Analysis of xx-top500-157-base.sdk
Contents
Original Sudoku
level: medium
position: 1...52.4.....6..........3.....3..7.65..7...........8....2....5..3.8.............1 initial
Autosolve
position: 1739526482..1635796594..312..13.572652.7..1343.721.8958126...53.35821.677..53.281 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B4: 4,8 => CTR => B4: 9 * PRF # B4: 9 => SOL * PRF # B4: 4,9 => SOL * DIS # B4: 8 => CTR => B4: 4,9 * DIS # F5: 9 => CTR => F5: 6,8 * PRF # B9: 4,6 => SOL * DIS # B9: 9 => CTR => B9: 4,6 * DIS # B4: 4,8 => CTR => B4: 9 * PRF # B4: 9 => SOL * DIS # F5: 8,9 => CTR => F5: 6 * PRF # F5: 6 => SOL * PRF # B9: 4,9 => SOL * DIS # B9: 6 => CTR => B9: 4,9 * PRF # B9: 4,6 => SOL * DIS # B9: 9 => CTR => B9: 4,6 * DIS # F7: 4,9 => CTR => F7: 7 * PRF # B9: 4,9 => SOL * DIS # B9: 6 => CTR => B9: 4,9 * DIS # F7: 4,9 => CTR => F7: 7 * CNT 19 HDP CHAINS / 24 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B4: 4,8 => CTR => B4: 9 * PRF B4: 9 => SOL * STA B4: 9 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1...52.4.....6..........3.....3..7.65..7...........8....2....5..3.8.............1 | initial |
| 1739526482..1635796594..312..13.572652.7..1343.721.8958126...53.35821.677..53.281 | autosolve |
| 173952648284163579659478312491385726528796134367214895812647953935821467746539281 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) B2: 4,8 C2: 4,8 E3: 7,8 F3: 7,8 A4: 4,9 C5: 6,8 B6: 4,6 E4: 4,8 E5: 8,9 F6: 4,6 A8: 4,9 C9: 4,6 F9: 4,9 G7: 4,9 G8: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,C2: 4.. / B2 = 4 => 0 pairs (X) / C2 = 4 => 0 pairs (_) E4,F6: 4.. / E4 = 4 => 0 pairs (X) / F6 = 4 => 0 pairs (_) G7,G8: 4.. / G7 = 4 => 0 pairs (X) / G8 = 4 => 0 pairs (_) B6,F6: 4.. / B6 = 4 => 0 pairs (X) / F6 = 4 => 0 pairs (_) A8,G8: 4.. / A8 = 4 => 0 pairs (X) / G8 = 4 => 0 pairs (_) A4,A8: 4.. / A4 = 4 => 0 pairs (*) / A8 = 4 => 0 pairs (X) C2,C9: 4.. / C2 = 4 => 0 pairs (*) / C9 = 4 => 0 pairs (X) E4,E7: 4.. / E4 = 4 => 0 pairs (X) / E7 = 4 => 0 pairs (_) C5,B6: 6.. / C5 = 6 => 0 pairs (X) / B6 = 6 => 0 pairs (_) F5,F6: 6.. / F5 = 6 => 0 pairs (*) / F6 = 6 => 0 pairs (X) B9,C9: 6.. / B9 = 6 => 0 pairs (X) / C9 = 6 => 0 pairs (_) C5,F5: 6.. / C5 = 6 => 0 pairs (X) / F5 = 6 => 0 pairs (_) B6,F6: 6.. / B6 = 6 => 0 pairs (*) / F6 = 6 => 0 pairs (X) B6,B9: 6.. / B6 = 6 => 0 pairs (*) / B9 = 6 => 0 pairs (X) C5,C9: 6.. / C5 = 6 => 0 pairs (X) / C9 = 6 => 0 pairs (_) E3,F3: 7.. / E3 = 7 => 15 pairs (_) / F3 = 7 => 0 pairs (X) E7,F7: 7.. / E7 = 7 => 0 pairs (X) / F7 = 7 => 15 pairs (_) E3,E7: 7.. / E3 = 7 => 15 pairs (_) / E7 = 7 => 0 pairs (X) F3,F7: 7.. / F3 = 7 => 0 pairs (X) / F7 = 7 => 15 pairs (_) B2,C2: 8.. / B2 = 8 => 0 pairs (*) / C2 = 8 => 0 pairs (X) E3,F3: 8.. / E3 = 8 => 0 pairs (X) / F3 = 8 => 15 pairs (_) B4,C5: 8.. / B4 = 8 => 0 pairs (X) / C5 = 8 => 0 pairs (_) B4,E4: 8.. / B4 = 8 => 0 pairs (X) / E4 = 8 => 0 pairs (_) B2,B4: 8.. / B2 = 8 => 0 pairs (*) / B4 = 8 => 0 pairs (X) C2,C5: 8.. / C2 = 8 => 0 pairs (X) / C5 = 8 => 0 pairs (_) F3,F5: 8.. / F3 = 8 => 15 pairs (_) / F5 = 8 => 0 pairs (X) A4,B4: 9.. / A4 = 9 => 0 pairs (X) / B4 = 9 => 0 pairs (_) E5,F5: 9.. / E5 = 9 => 16 pairs (_) / F5 = 9 => 0 pairs (X) A8,B9: 9.. / A8 = 9 => 0 pairs (*) / B9 = 9 => 0 pairs (X) G7,G8: 9.. / G7 = 9 => 0 pairs (*) / G8 = 9 => 0 pairs (X) A8,G8: 9.. / A8 = 9 => 0 pairs (*) / G8 = 9 => 0 pairs (X) B9,F9: 9.. / B9 = 9 => 0 pairs (X) / F9 = 9 => 0 pairs (_) A4,A8: 9.. / A4 = 9 => 0 pairs (X) / A8 = 9 => 0 pairs (_) B4,B9: 9.. / B4 = 9 => 0 pairs (*) / B9 = 9 => 0 pairs (X) E5,E7: 9.. / E5 = 9 => 16 pairs (_) / E7 = 9 => 0 pairs (X) * DURATION: 0:01:01.797063 START: 08:06:58.638262 END: 08:08:00.435325 2017-05-04 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A8,B2,B6,C2,C5,C9,E3,E4,E5,F3,F6,F9,G7,G8) * 1739526482..1635796594..312..13.572652.7..1343.721.8958126...53.35821.677..53.281 * PAIR B2: 4,8 COL B B4: 4,8,9 # reduction candidate for 4,8 B4: 4,8 => CTR * 1739526482..1635796594..3129.13.572652.7..1343.721.8958126...53435821967796534281 B4: 9 => SOLVED * 173952648284163579659478312491385726528796134367214895812647953935821467746539281 * PAIR A4: 4,9 BLK 4 B4: 4,9,8 # reduction candidate for 4,9 B4: 4,9 => SOLVED * 173952648284163579659478312491385726528796134367214895812647953935821467746539281 B4: 8 => CTR * 1739526482..1635796594..3129813457265267..13434721.8958126...53.35821.677..53.281 * PAIR C5: 6,8 ROW 5 F5: 6,8,9 # reduction candidate for 6,8 F5: 9 => CTR * 1739526482..1635796594.8312..13.572652678913434721.8958126...53.35821.677..53.281 F5: 6,8 # 16 pairs * PAIR B6: 4,6 COL B B9: 4,6,9 # reduction candidate for 4,6 B9: 4,6 => SOLVED * 173952648284163579659478312491385726528796134367214895812647953935821467746539281 B9: 9 => CTR * 1739526482..1635796594..312..13.572652.7..134367214895812647953935821.677..53.281 * PAIR E4: 4,8 ROW 4 B4: 4,8,9 # reduction candidate for 4,8 B4: 4,8 => CTR * 1739526482..1635796594..3129.13.572652.7..1343.721.8958126...53435821967796534281 B4: 9 => SOLVED * 173952648284163579659478312491385726528796134367214895812647953935821467746539281 * PAIR E5: 8,9 BLK 5 F5: 8,9,6 # reduction candidate for 8,9 F5: 8,9 => CTR * 1739526482..1635796594..312..13.57265267..1343472168958126...53435821.677..53.281 F5: 6 => SOLVED * 173952648284163579659478312491385726528796134367214895812647953935821467746539281 * PAIR A8: 4,9 BLK 7 B9: 4,9,6 # reduction candidate for 4,9 B9: 4,9 => SOLVED * 173952648284163579659478312491385726528796134367214895812647953935821467746539281 B9: 6 => CTR * 1739526482..1635796594..312.9138572652879613436721.8958126...53.35821.677..53.281 * PAIR C9: 4,6 BLK 7 B9: 4,6,9 # reduction candidate for 4,6 B9: 4,6 => SOLVED * 173952648284163579659478312491385726528796134367214895812647953935821467746539281 B9: 9 => CTR * 1739526482..1635796594..312..13.572652.7..134367214895812647953935821.677..53.281 * PAIR F9: 4,9 BLK 8 E7: 4,9,7 # reduction candidate for 4,9 E7: 4,9 # 15 pairs F7: 4,9,7 # reduction candidate for 4,9 F7: 4,9 => CTR * 1739526482..1635796594.7312..13.572652.7.81343.721689581267..53.35821.67764539281 F7: 7 # 15 pairs * PAIR F9: 4,9 ROW 9 B9: 4,9,6 # reduction candidate for 4,9 B9: 4,9 => SOLVED * 173952648284163579659478312491385726528796134367214895812647953935821467746539281 B9: 6 => CTR * 1739526482..1635796594..312.9138572652879613436721.8958126...53.35821.677..53.281 * PAIR G7: 4,9 ROW 7 E7: 4,9,7 # reduction candidate for 4,9 E7: 4,9 # 15 pairs F7: 4,9,7 # reduction candidate for 4,9 F7: 4,9 => CTR * 1739526482..1635796594.7312..13.572652.7.81343.721689581267..53.35821.67764539281 F7: 7 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-157-base-pr-000.dot * REASONING * DIS # B4: 4,8 => CTR => B4: 9 * PRF # B4: 9 => SOL * PRF # B4: 4,9 => SOL * DIS # B4: 8 => CTR => B4: 4,9 * DIS # F5: 9 => CTR => F5: 6,8 * PRF # B9: 4,6 => SOL * DIS # B9: 9 => CTR => B9: 4,6 * DIS # B4: 4,8 => CTR => B4: 9 * PRF # B4: 9 => SOL * DIS # F5: 8,9 => CTR => F5: 6 * PRF # F5: 6 => SOL * PRF # B9: 4,9 => SOL * DIS # B9: 6 => CTR => B9: 4,9 * PRF # B9: 4,6 => SOL * DIS # B9: 9 => CTR => B9: 4,6 * DIS # F7: 4,9 => CTR => F7: 7 * PRF # B9: 4,9 => SOL * DIS # B9: 6 => CTR => B9: 4,9 * DIS # F7: 4,9 => CTR => F7: 7 * CNT 19 HDP CHAINS / 24 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A8,B2,B6,C2,C5,C9,E3,E4,E5,F3,F6,F9,G7,G8) * 1739526482..1635796594..312..13.572652.7..1343.721.8958126...53.35821.677..53.281 * PAIR B2: 4,8 COL B B4: 4,8,9 # reduction candidate for 4,8 B4: 4,8 => CTR * 1739526482..1635796594..3129.13.572652.7..1343.721.8958126...53435821967796534281 B4: 9 => SOLVED * 173952648284163579659478312491385726528796134367214895812647953935821467746539281 * DURATION: 0:00:02.755548 START: 08:08:26.475514 END: 08:08:29.231062 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-157-base-pr-001.dot * REASONING * DIS # B4: 4,8 => CTR => B4: 9 * PRF B4: 9 => SOL * STA B4: 9 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 157 solution: 173952648284163579659478312491385726528796134367214895812647953935821467746539281 info: 1819 FNBWY S8.f 25339 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 173952648284163579659478312491385726528796134367214895812647953935821467746539281 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 # B4: 4,8 => CTR => B4: 9 * PRF # B4: 9 => SOL * PRF # B4: 4,9 => SOL * DIS # B4: 8 => CTR => B4: 4,9 * INC # F5: 6,8 => UNS * DIS # F5: 9 => CTR => F5: 6,8 * PRF # B9: 4,6 => SOL * DIS # B9: 9 => CTR => B9: 4,6 * DIS # B4: 4,8 => CTR => B4: 9 * PRF # B4: 9 => SOL * DIS # F5: 8,9 => CTR => F5: 6 * PRF # F5: 6 => SOL * PRF # B9: 4,9 => SOL * DIS # B9: 6 => CTR => B9: 4,9 * PRF # B9: 4,6 => SOL * DIS # B9: 9 => CTR => B9: 4,6 * INC # E7: 4,9 => UNS * DIS # F7: 4,9 => CTR => F7: 7 * INC # F7: 7 => UNS * PRF # B9: 4,9 => SOL * DIS # B9: 6 => CTR => B9: 4,9 * INC # E7: 4,9 => UNS * DIS # F7: 4,9 => CTR => F7: 7 * INC # F7: 7 => UNS * CNT 24 HDP CHAINS / 24 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B4: 4,8 => CTR => B4: 9 * PRF B4: 9 => SOL * STA B4: 9 * CNT 2 HDP CHAINS / 1 HYP OPENED