Analysis of xx-top500-029-base.sdk
Contents
Original Sudoku
level: medium
position: .4....86.....91...7........3.......1.2.4........5.....1.9.2..........54.2........ initial
Autosolve
position: 5412..869.32.9175479..45..33.59..4.192.41...541.5.....159724....731.95422.435...7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # F4: 6,8 => SOL * PRF # F4: 6,8 => SOL * CNT 2 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # F4: 6,8 => SOL * STA F4: 6,8 * CNT 1 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .4....86.....91...7........3.......1.2.4........5.....1.9.2..........54.2........ | initial |
| 5412..869.32.9175479..45..33.59..4.192.41...541.5.....159724....731.95422.435...7 | autosolve |
| 541237869832691754796845213365978421928413675417562938159724386673189542284356197 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (21) A2: 6,8 C3: 6,8 E1: 3,7 F1: 3,7 D2: 6,8 D3: 6,8 G3: 1,2 H3: 1,2 B4: 6,8 G5: 3,6 G6: 2,9 I6: 6,8 A8: 6,8 B9: 6,8 E8: 6,8 F9: 6,8 G7: 3,6 H7: 3,8 I7: 6,8 G9: 1,9 H9: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G3,H3: 1.. / G3 = 1 => 17 pairs (_) / H3 = 1 => 16 pairs (_) G9,H9: 1.. / G9 = 1 => 16 pairs (_) / H9 = 1 => 17 pairs (_) G3,G9: 1.. / G3 = 1 => 17 pairs (_) / G9 = 1 => 16 pairs (_) H3,H9: 1.. / H3 = 1 => 16 pairs (_) / H9 = 1 => 17 pairs (_) G3,H3: 2.. / G3 = 2 => 16 pairs (_) / H3 = 2 => 17 pairs (_) F4,F6: 2.. / F4 = 2 => 23 pairs (_) / F6 = 2 => 16 pairs (_) F4,H4: 2.. / F4 = 2 => 23 pairs (_) / H4 = 2 => 16 pairs (_) G3,G6: 2.. / G3 = 2 => 16 pairs (_) / G6 = 2 => 17 pairs (_) E1,F1: 3.. / E1 = 3 => 20 pairs (_) / F1 = 3 => 22 pairs (_) G7,H7: 3.. / G7 = 3 => 20 pairs (_) / H7 = 3 => 18 pairs (_) E1,E6: 3.. / E1 = 3 => 20 pairs (_) / E6 = 3 => 22 pairs (_) G5,G7: 3.. / G5 = 3 => 18 pairs (_) / G7 = 3 => 20 pairs (_) A2,C3: 6.. / A2 = 6 => 0 pairs (X) / C3 = 6 => 0 pairs (_) D2,D3: 6.. / D2 = 6 => 0 pairs (*) / D3 = 6 => 0 pairs (X) G5,I6: 6.. / G5 = 6 => 20 pairs (_) / I6 = 6 => 18 pairs (_) A8,B9: 6.. / A8 = 6 => 0 pairs (*) / B9 = 6 => 0 pairs (X) E8,F9: 6.. / E8 = 6 => 0 pairs (X) / F9 = 6 => 0 pairs (_) G7,I7: 6.. / G7 = 6 => 18 pairs (_) / I7 = 6 => 20 pairs (_) A2,D2: 6.. / A2 = 6 => 0 pairs (X) / D2 = 6 => 0 pairs (_) C3,D3: 6.. / C3 = 6 => 0 pairs (*) / D3 = 6 => 0 pairs (X) A8,E8: 6.. / A8 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) B9,F9: 6.. / B9 = 6 => 0 pairs (X) / F9 = 6 => 0 pairs (_) A2,A8: 6.. / A2 = 6 => 0 pairs (X) / A8 = 6 => 0 pairs (_) B4,B9: 6.. / B4 = 6 => 0 pairs (*) / B9 = 6 => 0 pairs (X) G5,G7: 6.. / G5 = 6 => 20 pairs (_) / G7 = 6 => 18 pairs (_) I6,I7: 6.. / I6 = 6 => 18 pairs (_) / I7 = 6 => 20 pairs (_) E1,F1: 7.. / E1 = 7 => 22 pairs (_) / F1 = 7 => 20 pairs (_) C5,C6: 7.. / C5 = 7 => 28 pairs (_) / C6 = 7 => 22 pairs (_) A2,C3: 8.. / A2 = 8 => 0 pairs (*) / C3 = 8 => 0 pairs (X) D2,D3: 8.. / D2 = 8 => 0 pairs (X) / D3 = 8 => 0 pairs (_) A8,B9: 8.. / A8 = 8 => 0 pairs (X) / B9 = 8 => 0 pairs (_) E8,F9: 8.. / E8 = 8 => 0 pairs (*) / F9 = 8 => 0 pairs (X) H7,I7: 8.. / H7 = 8 => 20 pairs (_) / I7 = 8 => 18 pairs (_) A2,D2: 8.. / A2 = 8 => 0 pairs (*) / D2 = 8 => 0 pairs (X) C3,D3: 8.. / C3 = 8 => 0 pairs (X) / D3 = 8 => 0 pairs (_) A8,E8: 8.. / A8 = 8 => 0 pairs (X) / E8 = 8 => 0 pairs (_) B9,F9: 8.. / B9 = 8 => 0 pairs (*) / F9 = 8 => 0 pairs (X) A2,A8: 8.. / A2 = 8 => 0 pairs (*) / A8 = 8 => 0 pairs (X) B4,B9: 8.. / B4 = 8 => 0 pairs (X) / B9 = 8 => 0 pairs (_) I6,I7: 8.. / I6 = 8 => 20 pairs (_) / I7 = 8 => 18 pairs (_) G6,H6: 9.. / G6 = 9 => 16 pairs (_) / H6 = 9 => 17 pairs (_) G9,H9: 9.. / G9 = 9 => 17 pairs (_) / H9 = 9 => 16 pairs (_) G6,G9: 9.. / G6 = 9 => 16 pairs (_) / G9 = 9 => 17 pairs (_) H6,H9: 9.. / H6 = 9 => 17 pairs (_) / H9 = 9 => 16 pairs (_) * DURATION: 0:01:25.683872 START: 03:37:11.706195 END: 03:38:37.390067 2017-05-04 * CP COUNT: (44) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B4,B9,C3,D2,D3,E1,E8,F1,F9,G3,G5,G6,G7,G9,H3,H7,H9,I6,I7) * 5412..869.32.9175479..45..33.59..4.192.41...541.5.....159724....731.95422.435...7 * PAIR C3: 6,8 COL C C5: 6,8,7 # reduction candidate for 6,8 C5: 6,8 # 22 pairs C6: 6,8,7 # reduction candidate for 6,8 C6: 6,8 # 28 pairs * PAIR E1: 3,7 COL E E6: 3,7,6,8 # reduction candidate for 3,7 E6: 3,7 # 25 pairs E6: 6,8 # 23 pairs * PAIR F1: 3,7 COL F F5: 3,7,6,8 # reduction candidate for 3,7 F5: 3,7 # 22 pairs F6: 3,7,2,6,8 # reduction candidate for 3,7 F6: 3,7 # 25 pairs * PAIR B4: 6,8 BLK 4 C5: 6,8,7 # reduction candidate for 6,8 C5: 6,8 # 22 pairs C6: 6,8,7 # reduction candidate for 6,8 C6: 6,8 # 28 pairs * PAIR B4: 6,8 ROW 4 E4: 6,8,7 # reduction candidate for 6,8 E4: 6,8 # 25 pairs F4: 6,8,2,7 # reduction candidate for 6,8 F4: 6,8 => SOLVED * 541237869832691754796845213365978421928413675417562938159724386673189542284356197 F4: 2,7 # 22 pairs * PAIR G5: 3,6 ROW 5 F5: 3,6,7,8 # reduction candidate for 3,6 F5: 3,6 # 24 pairs F5: 7,8 # 22 pairs * PAIR G6: 2,9 BLK 6 H6: 2,9,3,7,8 # reduction candidate for 2,9 H6: 2,9 # 23 pairs H6: 3,7,8 # 16 pairs * PAIR I6: 6,8 ROW 6 C6: 6,8,7 # reduction candidate for 6,8 C6: 6,8 # 28 pairs E6: 6,8,3,7 # reduction candidate for 6,8 E6: 6,8 # 23 pairs F6: 6,8,2,3,7 # reduction candidate for 6,8 F6: 6,8 # 24 pairs * PAIR E8: 6,8 COL E E4: 6,8,7 # reduction candidate for 6,8 E4: 6,8 # 25 pairs E6: 6,8,3,7 # reduction candidate for 6,8 E6: 6,8 # 23 pairs * PAIR F9: 6,8 COL F F4: 6,8,2,7 # reduction candidate for 6,8 F4: 6,8 => SOLVED * 541237869832691754796845213365978421928413675417562938159724386673189542284356197 F4: 2,7 # 22 pairs F5: 6,8,3,7 # reduction candidate for 6,8 F5: 6,8 # 23 pairs F6: 6,8,2,3,7 # reduction candidate for 6,8 F6: 6,8 # 24 pairs * PAIR H7: 3,8 COL H H5: 3,8,7 # reduction candidate for 3,8 H5: 3,8 # 23 pairs H6: 3,8,2,7,9 # reduction candidate for 3,8 H6: 3,8 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-029-base-pr-000.dot * REASONING * PRF # F4: 6,8 => SOL * PRF # F4: 6,8 => SOL * CNT 2 HDP CHAINS / 26 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B4,B9,C3,D2,D3,E1,E8,F1,F9,G3,G5,G6,G7,G9,H3,H7,H9,I6,I7) * 5412..869.32.9175479..45..33.59..4.192.41...541.5.....159724....731.95422.435...7 * PAIR C3: 6,8 COL C C5: 6,8,7 # reduction candidate for 6,8 C5: 6,8 # 22 pairs C6: 6,8,7 # reduction candidate for 6,8 C6: 6,8 # 28 pairs * PAIR E1: 3,7 COL E E6: 3,7,6,8 # reduction candidate for 3,7 E6: 3,7 # 25 pairs E6: 6,8 # 23 pairs * PAIR F1: 3,7 COL F F5: 3,7,6,8 # reduction candidate for 3,7 F5: 3,7 # 22 pairs F6: 3,7,2,6,8 # reduction candidate for 3,7 F6: 3,7 # 25 pairs * PAIR B4: 6,8 BLK 4 C5: 6,8,7 # reduction candidate for 6,8 C5: 6,8 # 22 pairs C6: 6,8,7 # reduction candidate for 6,8 C6: 6,8 # 28 pairs * PAIR B4: 6,8 ROW 4 E4: 6,8,7 # reduction candidate for 6,8 E4: 6,8 # 25 pairs F4: 6,8,2,7 # reduction candidate for 6,8 F4: 6,8 => SOLVED * 541237869832691754796845213365978421928413675417562938159724386673189542284356197 * DURATION: 0:00:11.453430 START: 03:39:06.320547 END: 03:39:17.773977 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-029-base-pr-001.dot * REASONING * PRF # F4: 6,8 => SOL * STA F4: 6,8 * CNT 1 HDP CHAINS / 10 HYP OPENED
Header Info
Top 500 Minimum 17 029 solution: 541237869832691754796845213365978421928413675417562938159724386673189542284356197 info: 1326 FNBTWX S8.f 18776 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 541237869832691754796845213365978421928413675417562938159724386673189542284356197 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 # C5: 6,8 => UNS * INC # C6: 6,8 => UNS * INC # E6: 3,7 => UNS * INC # E6: 6,8 => UNS * INC # F5: 3,7 => UNS * INC # F6: 3,7 => UNS * INC # C5: 6,8 => UNS * INC # C6: 6,8 => UNS * INC # E4: 6,8 => UNS * PRF # F4: 6,8 => SOL * INC # F4: 2,7 => UNS * INC # F5: 3,6 => UNS * INC # F5: 7,8 => UNS * INC # H6: 2,9 => UNS * INC # H6: 3,7,8 => UNS * INC # C6: 6,8 => UNS * INC # E6: 6,8 => UNS * INC # F6: 6,8 => UNS * INC # E4: 6,8 => UNS * INC # E6: 6,8 => UNS * PRF # F4: 6,8 => SOL * INC # F4: 2,7 => UNS * INC # F5: 6,8 => UNS * INC # F6: 6,8 => UNS * INC # H5: 3,8 => UNS * INC # H6: 3,8 => UNS * CNT 26 HDP CHAINS / 26 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C5: 6,8 => UNS * INC # C6: 6,8 => UNS * INC # E6: 3,7 => UNS * INC # E6: 6,8 => UNS * INC # F5: 3,7 => UNS * INC # F6: 3,7 => UNS * INC # C5: 6,8 => UNS * INC # C6: 6,8 => UNS * INC # E4: 6,8 => UNS * PRF # F4: 6,8 => SOL * STA F4: 6,8 * CNT 10 HDP CHAINS / 10 HYP OPENED