Analysis of xx-top500-319-base.sdk
Contents
Original Sudoku
level: medium
position: ..2.9.3..8.5......1.........9..6..4........58........1.7....2..3..5........1..... initial
Autosolve
position: 7.2.9.3..8.5......1.9.......9..6.74........58........1.7....2..3..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 * DIS # G8: 8 => CTR => G8: 1,4 * DIS # A6: 2,5 => CTR => A6: 4,6 * PRF # B6: 2,5 => SOL * DIS # B6: 8 => CTR => B6: 2,5 * DIS # F4: 2,5 => CTR => F4: 1,3,8 * PRF # F4: 1,3,8 => SOL * PRF # A9: 2,5 => SOL * DIS # A9: 4,6,9 => CTR => A9: 2,5 * PRF # F5: 1,2 => SOL * PRF # B8: 8 => 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 * CNT 20 HDP CHAINS / 34 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..3..5........1..... | initial |
| 7.2.9.3..8.5......1.9.......9..6.74........58........1.7....2..3..5........1..... | autosolve |
| 742895316835617429169234587598361742613742958427958631971483265386529174254176893 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) B1: 4,6 G2: 1,4 A4: 2,5 B5: 1,2 I4: 2,3 G5: 6,9 G6: 6,9 H6: 2,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) 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 => 0 pairs (*) / H6 = 2 => 0 pairs (X) B2,B3: 3.. / B2 = 3 => 9 pairs (_) / B3 = 3 => 9 pairs (_) I4,H6: 3.. / I4 = 3 => 14 pairs (_) / H6 = 3 => 0 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) G5,G6: 6.. / G5 = 6 => 7 pairs (_) / G6 = 6 => 6 pairs (_) C5,C6: 7.. / C5 = 7 => 9 pairs (_) / C6 = 7 => 8 pairs (_) H2,I2: 9.. / H2 = 9 => 8 pairs (_) / I2 = 9 => 8 pairs (_) G5,G6: 9.. / G5 = 9 => 6 pairs (_) / G6 = 9 => 7 pairs (_) A7,A9: 9.. / A7 = 9 => 0 pairs (*) / A9 = 9 => 0 pairs (X) * DURATION: 0:00:30.385900 START: 13:51:50.571172 END: 13:52:20.957072 2017-05-04 * CP COUNT: (20) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B1,B5,G2,G5,G6,H6,I4) * 7.2.9.3..8.5......1.9.......9..6.74........58........1.7....2..3..5........1..... * PAIR B1: 4,6 BLK 1 B2: 4,6,3 # reduction candidate for 4,6 B2: 4,6 # 9 pairs B3: 4,6,3 # reduction candidate for 4,6 B3: 4,6 # 9 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......29..65743.1.....58.5.....2157....2..3..5.....9..1..5.. D1: 8 => SOLVED * 742895316835617429169234587598361742613742958427958631971483265386529174254176893 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..3..5..1..9..1..5.. F1: 1,5,8 # 8 pairs I1: 4,6,5 # reduction candidate for 4,6 I1: 4,6 => SOLVED * 742895316835617429169234587598361742613742958427958631971483265386529174254176893 I1: 5 => CTR * 7.2.9.3.58.5......1.9......29..65743.1.....58.5.....2157....2..3..5.....9..1..5.. * PAIR G2: 1,4 ROW 2 E2: 1,4,2,3,7 # reduction candidate for 1,4 E2: 1,4 # 10 pairs F2: 1,4,2,3,6,7 # reduction candidate for 1,4 F2: 1,4 => CTR * 7.2.913.58.5..41..1.9......591.6.74..2..1..58........1.7....21.31.5.....2..1..... F2: 2,3,6,7 # 8 pairs * PAIR G2: 1,4 COL G G8: 1,4,8 # reduction candidate for 1,4 G8: 8 => CTR * 7.2.913.58.5...1..1.9...4...91.6.74..2..1..58........157....2..31.5..8.....1..... G8: 1,4 # 11 pairs * PAIR A4: 2,5 BLK 4 A6: 2,5,4,6 # reduction candidate for 2,5 A6: 2,5 => CTR * 7.2.9531.8.5.1.4..1.9...58.593861742.1.....5828..5..31.71...2.532.5..1.4.5.1..8.3 A6: 4,6 # 9 pairs B6: 2,5,8 # reduction candidate for 2,5 B6: 2,5 => SOLVED * 742895316835617429169234587598361742613742958427958631971483265386529174254176893 B6: 8 => CTR * 7.28953168.5...4..1.9...58.593.6.74........58.8..5...1.71...2.532.5..1...5.1..8.. * PAIR A4: 2,5 ROW 4 F4: 2,5,1,3,8 # reduction candidate for 2,5 F4: 2,5 => CTR * 7.2.913858.5...1..1.9...4..59186.743.2.....58.......21.7....21.31.5.....2..1...3. F4: 1,3,8 => SOLVED * 742895316835617429169234587598361742613742958427958631971483265386529174254176893 * PAIR A4: 2,5 COL A A9: 2,5,4,6,9 # reduction candidate for 2,5 A9: 2,5 => SOLVED * 742895316835617429169234587598361742613742958427958631971483265386529174254176893 A9: 4,6,9 => CTR * 7.2.953168.5.1.4..1.9...58.593861742.1.....58.8..5..31.71...2.53285..1...5.1..8.3 * PAIR B5: 1,2 ROW 5 E5: 1,2,3,4,7 # reduction candidate for 1,2 E5: 1,2 # 10 pairs F5: 1,2,3,4,7,9 # reduction candidate for 1,2 F5: 1,2 => SOLVED * 742895316835617429169234587598361742613742958427958631971483265386529174254176893 F5: 3,4,7,9 # 8 pairs * PAIR B5: 1,2 COL B B8: 1,2,8 # reduction candidate for 1,2 B8: 8 => SOLVED * 742895316835617429169234587598361742613742958427958631971483265386529174254176893 B8: 1,2 # 11 pairs * PAIR I4: 2,3 ROW 4 D4: 2,3,8 # reduction candidate for 2,3 D4: 2,3 => SOLVED * 742895316835617429169234587598361742613742958427958631971483265386529174254176893 D4: 8 => CTR * 7.2.9.3.58.5......1.9......29.865743.1.....58........157....2..3..5.....9..1..5.. 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....21531.5.....25.1..... F4: 1,5,8 # 8 pairs * PAIR H6: 2,3 ROW 6 D6: 2,3,4,7,8,9 # reduction candidate for 2,3 D6: 2,3 # 10 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....29..65743.1.....58.5.....2157....2..3..5.....9..1..5.. E6: 4,5,7,8 # 8 pairs F6: 2,3,4,5,7,8,9 # reduction candidate for 2,3 F6: 2,3 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-319-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 * DIS # G8: 8 => CTR => G8: 1,4 * DIS # A6: 2,5 => CTR => A6: 4,6 * PRF # B6: 2,5 => SOL * DIS # B6: 8 => CTR => B6: 2,5 * DIS # F4: 2,5 => CTR => F4: 1,3,8 * PRF # F4: 1,3,8 => SOL * PRF # A9: 2,5 => SOL * DIS # A9: 4,6,9 => CTR => A9: 2,5 * PRF # F5: 1,2 => SOL * PRF # B8: 8 => 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 * CNT 20 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B1,B5,G2,G5,G6,H6,I4) * 7.2.9.3..8.5......1.9.......9..6.74........58........1.7....2..3..5........1..... * PAIR B1: 4,6 BLK 1 B2: 4,6,3 # reduction candidate for 4,6 B2: 4,6 # 9 pairs B3: 4,6,3 # reduction candidate for 4,6 B3: 4,6 # 9 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......29..65743.1.....58.5.....2157....2..3..5.....9..1..5.. D1: 8 => SOLVED * 742895316835617429169234587598361742613742958427958631971483265386529174254176893 * DURATION: 0:00:02.970078 START: 13:52:49.708898 END: 13:52:52.678976 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-319-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 17 319 solution: 742895316835617429169234587598361742613742958427958631971483265386529174254176893 info: 2914 FNBTHWY S8.f 13278 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 742895316835617429169234587598361742613742958427958631971483265386529174254176893 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 # G8: 1,4 => UNS * DIS # G8: 8 => CTR => G8: 1,4 * DIS # A6: 2,5 => CTR => A6: 4,6 * INC # A6: 4,6 => UNS * PRF # B6: 2,5 => SOL * DIS # B6: 8 => CTR => B6: 2,5 * DIS # F4: 2,5 => CTR => F4: 1,3,8 * PRF # F4: 1,3,8 => SOL * PRF # A9: 2,5 => SOL * DIS # A9: 4,6,9 => CTR => A9: 2,5 * 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 * 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 # 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 * CNT 34 HDP CHAINS / 34 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