Analysis of xx-top500-488-base.sdk
Contents
Original Sudoku
level: medium
position: ...2...5.4...8..............516...........4.3......8..6..7..1...3..4....7......9. initial
Autosolve
position: ...2...544..385..15..4...38851634..9......4.3......8.56..7.3142.3..465877.....396 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B5: 2,9 => CTR => B5: 6,7 * PRF # C5: 2,9 => SOL * DIS # A6: 2,9 => CTR => A6: 3 * PRF # A6: 3 => SOL * DIS # B6: 2,9 => CTR => B6: 4,6,7 * DIS # F5: 2,9 => CTR => F5: 1,7,8 * DIS # A8: 2,9 => CTR => A8: 1 * PRF # A8: 1 => SOL * DIS # F5: 1,9 => CTR => F5: 2,7,8 * DIS # B1: 1,6,7 => CTR => B1: 8,9 * DIS # A8: 2,9 => CTR => A8: 1 * PRF # A8: 1 => SOL * PRF # C5: 2,9 => SOL * DIS # A8: 2 => CTR => A8: 1,9 * CNT 14 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 # B5: 2,9 => CTR => B5: 6,7 * PRF B5: 6,7 # C5: 2,9 => SOL * STA B5: 6,7 + C5: 2,9 * CNT 2 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...2...5.4...8..............516...........4.3......8..6..7..1...3..4....7......9. | initial |
| ...2...544..385..15..4...38851634..9......4.3......8.56..7.3142.3..465877.....396 | autosolve |
| 983217654426385971517469238851634729269578413374192865698753142132946587745821396 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) C1: 3,8 H2: 2,7 A5: 2,9 C6: 3,4 D5: 5,8 D6: 1,9 G4: 2,7 H4: 2,7 H5: 1,6 H6: 1,6 B7: 8,9 C7: 5,8 C8: 2,9 B9: 1,4 C9: 4,5 E7: 5,9 D8: 1,9 D9: 5,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H5,H6: 1.. / H5 = 1 => 16 pairs (_) / H6 = 1 => 0 pairs (X) A8,B9: 1.. / A8 = 1 => 0 pairs (*) / B9 = 1 => 0 pairs (X) A8,D8: 1.. / A8 = 1 => 0 pairs (*) / D8 = 1 => 0 pairs (X) A1,A8: 1.. / A1 = 1 => 0 pairs (X) / A8 = 1 => 0 pairs (_) D6,D8: 1.. / D6 = 1 => 0 pairs (*) / D8 = 1 => 0 pairs (X) G4,H4: 2.. / G4 = 2 => 15 pairs (_) / H4 = 2 => 16 pairs (_) A8,C8: 2.. / A8 = 2 => 0 pairs (X) / C8 = 2 => 18 pairs (_) E9,F9: 2.. / E9 = 2 => 19 pairs (_) / F9 = 2 => 17 pairs (_) H2,H4: 2.. / H2 = 2 => 15 pairs (_) / H4 = 2 => 16 pairs (_) A1,C1: 3.. / A1 = 3 => 0 pairs (X) / C1 = 3 => 0 pairs (_) A6,C6: 3.. / A6 = 3 => 0 pairs (*) / C6 = 3 => 0 pairs (X) A1,A6: 3.. / A1 = 3 => 0 pairs (X) / A6 = 3 => 0 pairs (_) C1,C6: 3.. / C1 = 3 => 0 pairs (*) / C6 = 3 => 0 pairs (X) B6,C6: 4.. / B6 = 4 => 0 pairs (X) / C6 = 4 => 0 pairs (_) B9,C9: 4.. / B9 = 4 => 0 pairs (*) / C9 = 4 => 0 pairs (X) B6,B9: 4.. / B6 = 4 => 0 pairs (X) / B9 = 4 => 0 pairs (_) C6,C9: 4.. / C6 = 4 => 0 pairs (*) / C9 = 4 => 0 pairs (X) D5,E5: 5.. / D5 = 5 => 17 pairs (_) / E5 = 5 => 0 pairs (X) C7,C9: 5.. / C7 = 5 => 0 pairs (X) / C9 = 5 => 0 pairs (_) C7,E7: 5.. / C7 = 5 => 0 pairs (X) / E7 = 5 => 0 pairs (_) D5,D9: 5.. / D5 = 5 => 17 pairs (_) / D9 = 5 => 0 pairs (X) E1,E3: 6.. / E1 = 6 => 19 pairs (_) / E3 = 6 => 18 pairs (_) H5,H6: 6.. / H5 = 6 => 0 pairs (X) / H6 = 6 => 16 pairs (_) B6,H6: 6.. / B6 = 6 => 0 pairs (X) / H6 = 6 => 16 pairs (_) G4,H4: 7.. / G4 = 7 => 16 pairs (_) / H4 = 7 => 15 pairs (_) H2,H4: 7.. / H2 = 7 => 16 pairs (_) / H4 = 7 => 15 pairs (_) B1,C1: 8.. / B1 = 8 => 0 pairs (*) / C1 = 8 => 0 pairs (X) D5,F5: 8.. / D5 = 8 => 0 pairs (X) / F5 = 8 => 17 pairs (_) B7,C7: 8.. / B7 = 8 => 0 pairs (X) / C7 = 8 => 0 pairs (_) D9,F9: 8.. / D9 = 8 => 17 pairs (_) / F9 = 8 => 0 pairs (X) B1,B7: 8.. / B1 = 8 => 0 pairs (*) / B7 = 8 => 0 pairs (X) C1,C7: 8.. / C1 = 8 => 0 pairs (X) / C7 = 8 => 0 pairs (_) D5,D9: 8.. / D5 = 8 => 0 pairs (X) / D9 = 8 => 17 pairs (_) F5,F9: 8.. / F5 = 8 => 17 pairs (_) / F9 = 8 => 0 pairs (X) E7,D8: 9.. / E7 = 9 => 0 pairs (X) / D8 = 9 => 0 pairs (_) B7,E7: 9.. / B7 = 9 => 0 pairs (*) / E7 = 9 => 0 pairs (X) D6,D8: 9.. / D6 = 9 => 0 pairs (X) / D8 = 9 => 0 pairs (_) * DURATION: 0:01:04.336850 START: 19:19:43.274967 END: 19:20:47.611817 2017-05-04 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B7,B9,C1,C6,C7,C8,C9,D5,D6,D8,D9,E7,G4,H2,H4,H5,H6) * ...2...544..385..15..4...38851634..9......4.3......8.56..7.3142.3..465877.....396 * PAIR H2: 2,7 BLK 3 G2: 2,7,6,9 # reduction candidate for 2,7 G2: 2,7 # 25 pairs G3: 2,7,6,9 # reduction candidate for 2,7 G3: 2,7 # 21 pairs * PAIR H2: 2,7 ROW 2 B2: 2,7,6,9 # reduction candidate for 2,7 B2: 2,7 # 21 pairs C2: 2,7,6,9 # reduction candidate for 2,7 C2: 2,7 # 21 pairs * PAIR A5: 2,9 BLK 4 B5: 2,9,6,7 # reduction candidate for 2,9 B5: 2,9 => CTR * .832...544..385..151.4...38851634..9...5.84.33.41..8656987531421329465877458..396 B5: 6,7 # 19 pairs C5: 2,9,6,7 # reduction candidate for 2,9 C5: 2,9 => SOLVED * 983217654426385971517469238851634729269578413374192865698753142132946587745821396 C5: 6,7 # 19 pairs A6: 2,9,3 # reduction candidate for 2,9 A6: 2,9 => CTR * 3.82...544..385..15..4...38851634..9......4.3..3...8.568579314213..465877.....396 A6: 3 => SOLVED * 983217654426385971517469238851634729269578413374192865698753142132946587745821396 B6: 2,9,4,6,7 # reduction candidate for 2,9 B6: 2,9 => CTR * 9832...544..3859.151.4..2388516347292.95.84133.4...8656.87531421329465877458..396 B6: 4,6,7 # 18 pairs * PAIR A5: 2,9 ROW 5 E5: 2,9,1,5,7 # reduction candidate for 2,9 E5: 2,9 # 18 pairs F5: 2,9,1,7,8 # reduction candidate for 2,9 F5: 2,9 => CTR * 1..2...544..385..15..4...38851634..9...85.413......8656.5793142.3.146587714528396 F5: 1,7,8 # 18 pairs * PAIR A5: 2,9 COL A A8: 2,9,1 # reduction candidate for 2,9 A8: 2,9 => CTR * 1.32...544..385..15..4...38851634..9......4.33.4...8.56.87.3142.3..465877.....396 A8: 1 => SOLVED * 983217654426385971517469238851634729269578413374192865698753142132946587745821396 * PAIR D6: 1,9 BLK 5 E5: 1,9,2,5,7 # reduction candidate for 1,9 E5: 1,9 # 21 pairs F5: 1,9,2,7,8 # reduction candidate for 1,9 F5: 1,9 => CTR * 1..2...544..385..15..4...38851634..9...85.4.3......8.56.5793142.3.146587714528396 F5: 2,7,8 # 18 pairs E6: 1,9,2,7 # reduction candidate for 1,9 E6: 1,9 # 19 pairs F6: 1,9,2,7 # reduction candidate for 1,9 F6: 1,9 # 21 pairs * PAIR G4: 2,7 COL G G2: 2,7,6,9 # reduction candidate for 2,7 G2: 2,7 # 25 pairs G3: 2,7,6,9 # reduction candidate for 2,7 G3: 2,7 # 21 pairs * PAIR B7: 8,9 COL B B1: 8,9,1,6,7 # reduction candidate for 8,9 B1: 1,6,7 => CTR * ..82...544..385..15..4...38851634..9......4.3..3...8.5685793142.3.146587714...396 B1: 8,9 # 19 pairs * PAIR C8: 2,9 BLK 7 A8: 2,9,1 # reduction candidate for 2,9 A8: 2,9 => CTR * 1.32...544..385..15..4...38851634..9......4.33.4...8.56.87.3142.3..465877.....396 A8: 1 => SOLVED * 983217654426385971517469238851634729269578413374192865698753142132946587745821396 * PAIR C8: 2,9 COL C C2: 2,9,6,7 # reduction candidate for 2,9 C2: 2,9 # 21 pairs C3: 2,9,6,7 # reduction candidate for 2,9 C3: 2,9 # 21 pairs C5: 2,9,6,7 # reduction candidate for 2,9 C5: 2,9 => SOLVED * 983217654426385971517469238851634729269578413374192865698753142132946587745821396 C5: 6,7 # 19 pairs * PAIR E7: 5,9 COL E E5: 5,9,1,2,7 # reduction candidate for 5,9 E5: 5,9 # 20 pairs E5: 1,2,7 # 18 pairs * PAIR D8: 1,9 ROW 8 A8: 1,9,2 # reduction candidate for 1,9 A8: 2 => CTR * 1.32...544..385..15..4...38851634..9......4.33.4...8.56.87.3142.3..465877.....396 A8: 1,9 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-488-base-pr-000.dot * REASONING * DIS # B5: 2,9 => CTR => B5: 6,7 * PRF # C5: 2,9 => SOL * DIS # A6: 2,9 => CTR => A6: 3 * PRF # A6: 3 => SOL * DIS # B6: 2,9 => CTR => B6: 4,6,7 * DIS # F5: 2,9 => CTR => F5: 1,7,8 * DIS # A8: 2,9 => CTR => A8: 1 * PRF # A8: 1 => SOL * DIS # F5: 1,9 => CTR => F5: 2,7,8 * DIS # B1: 1,6,7 => CTR => B1: 8,9 * DIS # A8: 2,9 => CTR => A8: 1 * PRF # A8: 1 => SOL * PRF # C5: 2,9 => SOL * DIS # A8: 2 => CTR => A8: 1,9 * CNT 14 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B7,B9,C1,C6,C7,C8,C9,D5,D6,D8,D9,E7,G4,H2,H4,H5,H6) * ...2...544..385..15..4...38851634..9......4.3......8.56..7.3142.3..465877.....396 * PAIR H2: 2,7 BLK 3 G2: 2,7,6,9 # reduction candidate for 2,7 G2: 2,7 # 25 pairs G3: 2,7,6,9 # reduction candidate for 2,7 G3: 2,7 # 21 pairs * PAIR H2: 2,7 ROW 2 B2: 2,7,6,9 # reduction candidate for 2,7 B2: 2,7 # 21 pairs C2: 2,7,6,9 # reduction candidate for 2,7 C2: 2,7 # 21 pairs * PAIR A5: 2,9 BLK 4 B5: 2,9,6,7 # reduction candidate for 2,9 B5: 2,9 => CTR * .832...544..385..151.4...38851634..9...5.84.33.41..8656987531421329465877458..396 C5: 2,9,6,7 # reduction candidate for 2,9 C5: 2,9 => SOLVED * 983217654426385971517469238851634729269578413374192865698753142132946587745821396 * DURATION: 0:00:07.704523 START: 19:21:23.339683 END: 19:21:31.044206 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-488-base-pr-001.dot * REASONING * DIS # B5: 2,9 => CTR => B5: 6,7 * PRF B5: 6,7 # C5: 2,9 => SOL * STA B5: 6,7 + C5: 2,9 * CNT 2 HDP CHAINS / 6 HYP OPENED
Header Info
Top 500 Minimum 17 488 solution: 983217654426385971517469238851634729269578413374192865698753142132946587745821396 info: 96227 FNBTXK S8.f 40266 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 983217654426385971517469238851634729269578413374192865698753142132946587745821396 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 # G2: 2,7 => UNS * INC # G3: 2,7 => UNS * INC # B2: 2,7 => UNS * INC # C2: 2,7 => UNS * DIS # B5: 2,9 => CTR => B5: 6,7 * INC # B5: 6,7 => UNS * PRF # C5: 2,9 => SOL * INC # C5: 6,7 => UNS * DIS # A6: 2,9 => CTR => A6: 3 * PRF # A6: 3 => SOL * DIS # B6: 2,9 => CTR => B6: 4,6,7 * INC # B6: 4,6,7 => UNS * INC # E5: 2,9 => UNS * DIS # F5: 2,9 => CTR => F5: 1,7,8 * INC # F5: 1,7,8 => UNS * DIS # A8: 2,9 => CTR => A8: 1 * PRF # A8: 1 => SOL * INC # E5: 1,9 => UNS * DIS # F5: 1,9 => CTR => F5: 2,7,8 * INC # F5: 2,7,8 => UNS * INC # E6: 1,9 => UNS * INC # F6: 1,9 => UNS * INC # G2: 2,7 => UNS * INC # G3: 2,7 => UNS * INC # B1: 8,9 => UNS * DIS # B1: 1,6,7 => CTR => B1: 8,9 * DIS # A8: 2,9 => CTR => A8: 1 * PRF # A8: 1 => SOL * INC # C2: 2,9 => UNS * INC # C3: 2,9 => UNS * PRF # C5: 2,9 => SOL * INC # C5: 6,7 => UNS * INC # E5: 5,9 => UNS * INC # E5: 1,2,7 => UNS * INC # A8: 1,9 => UNS * DIS # A8: 2 => CTR => A8: 1,9 * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G2: 2,7 => UNS * INC # G3: 2,7 => UNS * INC # B2: 2,7 => UNS * INC # C2: 2,7 => UNS * DIS # B5: 2,9 => CTR => B5: 6,7 * PRF B5: 6,7 # C5: 2,9 => SOL * STA B5: 6,7 + C5: 2,9 * CNT 6 HDP CHAINS / 6 HYP OPENED