: 6,8 BLK 8 D8: 6,8,5 # reduction candidate for 6,8 D8: 6,8 # 17 pairs D9: 6,8,5 # reduction candidate for 6,8 D9: 6,8 => SOLVED * 257649318896173245143285769485726193672391854319458672561932487738514926924867531 D9: 5 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-084-base-pr-000.dot * REASONING * DIS # A2: 3,9 => CTR => A2: 8 * DIS # C2: 3,9 => CTR => C2: 6,8 * PRF # D9: 6,8 => SOL * DIS # C3: 6,8 => CTR => C3: 3,9 * DIS # I3: 6,8 => CTR => I3: 5,9 * DIS # I2: 6,8 => CTR => I2: 5,9 * DIS # I3: 6,8 => CTR => I3: 5,9 * DIS # I2: 6,9 => CTR => I2: 5,8 * PRF # I3: 6,9 => SOL * DIS # C3: 6,9 => CTR => C3: 3,8 * DIS # A2: 3,9 => CTR => A2: 8 * DIS # C2: 3,9 => CTR => C2: 6,8 * DIS # C8: 3,9 => CTR => C8: 8 * DIS # C8: 3,9 => CTR => C8: 8 * PRF # D9: 6,8 => SOL * CNT 15 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B2,B8,C6,D1,E3,E9,F2,F3,G8,G9,H3,H4,H9,I1,I4,I8) * 257.4931....17.24.14.2..7..4857261..672391854.1.4586725619324877...14.2..24..7..1 * PAIR B2: 3,9 BLK 1 A2: 3,9,8 # reduction candidate for 3,9 A2: 3,9 => CTR * 257649318..817.24614.2..7..4857261..672391854.1.4586725619324877...14.2.824.67931 C2: 3,9,6 # reduction candidate for 3,9 C2: 3,9 => CTR * 257.4931.8..17.246146283795485726139672391854.1.4586725619324877.8614.2..24..7..1 * RESTART * PAIR D1: 6,8 COL D D9: 6,8,5 # reduction candidate for 6,8 D9: 6,8 => SOLVED * 257649318896173245143285769485726193672391854319458672561932487738514926924867531 * DURATION: 0:00:04.203229 START: 05:40:56.525418 END: 05:41:00.728647 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-084-base-pr-001.dot * REASONING * DIS # A2: 3,9 => CTR => A2: 8 * DIS A2: 8 # C2: 3,9 => CTR => C2: 6 * PRF A2: 8 + C2: 6 # D9: 6,8 => SOL * STA A2: 8 + C2: 6 + D9: 6,8 * CNT 3 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 084 solution: 257649318896173245143285769485726193672391854319458672561932487738514926924867531 info: 1558 FNBWXY S8.f 19764 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 257649318896173245143285769485726193672391854319458672561932487738514926924867531 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 # A2: 3,9 => CTR => A2: 8 * INC # A2: 8 => UNS * DIS # C2: 3,9 => CTR => C2: 6,8 * INC # C2: 6,8 => UNS * INC # C3: 3,9 => UNS * INC # D8: 6,8 => UNS * PRF # D9: 6,8 => SOL * INC # D9: 5 => UNS * DIS # C3: 6,8 => CTR => C3: 3,9 * INC # C3: 3,9 => UNS * DIS # I3: 6,8 => CTR => I3: 5,9 * INC # I3: 5,9 => UNS * DIS # I2: 6,8 => CTR => I2: 5,9 * INC # I2: 5,9 => UNS * DIS # I3: 6,8 => CTR => I3: 5,9 * INC # I3: 5,9 => UNS * DIS # I2: 6,9 => CTR => I2: 5,8 * INC # I2: 5,8 => UNS * PRF # I3: 6,9 => SOL * INC # I3: 5,8 => UNS * DIS # C3: 6,9 => CTR => C3: 3,8 * INC # C3: 3,8 => UNS * DIS # A2: 3,9 => CTR => A2: 8 * INC # A2: 8 => UNS * INC # A9: 3,9 => UNS * DIS # C2: 3,9 => CTR => C2: 6,8 * INC # C2: 6,8 => UNS * INC # C3: 3,9 => UNS * DIS # C8: 3,9 => CTR => C8: 8 * INC # C8: 8 => UNS * DIS # C8: 3,9 => CTR => C8: 8 * INC # C8: 8 => UNS * INC # A9: 3,9 => UNS * INC # D8: 6,8 => UNS * PRF # D9: 6,8 => SOL * INC # D9: 5 => UNS * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A2: 3,9 => CTR => A2: 8 * DIS A2: 8 # C2: 3,9 => CTR => C2: 6 * PRF A2: 8 + C2: 6 # D9: 6,8 => SOL * STA A2: 8 + C2: 6 + D9: 6,8 * CNT 3 HDP CHAINS / 3 HYP OPENED