Analysis of xx-top500-458-base.sdk
Contents
Original Sudoku
level: medium
position: 5....27...1.4..............26....8.....13........4.......6...31..9....4.7........ initial
Autosolve
position: 5...127...1.4..3........1..264...813...13.4.....24.......6...31..9....477........ autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 8,9 => CTR => A2: 6 * PRF # A2: 6 => SOL * DIS # A3: 8,9 => CTR => A3: 3,4,6 * DIS # B7: 4,8 => CTR => B7: 2,5 * PRF # A3: 4,8 => SOL * DIS # A3: 3,6,9 => CTR => A3: 4,8 * CNT 6 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 # A2: 8,9 => CTR => A2: 6 * PRF A2: 6 => SOL * STA A2: 6 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 5....27...1.4..............26....8.....13........4.......6...31..9....4.7........ | initial |
| 5...127...1.4..3........1..264...813...13.4.....24.......6...31..9....477........ | autosolve |
| 583912764612487359497563128264759813958136472371248596825674931139825647746391285 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) A5: 8,9 A6: 1,3 C6: 1,3 F5: 6,8 F6: 6,8 A7: 4,8 A8: 1,6 C9: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A6,C6: 1.. / A6 = 1 => 0 pairs (X) / C6 = 1 => 0 pairs (_) A8,C9: 1.. / A8 = 1 => 0 pairs (*) / C9 = 1 => 0 pairs (X) F8,F9: 1.. / F8 = 1 => 0 pairs (X) / F9 = 1 => 0 pairs (_) A8,F8: 1.. / A8 = 1 => 0 pairs (*) / F8 = 1 => 0 pairs (X) C9,F9: 1.. / C9 = 1 => 0 pairs (X) / F9 = 1 => 0 pairs (_) A6,A8: 1.. / A6 = 1 => 0 pairs (X) / A8 = 1 => 0 pairs (_) C6,C9: 1.. / C6 = 1 => 0 pairs (*) / C9 = 1 => 0 pairs (X) H5,I5: 2.. / H5 = 2 => 8 pairs (_) / I5 = 2 => 8 pairs (_) A6,C6: 3.. / A6 = 3 => 0 pairs (*) / C6 = 3 => 0 pairs (X) B8,B9: 3.. / B8 = 3 => 10 pairs (_) / B9 = 3 => 0 pairs (X) C1,D1: 3.. / C1 = 3 => 0 pairs (*) / D1 = 3 => 0 pairs (X) A3,A6: 3.. / A3 = 3 => 0 pairs (X) / A6 = 3 => 0 pairs (_) I1,I3: 4.. / I1 = 4 => 9 pairs (_) / I3 = 4 => 0 pairs (X) F7,F9: 4.. / F7 = 4 => 0 pairs (*) / F9 = 4 => 0 pairs (X) B1,I1: 4.. / B1 = 4 => 0 pairs (X) / I1 = 4 => 9 pairs (_) B9,F9: 4.. / B9 = 4 => 0 pairs (*) / F9 = 4 => 0 pairs (X) A3,A7: 4.. / A3 = 4 => 0 pairs (*) / A7 = 4 => 0 pairs (X) C5,C7: 5.. / C5 = 5 => 9 pairs (_) / C7 = 5 => 10 pairs (_) E2,E3: 6.. / E2 = 6 => 0 pairs (X) / E3 = 6 => 8 pairs (_) F5,F6: 6.. / F5 = 6 => 6 pairs (_) / F6 = 6 => 13 pairs (_) A8,C9: 6.. / A8 = 6 => 0 pairs (X) / C9 = 6 => 0 pairs (_) A8,G8: 6.. / A8 = 6 => 0 pairs (X) / G8 = 6 => 0 pairs (_) H5,H6: 7.. / H5 = 7 => 7 pairs (_) / H6 = 7 => 8 pairs (_) E7,F7: 7.. / E7 = 7 => 9 pairs (_) / F7 = 7 => 0 pairs (X) B6,H6: 7.. / B6 = 7 => 7 pairs (_) / H6 = 7 => 8 pairs (_) D3,D4: 7.. / D3 = 7 => 11 pairs (_) / D4 = 7 => 10 pairs (_) F5,F6: 8.. / F5 = 8 => 13 pairs (_) / F6 = 8 => 6 pairs (_) H9,I9: 8.. / H9 = 8 => 9 pairs (_) / I9 = 8 => 8 pairs (_) B6,F6: 8.. / B6 = 8 => 13 pairs (_) / F6 = 8 => 6 pairs (_) * DURATION: 0:00:53.386295 START: 18:24:24.458033 END: 18:25:17.844328 2017-05-04 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,A7,A8,C6,C9,F5,F6) * 5...127...1.4..3........1..264...813...13.4.....24.......6...31..9....477........ * PAIR A5: 8,9 BLK 4 B5: 8,9,5,7 # reduction candidate for 8,9 B5: 8,9 # 10 pairs B6: 8,9,5,7 # reduction candidate for 8,9 B6: 8,9 # 11 pairs * PAIR A5: 8,9 COL A A2: 8,9,6 # reduction candidate for 8,9 A2: 8,9 => CTR * 5...127...1.4..3.......31..264...813...13.4.....24....4..6...31..9..1.477.1..4... A2: 6 => SOLVED * 583912764612487359497563128264759813958136472371248596825674931139825647746391285 A3: 8,9,3,4,6 # reduction candidate for 8,9 A3: 8,9 => CTR * 5...127...1.4..3........1..264...813...13.4..3.124....4..6...311.9...6477.6...... A3: 3,4,6 # 8 pairs * PAIR A7: 4,8 BLK 7 B7: 4,8,2,5 # reduction candidate for 4,8 B7: 4,8 => CTR * 5...127...1.4..3.......31..264...813...13.4..3.124.......6...311.9....477........ B7: 2,5 # 9 pairs * PAIR A7: 4,8 COL A A3: 4,8,3,6,9 # reduction candidate for 4,8 A3: 4,8 => SOLVED * 583912764612487359497563128264759813958136472371248596825674931139825647746391285 A3: 3,6,9 => CTR * 5...127...1.4..3.......31..264...813...13.4.....24....4..6...31..9..1.477.1..4... * INCONCLUSIVE * SAVE PR GRAPH xx-top500-458-base-pr-000.dot * REASONING * DIS # A2: 8,9 => CTR => A2: 6 * PRF # A2: 6 => SOL * DIS # A3: 8,9 => CTR => A3: 3,4,6 * DIS # B7: 4,8 => CTR => B7: 2,5 * PRF # A3: 4,8 => SOL * DIS # A3: 3,6,9 => CTR => A3: 4,8 * CNT 6 HDP CHAINS / 10 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,A7,A8,C6,C9,F5,F6) * 5...127...1.4..3........1..264...813...13.4.....24.......6...31..9....477........ * PAIR A5: 8,9 BLK 4 B5: 8,9,5,7 # reduction candidate for 8,9 B5: 8,9 # 10 pairs B6: 8,9,5,7 # reduction candidate for 8,9 B6: 8,9 # 11 pairs * PAIR A5: 8,9 COL A A2: 8,9,6 # reduction candidate for 8,9 A2: 8,9 => CTR * 5...127...1.4..3.......31..264...813...13.4.....24....4..6...31..9..1.477.1..4... A2: 6 => SOLVED * 583912764612487359497563128264759813958136472371248596825674931139825647746391285 * DURATION: 0:00:03.815404 START: 18:25:29.226460 END: 18:25:33.041864 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-458-base-pr-001.dot * REASONING * DIS # A2: 8,9 => CTR => A2: 6 * PRF A2: 6 => SOL * STA A2: 6 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 458 solution: 583912764612487359497563128264759813958136472371248596825674931139825647746391285 info: 95523 FNBHYK S8.f 44295 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 583912764612487359497563128264759813958136472371248596825674931139825647746391285 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 # B5: 8,9 => UNS * INC # B6: 8,9 => UNS * DIS # A2: 8,9 => CTR => A2: 6 * PRF # A2: 6 => SOL * DIS # A3: 8,9 => CTR => A3: 3,4,6 * INC # A3: 3,4,6 => UNS * DIS # B7: 4,8 => CTR => B7: 2,5 * INC # B7: 2,5 => UNS * PRF # A3: 4,8 => SOL * DIS # A3: 3,6,9 => CTR => A3: 4,8 * CNT 10 HDP CHAINS / 10 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B5: 8,9 => UNS * INC # B6: 8,9 => UNS * DIS # A2: 8,9 => CTR => A2: 6 * PRF A2: 6 => SOL * STA A2: 6 * CNT 4 HDP CHAINS / 3 HYP OPENED