Analysis of xx-top500-193-base.sdk
Contents
Original Sudoku
level: medium
position: 2...6...7.8..2.........1.4.6.....2.1...4...........3...4.3...5...1............8.. initial
Autosolve
position: 213564987486.2.135...831642654.832.113.4.2568.281563.4.4231.756..16..42336.24.819 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 7,9 => CTR => A3: 5 * PRF # A3: 5 => SOL * PRF # C3: 7,9 => SOL * DIS # C3: 5 => CTR => C3: 7,9 * PRF # C3: 7,9 => SOL * DIS # C3: 5 => CTR => C3: 7,9 * DIS # A3: 7,9 => CTR => A3: 5 * PRF # A3: 5 => SOL * PRF # C3: 5,7 => SOL * DIS # C3: 9 => CTR => C3: 5,7 * CNT 10 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 7,9 => CTR => A3: 5 * PRF A3: 5 => SOL * STA A3: 5 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2...6...7.8..2.........1.4.6.....2.1...4...........3...4.3...5...1............8.. | initial |
| 213564987486.2.135...831642654.832.113.4.2568.281563.4.4231.756..16..42336.24.819 | autosolve |
| 213564987486729135597831642654983271139472568728156394942318756871695423365247819 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) B3: 7,9 D2: 7,9 F2: 7,9 C5: 7,9 A6: 7,9 D4: 7,9 E5: 7,9 H4: 7,9 H6: 7,9 A7: 8,9 A8: 5,8 B8: 7,9 C9: 5,7 F7: 8,9 E8: 7,9 F8: 5,8 F9: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A3,C3: 5.. / A3 = 5 => 0 pairs (*) / C3 = 5 => 0 pairs (X) A8,C9: 5.. / A8 = 5 => 0 pairs (X) / C9 = 5 => 0 pairs (_) F8,F9: 5.. / F8 = 5 => 0 pairs (*) / F9 = 5 => 0 pairs (X) A8,F8: 5.. / A8 = 5 => 0 pairs (X) / F8 = 5 => 0 pairs (_) C9,F9: 5.. / C9 = 5 => 0 pairs (*) / F9 = 5 => 0 pairs (X) A3,A8: 5.. / A3 = 5 => 0 pairs (*) / A8 = 5 => 0 pairs (X) C3,C9: 5.. / C3 = 5 => 0 pairs (X) / C9 = 5 => 0 pairs (_) D2,F2: 7.. / D2 = 7 => 0 pairs (*) / F2 = 7 => 0 pairs (X) C5,A6: 7.. / C5 = 7 => 0 pairs (X) / A6 = 7 => 0 pairs (_) D4,E5: 7.. / D4 = 7 => 0 pairs (X) / E5 = 7 => 0 pairs (_) H4,H6: 7.. / H4 = 7 => 0 pairs (*) / H6 = 7 => 0 pairs (X) B8,C9: 7.. / B8 = 7 => 0 pairs (*) / C9 = 7 => 0 pairs (X) E8,F9: 7.. / E8 = 7 => 0 pairs (X) / F9 = 7 => 0 pairs (_) D4,H4: 7.. / D4 = 7 => 0 pairs (X) / H4 = 7 => 0 pairs (_) C5,E5: 7.. / C5 = 7 => 0 pairs (X) / E5 = 7 => 0 pairs (_) A6,H6: 7.. / A6 = 7 => 0 pairs (*) / H6 = 7 => 0 pairs (X) B8,E8: 7.. / B8 = 7 => 0 pairs (*) / E8 = 7 => 0 pairs (X) C9,F9: 7.. / C9 = 7 => 0 pairs (X) / F9 = 7 => 0 pairs (_) A3,A6: 7.. / A3 = 7 => 0 pairs (X) / A6 = 7 => 0 pairs (_) B3,B8: 7.. / B3 = 7 => 0 pairs (X) / B8 = 7 => 0 pairs (_) D2,D4: 7.. / D2 = 7 => 0 pairs (*) / D4 = 7 => 0 pairs (X) E5,E8: 7.. / E5 = 7 => 0 pairs (*) / E8 = 7 => 0 pairs (X) F2,F9: 7.. / F2 = 7 => 0 pairs (X) / F9 = 7 => 0 pairs (_) A7,A8: 8.. / A7 = 8 => 0 pairs (X) / A8 = 8 => 0 pairs (_) F7,F8: 8.. / F7 = 8 => 0 pairs (*) / F8 = 8 => 0 pairs (X) A7,F7: 8.. / A7 = 8 => 0 pairs (X) / F7 = 8 => 0 pairs (_) A8,F8: 8.. / A8 = 8 => 0 pairs (*) / F8 = 8 => 0 pairs (X) D2,F2: 9.. / D2 = 9 => 0 pairs (X) / F2 = 9 => 0 pairs (_) C5,A6: 9.. / C5 = 9 => 0 pairs (*) / A6 = 9 => 0 pairs (X) D4,E5: 9.. / D4 = 9 => 0 pairs (*) / E5 = 9 => 0 pairs (X) H4,H6: 9.. / H4 = 9 => 0 pairs (X) / H6 = 9 => 0 pairs (_) A7,B8: 9.. / A7 = 9 => 0 pairs (*) / B8 = 9 => 0 pairs (X) F7,E8: 9.. / F7 = 9 => 0 pairs (X) / E8 = 9 => 0 pairs (_) D4,H4: 9.. / D4 = 9 => 0 pairs (*) / H4 = 9 => 0 pairs (X) C5,E5: 9.. / C5 = 9 => 0 pairs (*) / E5 = 9 => 0 pairs (X) A6,H6: 9.. / A6 = 9 => 0 pairs (X) / H6 = 9 => 0 pairs (_) A7,F7: 9.. / A7 = 9 => 0 pairs (*) / F7 = 9 => 0 pairs (X) B8,E8: 9.. / B8 = 9 => 0 pairs (X) / E8 = 9 => 0 pairs (_) B3,B8: 9.. / B3 = 9 => 0 pairs (*) / B8 = 9 => 0 pairs (X) C3,C5: 9.. / C3 = 9 => 0 pairs (X) / C5 = 9 => 0 pairs (_) D2,D4: 9.. / D2 = 9 => 0 pairs (X) / D4 = 9 => 0 pairs (_) E5,E8: 9.. / E5 = 9 => 0 pairs (X) / E8 = 9 => 0 pairs (_) F2,F7: 9.. / F2 = 9 => 0 pairs (*) / F7 = 9 => 0 pairs (X) * DURATION: 0:01:32.587323 START: 09:20:24.954696 END: 09:21:57.542019 2017-05-04 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A7,A8,B3,B8,C5,C9,D2,D4,E5,E8,F2,F7,F8,F9,H4,H6) * 213564987486.2.135...831642654.832.113.4.2568.281563.4.4231.756..16..42336.24.819 * PAIR B3: 7,9 BLK 1 A3: 7,9,5 # reduction candidate for 7,9 A3: 7,9 => CTR * 213564987486.2.135..5831642654.832.1139472568728156394.4231.7565716..42336.24.819 A3: 5 => SOLVED * 213564987486729135597831642654983271139472568728156394942318756871695423365247819 C3: 7,9,5 # reduction candidate for 7,9 C3: 7,9 => SOLVED * 213564987486729135597831642654983271139472568728156394942318756871695423365247819 C3: 5 => CTR * 213564987486.2.135..5831642654.832.1139472568728156394.4231.7565716..42336.24.819 * PAIR C5: 7,9 COL C C3: 7,9,5 # reduction candidate for 7,9 C3: 7,9 => SOLVED * 213564987486729135597831642654983271139472568728156394942318756871695423365247819 C3: 5 => CTR * 213564987486.2.135..5831642654.832.1139472568728156394.4231.7565716..42336.24.819 * PAIR A6: 7,9 COL A A3: 7,9,5 # reduction candidate for 7,9 A3: 7,9 => CTR * 213564987486.2.135..5831642654.832.1139472568728156394.4231.7565716..42336.24.819 A3: 5 => SOLVED * 213564987486729135597831642654983271139472568728156394942318756871695423365247819 * PAIR C9: 5,7 COL C C3: 5,7,9 # reduction candidate for 5,7 C3: 5,7 => SOLVED * 213564987486729135597831642654983271139472568728156394942318756871695423365247819 C3: 9 => CTR * 213564987486.2.135579831642654.832.113.4.2568.281563.4.4231.756..16..42336.24.819 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-193-base-pr-000.dot * REASONING * DIS # A3: 7,9 => CTR => A3: 5 * PRF # A3: 5 => SOL * PRF # C3: 7,9 => SOL * DIS # C3: 5 => CTR => C3: 7,9 * PRF # C3: 7,9 => SOL * DIS # C3: 5 => CTR => C3: 7,9 * DIS # A3: 7,9 => CTR => A3: 5 * PRF # A3: 5 => SOL * PRF # C3: 5,7 => SOL * DIS # C3: 9 => CTR => C3: 5,7 * CNT 10 HDP CHAINS / 10 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A7,A8,B3,B8,C5,C9,D2,D4,E5,E8,F2,F7,F8,F9,H4,H6) * 213564987486.2.135...831642654.832.113.4.2568.281563.4.4231.756..16..42336.24.819 * PAIR B3: 7,9 BLK 1 A3: 7,9,5 # reduction candidate for 7,9 A3: 7,9 => CTR * 213564987486.2.135..5831642654.832.1139472568728156394.4231.7565716..42336.24.819 A3: 5 => SOLVED * 213564987486729135597831642654983271139472568728156394942318756871695423365247819 * DURATION: 0:00:01.834059 START: 09:22:13.378545 END: 09:22:15.212604 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-193-base-pr-001.dot * REASONING * DIS # A3: 7,9 => CTR => A3: 5 * PRF A3: 5 => SOL * STA A3: 5 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 193 solution: 213564987486729135597831642654983271139472568728156394942318756871695423365247819 info: 1849 FNBTWX S8.f 46313 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 213564987486729135597831642654983271139472568728156394942318756871695423365247819 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 # A3: 7,9 => CTR => A3: 5 * PRF # A3: 5 => SOL * PRF # C3: 7,9 => SOL * DIS # C3: 5 => CTR => C3: 7,9 * PRF # C3: 7,9 => SOL * DIS # C3: 5 => CTR => C3: 7,9 * DIS # A3: 7,9 => CTR => A3: 5 * PRF # A3: 5 => SOL * PRF # C3: 5,7 => SOL * DIS # C3: 9 => CTR => C3: 5,7 * CNT 10 HDP CHAINS / 10 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A3: 7,9 => CTR => A3: 5 * PRF A3: 5 => SOL * STA A3: 5 * CNT 2 HDP CHAINS / 1 HYP OPENED