Analysis of xx-top500-329-base.sdk
Contents
Original Sudoku
level: medium
position: ..2.9.3..8.5......1.........9..6..4........58........1.7....2..4..5........1..... initial
Autosolve
position: 7.2.9.3..8.5......1.9.......9..6.74........58........1.7....2..4..5........1..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D1: 4,6 => CTR => D1: 8 * PRF # D1: 8 => SOL * DIS # F1: 4,6 => CTR => F1: 1,5,8 * PRF # I1: 4,6 => SOL * DIS # I1: 5 => CTR => I1: 4,6 * DIS # F2: 1,4 => CTR => F2: 2,3,6,7 * PRF # F5: 1,2 => SOL * PRF # B8: 8 => SOL * PRF # E5: 4,7 => SOL * DIS # E6: 4,7 => CTR => E6: 2,3,5,8 * DIS # A4: 2,3 => CTR => A4: 5 * PRF # A4: 5 => SOL * PRF # D4: 2,3 => SOL * DIS # D4: 8 => CTR => D4: 2,3 * DIS # F4: 2,3 => CTR => F4: 1,5,8 * DIS # E6: 2,3 => CTR => E6: 4,5,7,8 * DIS # H8: 1,8 => CTR => H8: 3,6,7,9 * DIS # C8: 1,8 => CTR => C8: 3,6 * CNT 18 HDP CHAINS / 41 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D1: 4,6 => CTR => D1: 8 * PRF D1: 8 => SOL * STA D1: 8 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..2.9.3..8.5......1.........9..6..4........58........1.7....2..4..5........1..... | initial |
| 7.2.9.3..8.5......1.9.......9..6.74........58........1.7....2..4..5........1..... | autosolve |
| 742895316835617429169234587598361742317942658624758931971483265486529173253176894 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) B1: 4,6 G2: 1,4 B5: 1,2 C5: 4,7 C6: 4,7 I4: 2,3 G5: 6,9 G6: 6,9 H6: 2,3 G8: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C4,B5: 1.. / C4 = 1 => 0 pairs (X) / B5 = 1 => 0 pairs (_) F1,H1: 1.. / F1 = 1 => 0 pairs (X) / H1 = 1 => 0 pairs (_) C4,F4: 1.. / C4 = 1 => 0 pairs (X) / F4 = 1 => 0 pairs (_) C7,H7: 1.. / C7 = 1 => 0 pairs (*) / H7 = 1 => 0 pairs (X) B5,B8: 1.. / B5 = 1 => 0 pairs (*) / B8 = 1 => 0 pairs (X) E2,E5: 1.. / E2 = 1 => 0 pairs (*) / E5 = 1 => 0 pairs (X) G2,G8: 1.. / G2 = 1 => 0 pairs (X) / G8 = 1 => 0 pairs (_) I4,H6: 2.. / I4 = 2 => 10 pairs (_) / H6 = 2 => 15 pairs (_) B2,B3: 3.. / B2 = 3 => 11 pairs (_) / B3 = 3 => 11 pairs (_) I4,H6: 3.. / I4 = 3 => 15 pairs (_) / H6 = 3 => 10 pairs (_) C5,C6: 4.. / C5 = 4 => 8 pairs (_) / C6 = 4 => 8 pairs (_) F1,I1: 5.. / F1 = 5 => 0 pairs (*) / I1 = 5 => 0 pairs (X) A4,F4: 5.. / A4 = 5 => 0 pairs (*) / F4 = 5 => 0 pairs (X) A7,I7: 5.. / A7 = 5 => 0 pairs (X) / I7 = 5 => 0 pairs (_) B6,B9: 5.. / B6 = 5 => 0 pairs (X) / B9 = 5 => 0 pairs (_) E3,E6: 5.. / E3 = 5 => 0 pairs (X) / E6 = 5 => 0 pairs (_) G3,G9: 5.. / G3 = 5 => 0 pairs (*) / G9 = 5 => 0 pairs (X) A5,A6: 6.. / A5 = 6 => 9 pairs (_) / A6 = 6 => 9 pairs (_) G5,G6: 6.. / G5 = 6 => 9 pairs (_) / G6 = 6 => 9 pairs (_) A5,G5: 6.. / A5 = 6 => 9 pairs (_) / G5 = 6 => 9 pairs (_) A6,G6: 6.. / A6 = 6 => 9 pairs (_) / G6 = 6 => 9 pairs (_) C5,C6: 7.. / C5 = 7 => 8 pairs (_) / C6 = 7 => 8 pairs (_) C4,B6: 8.. / C4 = 8 => 0 pairs (*) / B6 = 8 => 0 pairs (X) H2,I2: 9.. / H2 = 9 => 10 pairs (_) / I2 = 9 => 10 pairs (_) G5,G6: 9.. / G5 = 9 => 9 pairs (_) / G6 = 9 => 9 pairs (_) A7,A9: 9.. / A7 = 9 => 0 pairs (*) / A9 = 9 => 0 pairs (X) * DURATION: 0:00:39.321383 START: 14:04:05.045702 END: 14:04:44.367085 2017-05-04 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B5,C5,C6,G2,G5,G6,G8,H6,I4) * 7.2.9.3..8.5......1.9.......9..6.74........58........1.7....2..4..5........1..... * PAIR B1: 4,6 BLK 1 B2: 4,6,3 # reduction candidate for 4,6 B2: 4,6 # 11 pairs B3: 4,6,3 # reduction candidate for 4,6 B3: 4,6 # 11 pairs * PAIR B1: 4,6 ROW 1 D1: 4,6,8 # reduction candidate for 4,6 D1: 4,6 => CTR * 7.2.9.3.58.5......1.9.......9..6574........58.5......157....2..4..5.....9..1..5.. D1: 8 => SOLVED * 742895316835617429169234587598361742317942658624758931971483265486529173253176894 F1: 4,6,1,5,8 # reduction candidate for 4,6 F1: 4,6 => CTR * 7.2.9.3158.5...4..1.9...8...9..6.74........58........1571...2..4..5..1..9..1..5.. F1: 1,5,8 # 10 pairs I1: 4,6,5 # reduction candidate for 4,6 I1: 4,6 => SOLVED * 742895316835617429169234587598361742317942658624758931971483265486529173253176894 I1: 5 => CTR * 7.2.9.3.58.5......1.9.......9..6574........58.5......157....2..4..5.....9..1..5.. * PAIR G2: 1,4 ROW 2 E2: 1,4,2,3,7 # reduction candidate for 1,4 E2: 1,4 # 12 pairs F2: 1,4,2,3,6,7 # reduction candidate for 1,4 F2: 1,4 => CTR * 7.2.913.58.5...1..1.9.......91.6.74..2..1..58.8......1.7....21.41.5..8..25.1..4.. F2: 2,3,6,7 # 10 pairs * PAIR B5: 1,2 ROW 5 E5: 1,2,3,4,7 # reduction candidate for 1,2 E5: 1,2 # 12 pairs F5: 1,2,3,4,7,9 # reduction candidate for 1,2 F5: 1,2 => SOLVED * 742895316835617429169234587598361742317942658624758931971483265486529173253176894 F5: 3,4,7,9 # 10 pairs * PAIR B5: 1,2 COL B B8: 1,2,8 # reduction candidate for 1,2 B8: 8 => SOLVED * 742895316835617429169234587598361742317942658624758931971483265486529173253176894 B8: 1,2 # 13 pairs * PAIR C5: 4,7 ROW 5 D5: 4,7,2,3,9 # reduction candidate for 4,7 D5: 4,7 # 11 pairs E5: 4,7,1,2,3 # reduction candidate for 4,7 E5: 4,7 => SOLVED * 742895316835617429169234587598361742317942658624758931971483265486529173253176894 E5: 1,2,3 # 10 pairs F5: 4,7,1,2,3,9 # reduction candidate for 4,7 F5: 4,7 # 11 pairs * PAIR C6: 4,7 ROW 6 D6: 4,7,2,3,8,9 # reduction candidate for 4,7 D6: 4,7 # 11 pairs E6: 4,7,2,3,5,8 # reduction candidate for 4,7 E6: 4,7 => CTR * 7.2.9.3.58.5......1.9.5.....98.6.74........58.5......157....2..4..5.....9..1..5.. E6: 2,3,5,8 # 10 pairs F6: 4,7,2,3,5,8,9 # reduction candidate for 4,7 F6: 4,7 # 11 pairs * PAIR I4: 2,3 ROW 4 A4: 2,3,5 # reduction candidate for 2,3 A4: 2,3 => CTR * 7.2.9.3.58.5......1.9.5.....9186574..2.....58.8......157....2..4..5........1..... A4: 5 => SOLVED * 742895316835617429169234587598361742317942658624758931971483265486529173253176894 D4: 2,3,8 # reduction candidate for 2,3 D4: 2,3 => SOLVED * 742895316835617429169234587598361742317942658624758931971483265486529173253176894 D4: 8 => CTR * 7.2.953..8.5......1.9...5...9.86.74........58.8..5...1.7....2.54..5......5.1..... F4: 2,3,1,5,8 # reduction candidate for 2,3 F4: 2,3 => CTR * 7.2.9.3..8.5......1.9......59186.74..2.....58.8......1.7....21541.5..8..25.1..4.. F4: 1,5,8 # 10 pairs * PAIR H6: 2,3 ROW 6 A6: 2,3,5,6 # reduction candidate for 2,3 A6: 2,3 # 11 pairs D6: 2,3,4,7,8,9 # reduction candidate for 2,3 D6: 2,3 # 13 pairs E6: 2,3,4,5,7,8 # reduction candidate for 2,3 E6: 2,3 => CTR * 7.2.9.3.58.5......1.9.5.....98.6.74........58.5......157....2..4..5.....9..1..5.. E6: 4,5,7,8 # 10 pairs F6: 2,3,4,5,7,8,9 # reduction candidate for 2,3 F6: 2,3 # 13 pairs * PAIR G8: 1,8 BLK 9 H7: 1,8,3,6,9 # reduction candidate for 1,8 H7: 1,8 # 12 pairs H8: 1,8,3,6,7,9 # reduction candidate for 1,8 H8: 1,8 => CTR * 7.2.9.31.8.5.1.4..1.9...8..59..6174..1.....58.8......1.71...2..42.5..18....1..5.. H8: 3,6,7,9 # 10 pairs * PAIR G8: 1,8 ROW 8 B8: 1,8,2 # reduction candidate for 1,8 B8: 1,8 # 15 pairs C8: 1,8,3,6 # reduction candidate for 1,8 C8: 1,8 => CTR * 7.2.953168.5.1.4..1.9...58.593861742.1.....58.8..5..31.71.8.2.54285..1.3.561..8.4 C8: 3,6 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-329-base-pr-000.dot * REASONING * DIS # D1: 4,6 => CTR => D1: 8 * PRF # D1: 8 => SOL * DIS # F1: 4,6 => CTR => F1: 1,5,8 * PRF # I1: 4,6 => SOL * DIS # I1: 5 => CTR => I1: 4,6 * DIS # F2: 1,4 => CTR => F2: 2,3,6,7 * PRF # F5: 1,2 => SOL * PRF # B8: 8 => SOL * PRF # E5: 4,7 => SOL * DIS # E6: 4,7 => CTR => E6: 2,3,5,8 * DIS # A4: 2,3 => CTR => A4: 5 * PRF # A4: 5 => SOL * PRF # D4: 2,3 => SOL * DIS # D4: 8 => CTR => D4: 2,3 * DIS # F4: 2,3 => CTR => F4: 1,5,8 * DIS # E6: 2,3 => CTR => E6: 4,5,7,8 * DIS # H8: 1,8 => CTR => H8: 3,6,7,9 * DIS # C8: 1,8 => CTR => C8: 3,6 * CNT 18 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B5,C5,C6,G2,G5,G6,G8,H6,I4) * 7.2.9.3..8.5......1.9.......9..6.74........58........1.7....2..4..5........1..... * PAIR B1: 4,6 BLK 1 B2: 4,6,3 # reduction candidate for 4,6 B2: 4,6 # 11 pairs B3: 4,6,3 # reduction candidate for 4,6 B3: 4,6 # 11 pairs * PAIR B1: 4,6 ROW 1 D1: 4,6,8 # reduction candidate for 4,6 D1: 4,6 => CTR * 7.2.9.3.58.5......1.9.......9..6574........58.5......157....2..4..5.....9..1..5.. D1: 8 => SOLVED * 742895316835617429169234587598361742317942658624758931971483265486529173253176894 * DURATION: 0:00:03.090469 START: 14:05:18.172964 END: 14:05:21.263433 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-329-base-pr-001.dot * REASONING * DIS # D1: 4,6 => CTR => D1: 8 * PRF D1: 8 => SOL * STA D1: 8 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 329 solution: 742895316835617429169234587598361742317942658624758931971483265486529173253176894 info: 2982 FNBTHWY S8.f 13279 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 742895316835617429169234587598361742317942658624758931971483265486529173253176894 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 # B2: 4,6 => UNS * INC # B3: 4,6 => UNS * DIS # D1: 4,6 => CTR => D1: 8 * PRF # D1: 8 => SOL * DIS # F1: 4,6 => CTR => F1: 1,5,8 * INC # F1: 1,5,8 => UNS * PRF # I1: 4,6 => SOL * DIS # I1: 5 => CTR => I1: 4,6 * INC # E2: 1,4 => UNS * DIS # F2: 1,4 => CTR => F2: 2,3,6,7 * INC # F2: 2,3,6,7 => UNS * INC # E5: 1,2 => UNS * PRF # F5: 1,2 => SOL * INC # F5: 3,4,7,9 => UNS * INC # B8: 1,2 => UNS * PRF # B8: 8 => SOL * INC # D5: 4,7 => UNS * PRF # E5: 4,7 => SOL * INC # E5: 1,2,3 => UNS * INC # F5: 4,7 => UNS * INC # D6: 4,7 => UNS * DIS # E6: 4,7 => CTR => E6: 2,3,5,8 * INC # E6: 2,3,5,8 => UNS * INC # F6: 4,7 => UNS * DIS # A4: 2,3 => CTR => A4: 5 * PRF # A4: 5 => SOL * PRF # D4: 2,3 => SOL * DIS # D4: 8 => CTR => D4: 2,3 * DIS # F4: 2,3 => CTR => F4: 1,5,8 * INC # F4: 1,5,8 => UNS * INC # A6: 2,3 => UNS * INC # D6: 2,3 => UNS * DIS # E6: 2,3 => CTR => E6: 4,5,7,8 * INC # E6: 4,5,7,8 => UNS * INC # F6: 2,3 => UNS * INC # H7: 1,8 => UNS * DIS # H8: 1,8 => CTR => H8: 3,6,7,9 * INC # H8: 3,6,7,9 => UNS * INC # B8: 1,8 => UNS * DIS # C8: 1,8 => CTR => C8: 3,6 * INC # C8: 3,6 => UNS * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 4,6 => UNS * INC # B3: 4,6 => UNS * DIS # D1: 4,6 => CTR => D1: 8 * PRF D1: 8 => SOL * STA D1: 8 * CNT 4 HDP CHAINS / 3 HYP OPENED