Analysis of xx-top500-366-base.sdk
Contents
Original Sudoku
level: medium
position: ......24.5...3..........6.......5.83.2.6.......1......3.....7.1.6.4........2..... initial
Autosolve
position: 63815.24.542.3681....8426354.6.25183.236..574.513.49623.456.72126.4..3.8...2.34.6 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 7,9 => CTR => B3: 1 * PRF # F8: 7,9 => SOL * DIS # F8: 1 => CTR => F8: 7,9 * DIS # B3: 7,9 => CTR => B3: 1 * DIS # B9: 7,9 => CTR => B9: 1,8 * PRF # E5: 8,9 => SOL * DIS # E5: 1 => CTR => E5: 8,9 * DIS # F5: 8,9 => CTR => F5: 1 * PRF # F5: 1 => SOL * PRF # E9: 9 => SOL * PRF # B9: 8,9 => SOL * DIS # B9: 1,7 => CTR => B9: 8,9 * DIS # E9: 7 => CTR => E9: 8,9 * DIS # F5: 8,9 => CTR => F5: 1 * PRF # F5: 1 => SOL * DIS # C8: 7 => CTR => C8: 5,9 * CNT 16 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 7,9 => CTR => B3: 1 * PRF B3: 1 # F8: 7,9 => SOL * STA B3: 1 + F8: 7,9 * CNT 2 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ......24.5...3..........6.......5.83.2.6.......1......3.....7.1.6.4........2..... | initial |
| 63815.24.542.3681....8426354.6.25183.236..574.513.49623.456.72126.4..3.8...2.34.6 | autosolve |
| 638159247542736819719842635476925183923681574851374962394568721265417398187293456 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) C3: 7,9 F1: 7,9 D2: 7,9 I1: 7,9 I2: 7,9 B4: 7,9 A5: 8,9 A6: 7,8 D4: 7,9 E6: 7,8 B7: 8,9 F7: 8,9 H8: 5,9 H9: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A3,B3: 1.. / A3 = 1 => 0 pairs (X) / B3 = 1 => 15 pairs (_) E5,F5: 1.. / E5 = 1 => 0 pairs (X) / F5 = 1 => 0 pairs (_) A9,B9: 1.. / A9 = 1 => 15 pairs (_) / B9 = 1 => 0 pairs (X) E8,F8: 1.. / E8 = 1 => 0 pairs (*) / F8 = 1 => 0 pairs (X) A3,A9: 1.. / A3 = 1 => 0 pairs (X) / A9 = 1 => 15 pairs (_) B3,B9: 1.. / B3 = 1 => 15 pairs (_) / B9 = 1 => 0 pairs (X) E5,E8: 1.. / E5 = 1 => 0 pairs (X) / E8 = 1 => 0 pairs (_) F5,F8: 1.. / F5 = 1 => 0 pairs (*) / F8 = 1 => 0 pairs (X) C8,C9: 5.. / C8 = 5 => 16 pairs (_) / C9 = 5 => 17 pairs (_) H8,H9: 5.. / H8 = 5 => 17 pairs (_) / H9 = 5 => 16 pairs (_) C8,H8: 5.. / C8 = 5 => 16 pairs (_) / H8 = 5 => 17 pairs (_) C9,H9: 5.. / C9 = 5 => 17 pairs (_) / H9 = 5 => 16 pairs (_) F1,D2: 7.. / F1 = 7 => 0 pairs (X) / D2 = 7 => 0 pairs (_) I1,I2: 7.. / I1 = 7 => 0 pairs (*) / I2 = 7 => 0 pairs (X) B4,A6: 7.. / B4 = 7 => 0 pairs (*) / A6 = 7 => 0 pairs (X) D4,E6: 7.. / D4 = 7 => 0 pairs (X) / E6 = 7 => 0 pairs (_) F1,I1: 7.. / F1 = 7 => 0 pairs (X) / I1 = 7 => 0 pairs (_) D2,I2: 7.. / D2 = 7 => 0 pairs (*) / I2 = 7 => 0 pairs (X) B4,D4: 7.. / B4 = 7 => 0 pairs (*) / D4 = 7 => 0 pairs (X) A6,E6: 7.. / A6 = 7 => 0 pairs (X) / E6 = 7 => 0 pairs (_) D2,D4: 7.. / D2 = 7 => 0 pairs (*) / D4 = 7 => 0 pairs (X) F1,F8: 7.. / F1 = 7 => 0 pairs (X) / F8 = 7 => 0 pairs (_) A5,A6: 8.. / A5 = 8 => 0 pairs (X) / A6 = 8 => 0 pairs (_) B7,B9: 8.. / B7 = 8 => 0 pairs (X) / B9 = 8 => 0 pairs (_) F7,E9: 8.. / F7 = 8 => 0 pairs (*) / E9 = 8 => 0 pairs (X) A6,E6: 8.. / A6 = 8 => 0 pairs (*) / E6 = 8 => 0 pairs (X) B7,F7: 8.. / B7 = 8 => 0 pairs (X) / F7 = 8 => 0 pairs (_) B9,E9: 8.. / B9 = 8 => 0 pairs (*) / E9 = 8 => 0 pairs (X) F5,F7: 8.. / F5 = 8 => 0 pairs (X) / F7 = 8 => 0 pairs (_) F1,D2: 9.. / F1 = 9 => 0 pairs (*) / D2 = 9 => 0 pairs (X) I1,I2: 9.. / I1 = 9 => 0 pairs (X) / I2 = 9 => 0 pairs (_) B4,A5: 9.. / B4 = 9 => 0 pairs (X) / A5 = 9 => 0 pairs (_) H8,H9: 9.. / H8 = 9 => 16 pairs (_) / H9 = 9 => 17 pairs (_) F1,I1: 9.. / F1 = 9 => 0 pairs (*) / I1 = 9 => 0 pairs (X) D2,I2: 9.. / D2 = 9 => 0 pairs (X) / I2 = 9 => 0 pairs (_) B4,D4: 9.. / B4 = 9 => 0 pairs (X) / D4 = 9 => 0 pairs (_) B7,F7: 9.. / B7 = 9 => 0 pairs (*) / F7 = 9 => 0 pairs (X) D2,D4: 9.. / D2 = 9 => 0 pairs (X) / D4 = 9 => 0 pairs (_) * DURATION: 0:01:33.037775 START: 15:20:54.963206 END: 15:22:28.000981 2017-05-04 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B4,B7,C3,D2,D4,E6,F1,F7,H8,H9,I1,I2) * 63815.24.542.3681....8426354.6.25183.236..574.513.49623.456.72126.4..3.8...2.34.6 * PAIR C3: 7,9 BLK 1 A3: 7,9,1 # reduction candidate for 7,9 A3: 7,9 # 15 pairs B3: 7,9,1 # reduction candidate for 7,9 B3: 7,9 => CTR * 63815.24.542.3681.1..8426354.6.25183.236.857485137496238456972126.4..3.8.1.2834.6 B3: 1 # 15 pairs * PAIR C3: 7,9 COL C C8: 7,9,5 # reduction candidate for 7,9 C8: 7,9 # 17 pairs C9: 7,9,5 # reduction candidate for 7,9 C9: 7,9 # 16 pairs * PAIR F1: 7,9 COL F F8: 7,9,1 # reduction candidate for 7,9 F8: 7,9 => SOLVED * 638159247542736819719842635476925183923681574851374962394568721265417398187293456 F8: 1 => CTR * 638157249542936817...8426354967251838236..57475138496238456.72126.4..3.8...2.34.6 * PAIR B4: 7,9 COL B B3: 7,9,1 # reduction candidate for 7,9 B3: 7,9 => CTR * 63815.24.542.3681.1..8426354.6.25183.236.857485137496238456972126.4..3.8.1.2834.6 B3: 1 # 15 pairs B9: 7,9,1,8 # reduction candidate for 7,9 B9: 7,9 => CTR * 638157249542936817.1.842635496725183.236..574.513.496238456972126.4..3.81..2834.6 B9: 1,8 # 15 pairs * PAIR A5: 8,9 ROW 5 E5: 8,9,1 # reduction candidate for 8,9 E5: 8,9 => SOLVED * 638159247542736819719842635476925183923681574851374962394568721265417398187293456 E5: 1 => CTR * 638157249542936817...842635496725183823619574.513.49623.456.72126.4.13.8...2.34.6 F5: 8,9,1 # reduction candidate for 8,9 F5: 8,9 => CTR * 638157249542936817...842635496725183823619574.513.49623.456.72126.4.13.8...2.34.6 F5: 1 => SOLVED * 638159247542736819719842635476925183923681574851374962394568721265417398187293456 * PAIR E6: 7,8 COL E E9: 7,8,9 # reduction candidate for 7,8 E9: 9 => SOLVED * 638159247542736819719842635476925183923681574851374962394568721265417398187293456 E9: 7,8 # 17 pairs * PAIR B7: 8,9 BLK 7 B9: 8,9,1,7 # reduction candidate for 8,9 B9: 8,9 => SOLVED * 638159247542736819719842635476925183923681574851374962394568721265417398187293456 B9: 1,7 => CTR * 638157249542936817...842635496725183.236..574.513.496238456972126.4..3.8...2834.6 * PAIR F7: 8,9 BLK 8 E9: 8,9,7 # reduction candidate for 8,9 E9: 7 => CTR * 638157249542936817.1.8426354.6.25183.236..574.513.49623.456872126.4..3.8.8.2734.6 E9: 8,9 # 18 pairs * PAIR F7: 8,9 COL F F5: 8,9,1 # reduction candidate for 8,9 F5: 8,9 => CTR * 638157249542936817...842635496725183823619574.513.49623.456.72126.4.13.8...2.34.6 F5: 1 => SOLVED * 638159247542736819719842635476925183923681574851374962394568721265417398187293456 * PAIR H8: 5,9 ROW 8 C8: 5,9,7 # reduction candidate for 5,9 C8: 7 => CTR * 638157249542936817..98426354967251838236..57475138496238456.7212674..358..5273496 C8: 5,9 # 18 pairs * PAIR H9: 5,9 ROW 9 C9: 5,9,7 # reduction candidate for 5,9 C9: 5,9 # 19 pairs C9: 7 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-366-base-pr-000.dot * REASONING * DIS # B3: 7,9 => CTR => B3: 1 * PRF # F8: 7,9 => SOL * DIS # F8: 1 => CTR => F8: 7,9 * DIS # B3: 7,9 => CTR => B3: 1 * DIS # B9: 7,9 => CTR => B9: 1,8 * PRF # E5: 8,9 => SOL * DIS # E5: 1 => CTR => E5: 8,9 * DIS # F5: 8,9 => CTR => F5: 1 * PRF # F5: 1 => SOL * PRF # E9: 9 => SOL * PRF # B9: 8,9 => SOL * DIS # B9: 1,7 => CTR => B9: 8,9 * DIS # E9: 7 => CTR => E9: 8,9 * DIS # F5: 8,9 => CTR => F5: 1 * PRF # F5: 1 => SOL * DIS # C8: 7 => CTR => C8: 5,9 * CNT 16 HDP CHAINS / 27 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B4,B7,C3,D2,D4,E6,F1,F7,H8,H9,I1,I2) * 63815.24.542.3681....8426354.6.25183.236..574.513.49623.456.72126.4..3.8...2.34.6 * PAIR C3: 7,9 BLK 1 A3: 7,9,1 # reduction candidate for 7,9 A3: 7,9 # 15 pairs B3: 7,9,1 # reduction candidate for 7,9 B3: 7,9 => CTR * 63815.24.542.3681.1..8426354.6.25183.236.857485137496238456972126.4..3.8.1.2834.6 * RESTART * PAIR C3: 7,9 COL C C8: 7,9,5 # reduction candidate for 7,9 C8: 7,9 # 18 pairs C9: 7,9,5 # reduction candidate for 7,9 C9: 7,9 # 17 pairs * PAIR F1: 7,9 COL F F8: 7,9,1 # reduction candidate for 7,9 F8: 7,9 => SOLVED * 638159247542736819719842635476925183923681574851374962394568721265417398187293456 * DURATION: 0:00:08.227301 START: 15:23:08.700837 END: 15:23:16.928138 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-366-base-pr-001.dot * REASONING * DIS # B3: 7,9 => CTR => B3: 1 * PRF B3: 1 # F8: 7,9 => SOL * STA B3: 1 + F8: 7,9 * CNT 2 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 366 solution: 638159247542736819719842635476925183923681574851374962394568721265417398187293456 info: 5021 FNBHWY S8.f 1066 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 638159247542736819719842635476925183923681574851374962394568721265417398187293456 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 # A3: 7,9 => UNS * DIS # B3: 7,9 => CTR => B3: 1 * INC # B3: 1 => UNS * INC # C8: 7,9 => UNS * INC # C9: 7,9 => UNS * PRF # F8: 7,9 => SOL * DIS # F8: 1 => CTR => F8: 7,9 * DIS # B3: 7,9 => CTR => B3: 1 * INC # B3: 1 => UNS * DIS # B9: 7,9 => CTR => B9: 1,8 * INC # B9: 1,8 => UNS * PRF # E5: 8,9 => SOL * DIS # E5: 1 => CTR => E5: 8,9 * DIS # F5: 8,9 => CTR => F5: 1 * PRF # F5: 1 => SOL * INC # E9: 7,8 => UNS * PRF # E9: 9 => SOL * PRF # B9: 8,9 => SOL * DIS # B9: 1,7 => CTR => B9: 8,9 * INC # E9: 8,9 => UNS * DIS # E9: 7 => CTR => E9: 8,9 * DIS # F5: 8,9 => CTR => F5: 1 * PRF # F5: 1 => SOL * INC # C8: 5,9 => UNS * DIS # C8: 7 => CTR => C8: 5,9 * INC # C9: 5,9 => UNS * INC # C9: 7 => UNS * CNT 27 HDP CHAINS / 27 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 7,9 => UNS * DIS # B3: 7,9 => CTR => B3: 1 * INC B3: 1 # C8: 7,9 => UNS * INC B3: 1 # C9: 7,9 => UNS * PRF B3: 1 # F8: 7,9 => SOL * STA B3: 1 + F8: 7,9 * CNT 5 HDP CHAINS / 5 HYP OPENED