Analysis of xx-top500-249-base.sdk
Contents
Original Sudoku
level: medium
position: ..2.63.........4.1..........3....56.4..8..................2.63.17.4.....8........ initial
Autosolve
position: .42163..536..8.4.1.81...3.623891.56.4..8.62.36..3.2..9..4721638176438952823695... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 5 => CTR => A3: 7,9 * DIS # H1: 7,9 => CTR => H1: 8 * PRF # H1: 8 => SOL * DIS # A3: 5,9 => CTR => A3: 7 * PRF # A3: 7 => SOL * DIS # C5: 7 => CTR => C5: 5,9 * PRF # F3: 7,9 => SOL * DIS # F3: 4 => CTR => F3: 7,9 * DIS # H2: 2 => CTR => H2: 7,9 * DIS # F3: 4,7 => CTR => F3: 9 * PRF # F3: 9 => SOL * PRF # E6: 5 => SOL * PRF # H1: 7,8 => SOL * DIS # H1: 9 => CTR => H1: 7,8 * DIS # G6: 1 => CTR => G6: 7,8 * DIS # B5: 9 => CTR => B5: 1,5 * DIS # C5: 5,7 => CTR => C5: 9 * PRF # E6: 5,7 => SOL * DIS # E6: 4 => CTR => E6: 5,7 * PRF # E6: 5 => SOL * DIS # F3: 4,7 => CTR => F3: 9 * PRF # F3: 9 => SOL * PRF # E6: 5,7 => SOL * DIS # E6: 4 => CTR => E6: 5,7 * DIS # C5: 5,7 => CTR => C5: 9 * PRF # H6: 4,7 => SOL * DIS # H6: 1,8 => CTR => H6: 4,7 * DIS # G6: 1,7 => CTR => G6: 8 * PRF # G6: 8 => SOL * DIS # H6: 1,7 => CTR => H6: 4,8 * PRF # H9: 1,7 => SOL * DIS # H9: 4 => CTR => H9: 1,7 * DIS # A3: 5,9 => CTR => A3: 7 * PRF # A3: 7 => SOL * DIS # B5: 1 => CTR => B5: 5,9 * PRF # H9: 1,7 => SOL * DIS # H9: 4 => CTR => H9: 1,7 * DIS # G6: 1,7 => CTR => G6: 8 * PRF # G6: 8 => SOL * DIS # H9: 1 => CTR => H9: 4,7 * CNT 40 HDP CHAINS / 52 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 5 => CTR => A3: 7,9 * DIS A3: 7,9 # H1: 7,9 => CTR => H1: 8 * PRF A3: 7,9 + H1: 8 => SOL * STA A3: 7,9 + H1: 8 * CNT 3 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..2.63.........4.1..........3....56.4..8..................2.63.17.4.....8........ | initial |
| .42163..536..8.4.1.81...3.623891.56.4..8.62.36..3.2..9..4721638176438952823695... | autosolve |
| 942163785365287491781549326238914567459876213617352849594721638176438952823695174 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) A1: 7,9 C2: 5,9 D2: 2,5 F2: 7,9 D3: 2,5 E3: 4,7 G1: 7,8 B6: 1,5 C6: 5,7 F4: 4,7 E5: 5,7 I4: 4,7 H5: 1,7 A7: 5,9 B7: 5,9 G9: 1,7 I9: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B5,B6: 1.. / B5 = 1 => 0 pairs (X) / B6 = 1 => 17 pairs (_) G9,H9: 1.. / G9 = 1 => 18 pairs (_) / H9 = 1 => 0 pairs (X) B5,H5: 1.. / B5 = 1 => 0 pairs (X) / H5 = 1 => 17 pairs (_) G6,G9: 1.. / G6 = 1 => 0 pairs (X) / G9 = 1 => 18 pairs (_) D2,D3: 2.. / D2 = 2 => 16 pairs (_) / D3 = 2 => 0 pairs (X) H2,H3: 2.. / H2 = 2 => 0 pairs (X) / H3 = 2 => 16 pairs (_) D2,H2: 2.. / D2 = 2 => 16 pairs (_) / H2 = 2 => 0 pairs (X) D3,H3: 2.. / D3 = 2 => 0 pairs (X) / H3 = 2 => 16 pairs (_) E3,F3: 4.. / E3 = 4 => 0 pairs (*) / F3 = 4 => 0 pairs (X) F4,E6: 4.. / F4 = 4 => 0 pairs (*) / E6 = 4 => 0 pairs (X) I4,H6: 4.. / I4 = 4 => 0 pairs (X) / H6 = 4 => 0 pairs (_) H9,I9: 4.. / H9 = 4 => 0 pairs (X) / I9 = 4 => 0 pairs (_) F4,I4: 4.. / F4 = 4 => 0 pairs (*) / I4 = 4 => 0 pairs (X) E6,H6: 4.. / E6 = 4 => 0 pairs (X) / H6 = 4 => 0 pairs (_) E3,E6: 4.. / E3 = 4 => 0 pairs (*) / E6 = 4 => 0 pairs (X) F3,F4: 4.. / F3 = 4 => 0 pairs (X) / F4 = 4 => 0 pairs (_) H6,H9: 4.. / H6 = 4 => 0 pairs (*) / H9 = 4 => 0 pairs (X) I4,I9: 4.. / I4 = 4 => 0 pairs (X) / I9 = 4 => 0 pairs (_) C2,A3: 5.. / C2 = 5 => 16 pairs (_) / A3 = 5 => 0 pairs (X) D2,D3: 5.. / D2 = 5 => 0 pairs (X) / D3 = 5 => 16 pairs (_) E5,E6: 5.. / E5 = 5 => 19 pairs (_) / E6 = 5 => 0 pairs (*) A7,B7: 5.. / A7 = 5 => 16 pairs (_) / B7 = 5 => 0 pairs (X) C2,D2: 5.. / C2 = 5 => 16 pairs (_) / D2 = 5 => 0 pairs (X) A3,D3: 5.. / A3 = 5 => 0 pairs (X) / D3 = 5 => 16 pairs (_) A3,A7: 5.. / A3 = 5 => 0 pairs (X) / A7 = 5 => 16 pairs (_) A1,A3: 7.. / A1 = 7 => 0 pairs (X) / A3 = 7 => 0 pairs (_) C5,C6: 7.. / C5 = 7 => 0 pairs (X) / C6 = 7 => 19 pairs (_) F2,H2: 7.. / F2 = 7 => 0 pairs (*) / H2 = 7 => 0 pairs (X) F4,I4: 7.. / F4 = 7 => 0 pairs (X) / I4 = 7 => 0 pairs (_) I4,I9: 7.. / I4 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) G1,H1: 8.. / G1 = 8 => 0 pairs (X) / H1 = 8 => 0 pairs (_) G6,H6: 8.. / G6 = 8 => 0 pairs (*) / H6 = 8 => 0 pairs (X) G1,G6: 8.. / G1 = 8 => 0 pairs (X) / G6 = 8 => 0 pairs (_) H1,H6: 8.. / H1 = 8 => 0 pairs (*) / H6 = 8 => 0 pairs (X) F2,F3: 9.. / F2 = 9 => 0 pairs (X) / F3 = 9 => 0 pairs (_) B5,C5: 9.. / B5 = 9 => 0 pairs (X) / C5 = 9 => 16 pairs (_) A7,B7: 9.. / A7 = 9 => 0 pairs (X) / B7 = 9 => 16 pairs (_) A1,H1: 9.. / A1 = 9 => 0 pairs (*) / H1 = 9 => 0 pairs (X) B5,B7: 9.. / B5 = 9 => 0 pairs (X) / B7 = 9 => 16 pairs (_) C2,C5: 9.. / C2 = 9 => 0 pairs (X) / C5 = 9 => 16 pairs (_) * DURATION: 0:01:08.692822 START: 11:17:43.896621 END: 11:18:52.589443 2017-05-04 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A7,B6,B7,C2,C6,D2,D3,E3,E5,F2,F4,G1,G9,H5,I4,I9) * .42163..536..8.4.1.81...3.623891.56.4..8.62.36..3.2..9..4721638176438952823695... * PAIR A1: 7,9 BLK 1 A3: 7,9,5 # reduction candidate for 7,9 A3: 5 => CTR * 74216389536958742158124937623891.56.4..8.62.36..3.2..9..4721638176438952823695... A3: 7,9 # 16 pairs * PAIR A1: 7,9 ROW 1 H1: 7,9,8 # reduction candidate for 7,9 H1: 7,9 => CTR * .421638.536..8.4.1.81...3.62389175644..856213615342789.54721638176438952823695147 H1: 8 => SOLVED * 942163785365287491781549326238914567459876213617352849594721638176438952823695174 * PAIR C2: 5,9 BLK 1 A3: 5,9,7 # reduction candidate for 5,9 A3: 5,9 => CTR * 74216389536..8.4.1.81...3.62389175644..856213615342789.54721638176438952823695147 A3: 7 => SOLVED * 942163785365287491781549326238914567459876213617352849594721638176438952823695174 * PAIR C2: 5,9 COL C C5: 5,9,7 # reduction candidate for 5,9 C5: 7 => CTR * .42163..53695874215812493762389145674978562136153728.9..4721638176438952823695... C5: 5,9 # 19 pairs * PAIR F2: 7,9 BLK 2 F3: 7,9,4 # reduction candidate for 7,9 F3: 7,9 => SOLVED * 942163785365287491781549326238914567459876213617352849594721638176438952823695174 F3: 4 => CTR * .42163..536..89471.81.743262389175644..8.62.36..3.2..9..4721638176438952823695... * PAIR F2: 7,9 ROW 2 H2: 7,9,2 # reduction candidate for 7,9 H2: 2 => CTR * .42163..536..87421.812493762389145674..8.621361.3.28.9..4721638176438952823695... H2: 7,9 # 16 pairs * PAIR E3: 4,7 BLK 2 F3: 4,7,9 # reduction candidate for 4,7 F3: 4,7 => CTR * .42163..536..89471.81...32623891.56.4.98762136173528.9..4721638176438952823695... F3: 9 => SOLVED * 942163785365287491781549326238914567459876213617352849594721638176438952823695174 * PAIR E3: 4,7 COL E E6: 4,7,5 # reduction candidate for 4,7 E6: 5 => SOLVED * 942163785365287491781549326238914567459876213617352849594721638176438952823695174 E6: 4,7 # 19 pairs * PAIR G1: 7,8 BLK 3 H1: 7,8,9 # reduction candidate for 7,8 H1: 7,8 => SOLVED * 942163785365287491781549326238914567459876213617352849594721638176438952823695174 H1: 9 => CTR * 74216389536..8.4.1.81...3.62389175644..856213615342789.54721638176438952823695147 * PAIR G1: 7,8 COL G G6: 7,8,1 # reduction candidate for 7,8 G6: 1 => CTR * .421638.536..8.4.1.81...3.623891.56.4..8.62.36..3.2189..47216381764389528236957.. G6: 7,8 # 18 pairs * PAIR B6: 1,5 BLK 4 B5: 1,5,9 # reduction candidate for 1,5 B5: 9 => CTR * 74216389536958742158124937623891.56.49.8.621361.3.2..99547216381764389528236951.. B5: 1,5 # 16 pairs * PAIR C6: 5,7 BLK 4 C5: 5,7,9 # reduction candidate for 5,7 C5: 5,7 => CTR * .42163..536958742158124937623891456749.8.621361.3.28.9..4721638176438952823695... C5: 9 # 16 pairs * PAIR C6: 5,7 ROW 6 E6: 5,7,4 # reduction candidate for 5,7 E6: 5,7 => SOLVED * 942163785365287491781549326238914567459876213617352849594721638176438952823695174 E6: 4 => CTR * 74216389536..894719815743262389175644..8562.36..342..9..4721638176438952823695147 * PAIR F4: 4,7 BLK 5 E6: 4,7,5 # reduction candidate for 4,7 E6: 5 => SOLVED * 942163785365287491781549326238914567459876213617352849594721638176438952823695174 E6: 4,7 # 19 pairs * PAIR F4: 4,7 COL F F3: 4,7,9 # reduction candidate for 4,7 F3: 4,7 => CTR * .42163..536..89471.81...32623891.56.4.98762136173528.9..4721638176438952823695... F3: 9 => SOLVED * 942163785365287491781549326238914567459876213617352849594721638176438952823695174 * PAIR E5: 5,7 BLK 5 E6: 5,7,4 # reduction candidate for 5,7 E6: 5,7 => SOLVED * 942163785365287491781549326238914567459876213617352849594721638176438952823695174 E6: 4 => CTR * 74216389536..894719815743262389175644..8562.36..342..9..4721638176438952823695147 * PAIR E5: 5,7 ROW 5 C5: 5,7,9 # reduction candidate for 5,7 C5: 5,7 => CTR * .42163..536958742158124937623891456749.8.621361.3.28.9..4721638176438952823695... C5: 9 # 16 pairs * PAIR I4: 4,7 BLK 6 H6: 4,7,1,8 # reduction candidate for 4,7 H6: 4,7 => SOLVED * 942163785365287491781549326238914567459876213617352849594721638176438952823695174 H6: 1,8 => CTR * 74216389536..894719815743262389175644..8562.36..342..9..4721638176438952823695147 * PAIR H5: 1,7 BLK 6 G6: 1,7,8 # reduction candidate for 1,7 G6: 1,7 => CTR * .421638.536..8.4.1.81...3.62389175644..856213615342789.54721638176438952823695147 G6: 8 => SOLVED * 942163785365287491781549326238914567459876213617352849594721638176438952823695174 H6: 1,7,4,8 # reduction candidate for 1,7 H6: 1,7 => CTR * 9421637853652874.1.81...3.623891.5644..8.62.36..3428.9..4721638176438952823695147 H6: 4,8 # 18 pairs * PAIR H5: 1,7 COL H H9: 1,7,4 # reduction candidate for 1,7 H9: 1,7 => SOLVED * 942163785365287491781549326238914567459876213617352849594721638176438952823695174 H9: 4 => CTR * .42163..536..89471.81.743262389175644..8562.36..342..9..4721638176438952823695147 * PAIR A7: 5,9 COL A A3: 5,9,7 # reduction candidate for 5,9 A3: 5,9 => CTR * 74216389536..8.4.1.81...3.62389175644..856213615342789.54721638176438952823695147 A3: 7 => SOLVED * 942163785365287491781549326238914567459876213617352849594721638176438952823695174 * PAIR B7: 5,9 COL B B5: 5,9,1 # reduction candidate for 5,9 B5: 1 => CTR * .421637853652874.1.81...3.623891.56.419856273657342..9594721638176438952823695.47 B5: 5,9 # 17 pairs * PAIR G9: 1,7 BLK 9 H9: 1,7,4 # reduction candidate for 1,7 H9: 1,7 => SOLVED * 942163785365287491781549326238914567459876213617352849594721638176438952823695174 H9: 4 => CTR * .42163..536..89471.81.743262389175644..8562.36..342..9..4721638176438952823695147 * PAIR G9: 1,7 COL G G6: 1,7,8 # reduction candidate for 1,7 G6: 1,7 => CTR * .421638.536..8.4.1.81...3.62389175644..856213615342789.54721638176438952823695147 G6: 8 => SOLVED * 942163785365287491781549326238914567459876213617352849594721638176438952823695174 * PAIR I9: 4,7 BLK 9 H9: 4,7,1 # reduction candidate for 4,7 H9: 1 => CTR * .42163..536..8.4.1.81...3.623891.56.4..8.62.36..3.2.49..4721638176438952823695.14 H9: 4,7 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-249-base-pr-000.dot * REASONING * DIS # A3: 5 => CTR => A3: 7,9 * DIS # H1: 7,9 => CTR => H1: 8 * PRF # H1: 8 => SOL * DIS # A3: 5,9 => CTR => A3: 7 * PRF # A3: 7 => SOL * DIS # C5: 7 => CTR => C5: 5,9 * PRF # F3: 7,9 => SOL * DIS # F3: 4 => CTR => F3: 7,9 * DIS # H2: 2 => CTR => H2: 7,9 * DIS # F3: 4,7 => CTR => F3: 9 * PRF # F3: 9 => SOL * PRF # E6: 5 => SOL * PRF # H1: 7,8 => SOL * DIS # H1: 9 => CTR => H1: 7,8 * DIS # G6: 1 => CTR => G6: 7,8 * DIS # B5: 9 => CTR => B5: 1,5 * DIS # C5: 5,7 => CTR => C5: 9 * PRF # E6: 5,7 => SOL * DIS # E6: 4 => CTR => E6: 5,7 * PRF # E6: 5 => SOL * DIS # F3: 4,7 => CTR => F3: 9 * PRF # F3: 9 => SOL * PRF # E6: 5,7 => SOL * DIS # E6: 4 => CTR => E6: 5,7 * DIS # C5: 5,7 => CTR => C5: 9 * PRF # H6: 4,7 => SOL * DIS # H6: 1,8 => CTR => H6: 4,7 * DIS # G6: 1,7 => CTR => G6: 8 * PRF # G6: 8 => SOL * DIS # H6: 1,7 => CTR => H6: 4,8 * PRF # H9: 1,7 => SOL * DIS # H9: 4 => CTR => H9: 1,7 * DIS # A3: 5,9 => CTR => A3: 7 * PRF # A3: 7 => SOL * DIS # B5: 1 => CTR => B5: 5,9 * PRF # H9: 1,7 => SOL * DIS # H9: 4 => CTR => H9: 1,7 * DIS # G6: 1,7 => CTR => G6: 8 * PRF # G6: 8 => SOL * DIS # H9: 1 => CTR => H9: 4,7 * CNT 40 HDP CHAINS / 52 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A7,B6,B7,C2,C6,D2,D3,E3,E5,F2,F4,G1,G9,H5,I4,I9) * .42163..536..8.4.1.81...3.623891.56.4..8.62.36..3.2..9..4721638176438952823695... * PAIR A1: 7,9 BLK 1 A3: 7,9,5 # reduction candidate for 7,9 A3: 5 => CTR * 74216389536958742158124937623891.56.4..8.62.36..3.2..9..4721638176438952823695... * PAIR A1: 7,9 ROW 1 H1: 7,9,8 # reduction candidate for 7,9 H1: 7,9 => CTR * .421638.536528.4.1.815..32623891.56.4.98.62.36.73.21895947216381764389528236957.. H1: 8 => SOLVED * 942163785365287491781549326238914567459876213617352849594721638176438952823695174 * DURATION: 0:00:04.811045 START: 11:19:47.532270 END: 11:19:52.343315 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-249-base-pr-001.dot * REASONING * DIS # A3: 5 => CTR => A3: 7,9 * DIS A3: 7,9 # H1: 7,9 => CTR => H1: 8 * PRF A3: 7,9 + H1: 8 => SOL * STA A3: 7,9 + H1: 8 * CNT 3 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 249 solution: 942163785365287491781549326238914567459876213617352849594721638176438952823695174 info: 2073 FNBWXY S8.f 13260 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 942163785365287491781549326238914567459876213617352849594721638176438952823695174 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 # A3: 7,9 => UNS * DIS # A3: 5 => CTR => A3: 7,9 * DIS # H1: 7,9 => CTR => H1: 8 * PRF # H1: 8 => SOL * DIS # A3: 5,9 => CTR => A3: 7 * PRF # A3: 7 => SOL * INC # C5: 5,9 => UNS * DIS # C5: 7 => CTR => C5: 5,9 * PRF # F3: 7,9 => SOL * DIS # F3: 4 => CTR => F3: 7,9 * INC # H2: 7,9 => UNS * DIS # H2: 2 => CTR => H2: 7,9 * DIS # F3: 4,7 => CTR => F3: 9 * PRF # F3: 9 => SOL * INC # E6: 4,7 => UNS * PRF # E6: 5 => SOL * PRF # H1: 7,8 => SOL * DIS # H1: 9 => CTR => H1: 7,8 * INC # G6: 7,8 => UNS * DIS # G6: 1 => CTR => G6: 7,8 * INC # B5: 1,5 => UNS * DIS # B5: 9 => CTR => B5: 1,5 * DIS # C5: 5,7 => CTR => C5: 9 * INC # C5: 9 => UNS * PRF # E6: 5,7 => SOL * DIS # E6: 4 => CTR => E6: 5,7 * INC # E6: 4,7 => UNS * PRF # E6: 5 => SOL * DIS # F3: 4,7 => CTR => F3: 9 * PRF # F3: 9 => SOL * PRF # E6: 5,7 => SOL * DIS # E6: 4 => CTR => E6: 5,7 * DIS # C5: 5,7 => CTR => C5: 9 * INC # C5: 9 => UNS * PRF # H6: 4,7 => SOL * DIS # H6: 1,8 => CTR => H6: 4,7 * DIS # G6: 1,7 => CTR => G6: 8 * PRF # G6: 8 => SOL * DIS # H6: 1,7 => CTR => H6: 4,8 * INC # H6: 4,8 => UNS * PRF # H9: 1,7 => SOL * DIS # H9: 4 => CTR => H9: 1,7 * DIS # A3: 5,9 => CTR => A3: 7 * PRF # A3: 7 => SOL * INC # B5: 5,9 => UNS * DIS # B5: 1 => CTR => B5: 5,9 * PRF # H9: 1,7 => SOL * DIS # H9: 4 => CTR => H9: 1,7 * DIS # G6: 1,7 => CTR => G6: 8 * PRF # G6: 8 => SOL * INC # H9: 4,7 => UNS * DIS # H9: 1 => CTR => H9: 4,7 * CNT 52 HDP CHAINS / 52 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 7,9 => UNS * DIS # A3: 5 => CTR => A3: 7,9 * DIS A3: 7,9 # H1: 7,9 => CTR => H1: 8 * PRF A3: 7,9 + H1: 8 => SOL * STA A3: 7,9 + H1: 8 * CNT 4 HDP CHAINS / 3 HYP OPENED