Analysis of xx-top500-033-base.sdk
Contents
Original Sudoku
level: medium
position: ..26...3.4...7.................1.4.7.83............1.....3.2.6.75..........8..... initial
Autosolve
position: 8726...3.43..7...669..3..7.2695134871837246..547986123914352768758.6.3.23268.7... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # F2: 1,5 => SOL * DIS # H2: 1,5 => CTR => H2: 9 * PRF # H2: 9 => SOL * DIS # F3: 1,5 => CTR => F3: 8 * PRF # I3: 1,5 => SOL * DIS # I3: 4 => CTR => I3: 1,5 * PRF # I1: 4,9 => SOL * DIS # I1: 1,5 => CTR => I1: 4,9 * DIS # D3: 1,2 => CTR => D3: 4 * PRF # D3: 4 => SOL * DIS # I1: 5,9 => CTR => I1: 1,4 * PRF # H2: 5,9 => SOL * DIS # H2: 1 => CTR => H2: 5,9 * DIS # F1: 5,9 => CTR => F1: 1 * PRF # F1: 1 => SOL * PRF # H2: 5,9 => SOL * DIS # H2: 1 => CTR => H2: 5,9 * DIS # H9: 5,9 => CTR => H9: 1,4 * DIS # I1: 5,9 => CTR => I1: 1,4 * PRF # I9: 5,9 => SOL * DIS # I9: 1 => CTR => I9: 5,9 * DIS # D3: 2 => CTR => D3: 1,4 * PRF # F1: 1,9 => SOL * DIS # F1: 5 => CTR => F1: 1,9 * DIS # F2: 1,9 => CTR => F2: 5,8 * PRF # F2: 5,8 => SOL * DIS # H9: 4,9 => CTR => H9: 1,5 * PRF # H9: 1,5 => SOL * DIS # H9: 4,9 => CTR => H9: 1,5 * PRF # H9: 1,5 => SOL * DIS # H9: 5,9 => CTR => H9: 1,4 * PRF # I9: 5,9 => SOL * DIS # I9: 1 => CTR => I9: 5,9 * CNT 33 HDP CHAINS / 40 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # F2: 1,5 => SOL * STA F2: 1,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..26...3.4...7.................1.4.7.83............1.....3.2.6.75..........8..... | initial |
| 8726...3.43..7...669..3..7.2695134871837246..547986123914352768758.6.3.23268.7... | autosolve |
| 872691534431275896695438271269513487183724659547986123914352768758169342326847915 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) C2: 1,5 C3: 1,5 E1: 4,9 D2: 1,2 G1: 5,9 G2: 2,8 G3: 2,8 H5: 5,9 I5: 5,9 D8: 1,4 F8: 1,9 E9: 4,9 H8: 4,9 G9: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,C3: 1.. / C2 = 1 => 0 pairs (*) / C3 = 1 => 0 pairs (X) D8,F8: 1.. / D8 = 1 => 0 pairs (*) / F8 = 1 => 0 pairs (X) H9,I9: 1.. / H9 = 1 => 0 pairs (*) / I9 = 1 => 0 pairs (X) F1,I1: 1.. / F1 = 1 => 0 pairs (*) / I1 = 1 => 0 pairs (X) H2,H9: 1.. / H2 = 1 => 0 pairs (X) / H9 = 1 => 0 pairs (_) D2,D3: 2.. / D2 = 2 => 12 pairs (_) / D3 = 2 => 0 pairs (X) G2,G3: 2.. / G2 = 2 => 0 pairs (X) / G3 = 2 => 12 pairs (_) D2,G2: 2.. / D2 = 2 => 12 pairs (_) / G2 = 2 => 0 pairs (X) D3,G3: 2.. / D3 = 2 => 0 pairs (X) / G3 = 2 => 12 pairs (_) E1,D3: 4.. / E1 = 4 => 0 pairs (X) / D3 = 4 => 0 pairs (_) I1,I3: 4.. / I1 = 4 => 0 pairs (*) / I3 = 4 => 0 pairs (X) D8,E9: 4.. / D8 = 4 => 0 pairs (X) / E9 = 4 => 0 pairs (_) H8,H9: 4.. / H8 = 4 => 0 pairs (*) / H9 = 4 => 0 pairs (X) E1,I1: 4.. / E1 = 4 => 0 pairs (X) / I1 = 4 => 0 pairs (_) D3,I3: 4.. / D3 = 4 => 0 pairs (*) / I3 = 4 => 0 pairs (X) D8,H8: 4.. / D8 = 4 => 0 pairs (X) / H8 = 4 => 0 pairs (_) E9,H9: 4.. / E9 = 4 => 0 pairs (*) / H9 = 4 => 0 pairs (X) D3,D8: 4.. / D3 = 4 => 0 pairs (*) / D8 = 4 => 0 pairs (X) E1,E9: 4.. / E1 = 4 => 0 pairs (X) / E9 = 4 => 0 pairs (_) C2,C3: 5.. / C2 = 5 => 16 pairs (_) / C3 = 5 => 0 pairs (*) H5,I5: 5.. / H5 = 5 => 14 pairs (_) / I5 = 5 => 0 pairs (X) G1,G9: 5.. / G1 = 5 => 0 pairs (*) / G9 = 5 => 0 pairs (X) F2,F3: 8.. / F2 = 8 => 0 pairs (X) / F3 = 8 => 12 pairs (_) G2,G3: 8.. / G2 = 8 => 12 pairs (_) / G3 = 8 => 0 pairs (X) F2,G2: 8.. / F2 = 8 => 0 pairs (X) / G2 = 8 => 12 pairs (_) F3,G3: 8.. / F3 = 8 => 12 pairs (_) / G3 = 8 => 0 pairs (X) H5,I5: 9.. / H5 = 9 => 0 pairs (X) / I5 = 9 => 14 pairs (_) F8,E9: 9.. / F8 = 9 => 0 pairs (*) / E9 = 9 => 0 pairs (X) F2,H2: 9.. / F2 = 9 => 0 pairs (X) / H2 = 9 => 0 pairs (_) F8,H8: 9.. / F8 = 9 => 0 pairs (*) / H8 = 9 => 0 pairs (X) E1,E9: 9.. / E1 = 9 => 0 pairs (*) / E9 = 9 => 0 pairs (X) G1,G9: 9.. / G1 = 9 => 0 pairs (X) / G9 = 9 => 0 pairs (_) * DURATION: 0:01:21.361329 START: 03:47:12.484247 END: 03:48:33.845576 2017-05-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C2,C3,D2,D8,E1,E9,F8,G1,G2,G3,G9,H5,H8,I5) * 8726...3.43..7...669..3..7.2695134871837246..547986123914352768758.6.3.23268.7... * PAIR C2: 1,5 ROW 2 F2: 1,5,8,9 # reduction candidate for 1,5 F2: 1,5 => SOLVED * 872691534431275896695438271269513487183724659547986123914352768758169342326847915 F2: 8,9 # 15 pairs H2: 1,5,9 # reduction candidate for 1,5 H2: 1,5 => CTR * 8726...3.43..798.669..3827.2695134871837246..547986123914352768758.61392326897541 H2: 9 => SOLVED * 872691534431275896695438271269513487183724659547986123914352768758169342326847915 * PAIR C3: 1,5 ROW 3 F3: 1,5,8 # reduction candidate for 1,5 F3: 1,5 => CTR * 8726...3.43..7829669.23.87426951348718372465954798612391435276875846.3.23268.7... F3: 8 # 12 pairs I3: 1,5,4 # reduction candidate for 1,5 I3: 1,5 => SOLVED * 872691534431275896695438271269513487183724659547986123914352768758169342326847915 I3: 4 => CTR * 8726...3.43..7...669..3..742695134871837246..547986123914352768758461392326897541 * PAIR E1: 4,9 ROW 1 I1: 4,9,1,5 # reduction candidate for 4,9 I1: 4,9 => SOLVED * 872691534431275896695438271269513487183724659547986123914352768758169342326847915 I1: 1,5 => CTR * 87264..3.43..7...669..3..742695134871837246..547986123914352768758461392326897541 * PAIR D2: 1,2 BLK 2 D3: 1,2,4 # reduction candidate for 1,2 D3: 1,2 => CTR * 87264..3.43..7...669..3..742695134871837246..547986123914352768758461392326897541 D3: 4 => SOLVED * 872691534431275896695438271269513487183724659547986123914352768758169342326847915 * PAIR G1: 5,9 BLK 3 I1: 5,9,1,4 # reduction candidate for 5,9 I1: 5,9 => CTR * 872641.3.43.27...669..3..7.2695134871837246..547986123914352768758.6.3.23268.7... I1: 1,4 # 15 pairs H2: 5,9,1 # reduction candidate for 5,9 H2: 5,9 => SOLVED * 872691534431275896695438271269513487183724659547986123914352768758169342326847915 H2: 1 => CTR * 8726...3.43..79816691.3827526951348718372465954798612391435276875816.3.23268.7... * PAIR G1: 5,9 ROW 1 F1: 5,9,1 # reduction candidate for 5,9 F1: 5,9 => CTR * 8726...3143..7...669..3..742695134871837246..5479861239143527687584613923268.7... F1: 1 => SOLVED * 872691534431275896695438271269513487183724659547986123914352768758169342326847915 * PAIR H5: 5,9 COL H H2: 5,9,1 # reduction candidate for 5,9 H2: 5,9 => SOLVED * 872691534431275896695438271269513487183724659547986123914352768758169342326847915 H2: 1 => CTR * 8726...3.43..79816691.3827526951348718372465954798612391435276875816.3.23268.7... H9: 5,9,1,4 # reduction candidate for 5,9 H9: 5,9 => CTR * 8726...3.43..7..16691.3..7.2695134871837246..547986123914352768758169342326847..1 H9: 1,4 # 15 pairs * PAIR I5: 5,9 COL I I1: 5,9,1,4 # reduction candidate for 5,9 I1: 5,9 => CTR * 872641.3.43.27...669..3..7.2695134871837246..547986123914352768758.6.3.23268.7... I1: 1,4 # 15 pairs I9: 5,9,1 # reduction candidate for 5,9 I9: 5,9 => SOLVED * 872691534431275896695438271269513487183724659547986123914352768758169342326847915 I9: 1 => CTR * 8726.1.3.43.27.8166914382752695134871837246595479861239143527687581693.23268.7..1 * PAIR D8: 1,4 COL D D3: 1,4,2 # reduction candidate for 1,4 D3: 2 => CTR * 87264..3.43..7...669.23.8742695134871837246..547986123914352768758461392326897541 D3: 1,4 # 12 pairs * PAIR F8: 1,9 COL F F1: 1,9,5 # reduction candidate for 1,9 F1: 1,9 => SOLVED * 872691534431275896695438271269513487183724659547986123914352768758169342326847915 F1: 5 => CTR * 8726.593143..79856695.3827426951348718372469554798612391435276875846.3.23268.7... F2: 1,9,5,8 # reduction candidate for 1,9 F2: 1,9 => CTR * 8726.593143.27985669513827426951348718372469554798612391435276875846.3.23268.7... F2: 5,8 => SOLVED * 872691534431275896695438271269513487183724659547986123914352768758169342326847915 * PAIR E9: 4,9 ROW 9 H9: 4,9,1,5 # reduction candidate for 4,9 H9: 4,9 => CTR * 8726...3.43..7..16691.3..7.269513487183724659547986123914352768758169342326847.91 H9: 1,5 => SOLVED * 872691534431275896695438271269513487183724659547986123914352768758169342326847915 * PAIR H8: 4,9 BLK 9 H9: 4,9,1,5 # reduction candidate for 4,9 H9: 4,9 => CTR * 8726...3.43..7..16691.3..7.269513487183724659547986123914352768758169342326847.91 H9: 1,5 => SOLVED * 872691534431275896695438271269513487183724659547986123914352768758169342326847915 * PAIR G9: 5,9 BLK 9 H9: 5,9,1,4 # reduction candidate for 5,9 H9: 5,9 => CTR * 8726...3.43..7..16691.3..7.2695134871837246..547986123914352768758169342326847..1 H9: 1,4 # 15 pairs I9: 5,9,1 # reduction candidate for 5,9 I9: 5,9 => SOLVED * 872691534431275896695438271269513487183724659547986123914352768758169342326847915 I9: 1 => CTR * 8726.1.3.43.27.8166914382752695134871837246595479861239143527687581693.23268.7..1 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-033-base-pr-000.dot * REASONING * PRF # F2: 1,5 => SOL * DIS # H2: 1,5 => CTR => H2: 9 * PRF # H2: 9 => SOL * DIS # F3: 1,5 => CTR => F3: 8 * PRF # I3: 1,5 => SOL * DIS # I3: 4 => CTR => I3: 1,5 * PRF # I1: 4,9 => SOL * DIS # I1: 1,5 => CTR => I1: 4,9 * DIS # D3: 1,2 => CTR => D3: 4 * PRF # D3: 4 => SOL * DIS # I1: 5,9 => CTR => I1: 1,4 * PRF # H2: 5,9 => SOL * DIS # H2: 1 => CTR => H2: 5,9 * DIS # F1: 5,9 => CTR => F1: 1 * PRF # F1: 1 => SOL * PRF # H2: 5,9 => SOL * DIS # H2: 1 => CTR => H2: 5,9 * DIS # H9: 5,9 => CTR => H9: 1,4 * DIS # I1: 5,9 => CTR => I1: 1,4 * PRF # I9: 5,9 => SOL * DIS # I9: 1 => CTR => I9: 5,9 * DIS # D3: 2 => CTR => D3: 1,4 * PRF # F1: 1,9 => SOL * DIS # F1: 5 => CTR => F1: 1,9 * DIS # F2: 1,9 => CTR => F2: 5,8 * PRF # F2: 5,8 => SOL * DIS # H9: 4,9 => CTR => H9: 1,5 * PRF # H9: 1,5 => SOL * DIS # H9: 4,9 => CTR => H9: 1,5 * PRF # H9: 1,5 => SOL * DIS # H9: 5,9 => CTR => H9: 1,4 * PRF # I9: 5,9 => SOL * DIS # I9: 1 => CTR => I9: 5,9 * CNT 33 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C2,C3,D2,D8,E1,E9,F8,G1,G2,G3,G9,H5,H8,I5) * 8726...3.43..7...669..3..7.2695134871837246..547986123914352768758.6.3.23268.7... * PAIR C2: 1,5 ROW 2 F2: 1,5,8,9 # reduction candidate for 1,5 F2: 1,5 => SOLVED * 872691534431275896695438271269513487183724659547986123914352768758169342326847915 * DURATION: 0:00:02.529002 START: 03:49:39.650811 END: 03:49:42.179813 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-033-base-pr-001.dot * REASONING * PRF # F2: 1,5 => SOL * STA F2: 1,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 033 solution: 872691534431275896695438271269513487183724659547986123914352768758169342326847915 info: 1338 FNBTWY S8.f 13329 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 872691534431275896695438271269513487183724659547986123914352768758169342326847915 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:
* PRF # F2: 1,5 => SOL * INC # F2: 8,9 => UNS * DIS # H2: 1,5 => CTR => H2: 9 * PRF # H2: 9 => SOL * DIS # F3: 1,5 => CTR => F3: 8 * INC # F3: 8 => UNS * PRF # I3: 1,5 => SOL * DIS # I3: 4 => CTR => I3: 1,5 * PRF # I1: 4,9 => SOL * DIS # I1: 1,5 => CTR => I1: 4,9 * DIS # D3: 1,2 => CTR => D3: 4 * PRF # D3: 4 => SOL * DIS # I1: 5,9 => CTR => I1: 1,4 * INC # I1: 1,4 => UNS * PRF # H2: 5,9 => SOL * DIS # H2: 1 => CTR => H2: 5,9 * DIS # F1: 5,9 => CTR => F1: 1 * PRF # F1: 1 => SOL * PRF # H2: 5,9 => SOL * DIS # H2: 1 => CTR => H2: 5,9 * DIS # H9: 5,9 => CTR => H9: 1,4 * INC # H9: 1,4 => UNS * DIS # I1: 5,9 => CTR => I1: 1,4 * INC # I1: 1,4 => UNS * PRF # I9: 5,9 => SOL * DIS # I9: 1 => CTR => I9: 5,9 * INC # D3: 1,4 => UNS * DIS # D3: 2 => CTR => D3: 1,4 * PRF # F1: 1,9 => SOL * DIS # F1: 5 => CTR => F1: 1,9 * DIS # F2: 1,9 => CTR => F2: 5,8 * PRF # F2: 5,8 => SOL * DIS # H9: 4,9 => CTR => H9: 1,5 * PRF # H9: 1,5 => SOL * DIS # H9: 4,9 => CTR => H9: 1,5 * PRF # H9: 1,5 => SOL * DIS # H9: 5,9 => CTR => H9: 1,4 * INC # H9: 1,4 => UNS * PRF # I9: 5,9 => SOL * DIS # I9: 1 => CTR => I9: 5,9 * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # F2: 1,5 => SOL * STA F2: 1,5 * CNT 1 HDP CHAINS / 1 HYP OPENED