Analysis of xx-top500-119-base.sdk
Contents
Original Sudoku
level: medium
position: .2..7....5.....1........8......2..731..5.................1..5.6.73....4....8..... initial
Autosolve
position: .2167835.58.3..1.773..158...58.216731.7563..836278..152..137586873.56.416158..73. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C2: 4,9 => SOL * DIS # C2: 6 => CTR => C2: 4,9 * DIS # C3: 4,9 => CTR => C3: 6 * PRF # C3: 6 => SOL * DIS # F2: 4,9 => CTR => F2: 2 * PRF # F2: 2 => SOL * PRF # D3: 4,9 => SOL * DIS # D3: 2 => CTR => D3: 4,9 * PRF # C2: 4,9 => SOL * DIS # C2: 6 => CTR => C2: 4,9 * PRF # I3: 4,9 => SOL * DIS # I3: 2 => CTR => I3: 4,9 * DIS # G5: 4,9 => CTR => G5: 2 * PRF # G5: 2 => SOL * PRF # D3: 4,9 => SOL * DIS # D3: 2 => CTR => D3: 4,9 * DIS # F2: 4,9 => CTR => F2: 2 * PRF # F2: 2 => SOL * PRF # F9: 4,9 => SOL * DIS # F9: 2 => CTR => F9: 4,9 * PRF # G5: 2,9 => SOL * DIS # G5: 4 => CTR => G5: 2,9 * DIS # H2: 2,9 => CTR => H2: 6 * PRF # H2: 6 => SOL * PRF # H3: 2,9 => SOL * DIS # H3: 6 => CTR => H3: 2,9 * DIS # G5: 4,9 => CTR => G5: 2 * PRF # G5: 2 => SOL * PRF # C2: 4,9 => SOL * DIS # C2: 6 => CTR => C2: 4,9 * DIS # C3: 4,9 => CTR => C3: 6 * PRF # C3: 6 => SOL * PRF # F9: 4 => SOL * PRF # D3: 2,9 => SOL * DIS # D3: 4 => CTR => D3: 2,9 * PRF # F9: 4,9 => SOL * DIS # F9: 2 => CTR => F9: 4,9 * PRF # G5: 2,9 => SOL * DIS # G5: 4 => CTR => G5: 2,9 * PRF # F9: 4 => SOL * DIS # I3: 2,9 => CTR => I3: 4 * PRF # I3: 4 => SOL * CNT 42 HDP CHAINS / 44 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C2: 4,9 => SOL * STA C2: 4,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2..7....5.....1........8......2..731..5.................1..5.6.73....4....8..... | initial |
| .2167835.58.3..1.773..158...58.216731.7563..836278..152..137586873.56.416158..73. | autosolve |
| 421678359589342167736915824958421673147563298362789415294137586873256941615894732 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) A1: 4,9 E2: 4,9 I1: 4,9 A4: 4,9 B5: 4,9 D4: 4,9 F6: 4,9 H5: 2,9 G6: 4,9 B7: 4,9 C7: 4,9 D8: 2,9 E9: 4,9 G8: 2,9 I9: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F2,D3: 2.. / F2 = 2 => 0 pairs (*) / D3 = 2 => 0 pairs (X) G5,H5: 2.. / G5 = 2 => 0 pairs (*) / H5 = 2 => 0 pairs (X) D8,F9: 2.. / D8 = 2 => 0 pairs (*) / F9 = 2 => 0 pairs (X) G8,I9: 2.. / G8 = 2 => 0 pairs (X) / I9 = 2 => 0 pairs (_) F2,H2: 2.. / F2 = 2 => 0 pairs (*) / H2 = 2 => 0 pairs (X) D8,G8: 2.. / D8 = 2 => 0 pairs (*) / G8 = 2 => 0 pairs (X) F9,I9: 2.. / F9 = 2 => 0 pairs (X) / I9 = 2 => 0 pairs (_) D3,D8: 2.. / D3 = 2 => 0 pairs (X) / D8 = 2 => 0 pairs (_) F2,F9: 2.. / F2 = 2 => 0 pairs (*) / F9 = 2 => 0 pairs (X) G5,G8: 2.. / G5 = 2 => 0 pairs (*) / G8 = 2 => 0 pairs (X) I3,I9: 2.. / I3 = 2 => 0 pairs (X) / I9 = 2 => 0 pairs (_) I1,I3: 4.. / I1 = 4 => 0 pairs (X) / I3 = 4 => 0 pairs (_) A4,B5: 4.. / A4 = 4 => 0 pairs (X) / B5 = 4 => 0 pairs (_) D4,F6: 4.. / D4 = 4 => 0 pairs (*) / F6 = 4 => 0 pairs (X) G5,G6: 4.. / G5 = 4 => 0 pairs (X) / G6 = 4 => 0 pairs (_) B7,C7: 4.. / B7 = 4 => 0 pairs (X) / C7 = 4 => 0 pairs (_) E9,F9: 4.. / E9 = 4 => 18 pairs (_) / F9 = 4 => 0 pairs (*) A1,I1: 4.. / A1 = 4 => 0 pairs (*) / I1 = 4 => 0 pairs (X) A4,D4: 4.. / A4 = 4 => 0 pairs (X) / D4 = 4 => 0 pairs (_) B5,G5: 4.. / B5 = 4 => 0 pairs (*) / G5 = 4 => 0 pairs (X) F6,G6: 4.. / F6 = 4 => 0 pairs (X) / G6 = 4 => 0 pairs (_) A1,A4: 4.. / A1 = 4 => 0 pairs (*) / A4 = 4 => 0 pairs (X) B5,B7: 4.. / B5 = 4 => 0 pairs (*) / B7 = 4 => 0 pairs (X) D3,D4: 4.. / D3 = 4 => 0 pairs (X) / D4 = 4 => 0 pairs (_) E2,E9: 4.. / E2 = 4 => 0 pairs (*) / E9 = 4 => 0 pairs (X) C2,C3: 6.. / C2 = 6 => 0 pairs (X) / C3 = 6 => 0 pairs (_) H2,H3: 6.. / H2 = 6 => 0 pairs (*) / H3 = 6 => 0 pairs (X) C2,H2: 6.. / C2 = 6 => 0 pairs (X) / H2 = 6 => 0 pairs (_) C3,H3: 6.. / C3 = 6 => 0 pairs (*) / H3 = 6 => 0 pairs (X) A4,B5: 9.. / A4 = 9 => 0 pairs (*) / B5 = 9 => 0 pairs (X) D4,F6: 9.. / D4 = 9 => 0 pairs (X) / F6 = 9 => 0 pairs (_) B7,C7: 9.. / B7 = 9 => 0 pairs (*) / C7 = 9 => 0 pairs (X) G8,I9: 9.. / G8 = 9 => 0 pairs (*) / I9 = 9 => 0 pairs (X) A1,I1: 9.. / A1 = 9 => 0 pairs (X) / I1 = 9 => 0 pairs (_) A4,D4: 9.. / A4 = 9 => 0 pairs (*) / D4 = 9 => 0 pairs (X) F6,G6: 9.. / F6 = 9 => 0 pairs (*) / G6 = 9 => 0 pairs (X) D8,G8: 9.. / D8 = 9 => 0 pairs (X) / G8 = 9 => 0 pairs (_) A1,A4: 9.. / A1 = 9 => 0 pairs (X) / A4 = 9 => 0 pairs (_) B5,B7: 9.. / B5 = 9 => 0 pairs (X) / B7 = 9 => 0 pairs (_) E2,E9: 9.. / E2 = 9 => 18 pairs (_) / E9 = 9 => 0 pairs (*) * DURATION: 0:01:04.127851 START: 06:50:55.572752 END: 06:51:59.700603 2017-05-04 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B5,B7,C7,D4,D8,E2,E9,F6,G6,G8,H5,I1,I9) * .2167835.58.3..1.773..158...58.216731.7563..836278..152..137586873.56.416158..73. * PAIR A1: 4,9 BLK 1 C2: 4,9,6 # reduction candidate for 4,9 C2: 4,9 => SOLVED * 421678359589342167736915824958421673147563298362789415294137586873256941615894732 C2: 6 => CTR * 4216783595863941277392158649584216731475632.8362789415294137586873.56.416158..73. C3: 4,9,6 # reduction candidate for 4,9 C3: 4,9 => CTR * 4216783595863941277392158649584216731475632.8362789415294137586873.56.416158..73. C3: 6 => SOLVED * 421678359589342167736915824958421673147563298362789415294137586873256941615894732 * PAIR E2: 4,9 BLK 2 F2: 4,9,2 # reduction candidate for 4,9 F2: 4,9 => CTR * .2167835.58.3..12773.21586..58421673147563298362789415294137586873956.416158..73. F2: 2 => SOLVED * 421678359589342167736915824958421673147563298362789415294137586873256941615894732 D3: 4,9,2 # reduction candidate for 4,9 D3: 4,9 => SOLVED * 421678359589342167736915824958421673147563298362789415294137586873256941615894732 D3: 2 => CTR * .2167835.58.3..1.773.2158...58421673147563..83627894152941375868739562416158..73. * PAIR E2: 4,9 ROW 2 C2: 4,9,6 # reduction candidate for 4,9 C2: 4,9 => SOLVED * 421678359589342167736915824958421673147563298362789415294137586873256941615894732 C2: 6 => CTR * 4216783595863941277392158649584216731475632.8362789415294137586873.56.416158..73. * PAIR I1: 4,9 BLK 3 I3: 4,9,2 # reduction candidate for 4,9 I3: 4,9 => SOLVED * 421678359589342167736915824958421673147563298362789415294137586873256941615894732 I3: 2 => CTR * .2167835458.3..1.773..158.24589216731975634.836278..152..137586873.56.416158..73. * PAIR B5: 4,9 ROW 5 G5: 4,9,2 # reduction candidate for 4,9 G5: 4,9 => CTR * .2167835.58.3..1.773..158...58.216731.7563.2836278..152..137586873.562416158.2739 G5: 2 => SOLVED * 421678359589342167736915824958421673147563298362789415294137586873256941615894732 * PAIR D4: 4,9 COL D D3: 4,9,2 # reduction candidate for 4,9 D3: 4,9 => SOLVED * 421678359589342167736915824958421673147563298362789415294137586873256941615894732 D3: 2 => CTR * .2167835.58.3..1.773.2158...58421673147563..83627894152941375868739562416158..73. * PAIR F6: 4,9 COL F F2: 4,9,2 # reduction candidate for 4,9 F2: 4,9 => CTR * .2167835.58.3..12773.21586..58421673147563298362789415294137586873956.416158..73. F2: 2 => SOLVED * 421678359589342167736915824958421673147563298362789415294137586873256941615894732 F9: 4,9,2 # reduction candidate for 4,9 F9: 4,9 => SOLVED * 421678359589342167736915824958421673147563298362789415294137586873256941615894732 F9: 2 => CTR * 92167835458.39412773..158...58.216731.7563..836278..152..137586873.56.41615842739 * PAIR H5: 2,9 BLK 6 G5: 2,9,4 # reduction candidate for 2,9 G5: 2,9 => SOLVED * 421678359589342167736915824958421673147563298362789415294137586873256941615894732 G5: 4 => CTR * .2167835.58.3..1.773..158...58.216731.7563428362784915249137586873956.416158..73. * PAIR H5: 2,9 COL H H2: 2,9,6 # reduction candidate for 2,9 H2: 2,9 => CTR * 4216783595863941277392158649584216731475632.8362789415294137586873.56.416158..73. H2: 6 => SOLVED * 421678359589342167736915824958421673147563298362789415294137586873256941615894732 H3: 2,9,6 # reduction candidate for 2,9 H3: 2,9 => SOLVED * 421678359589342167736915824958421673147563298362789415294137586873256941615894732 H3: 6 => CTR * 4216783595863941277392158649584216731475632.8362789415294137586873.56.416158..73. * PAIR G6: 4,9 BLK 6 G5: 4,9,2 # reduction candidate for 4,9 G5: 4,9 => CTR * .2167835.58.3..1.773..158...58.216731.7563.2836278..152..137586873.562416158.2739 G5: 2 => SOLVED * 421678359589342167736915824958421673147563298362789415294137586873256941615894732 * PAIR C7: 4,9 COL C C2: 4,9,6 # reduction candidate for 4,9 C2: 4,9 => SOLVED * 421678359589342167736915824958421673147563298362789415294137586873256941615894732 C2: 6 => CTR * 4216783595863941277392158649584216731475632.8362789415294137586873.56.416158..73. C3: 4,9,6 # reduction candidate for 4,9 C3: 4,9 => CTR * 4216783595863941277392158649584216731475632.8362789415294137586873.56.416158..73. C3: 6 => SOLVED * 421678359589342167736915824958421673147563298362789415294137586873256941615894732 * PAIR D8: 2,9 BLK 8 F9: 2,9,4 # reduction candidate for 2,9 F9: 4 => SOLVED * 421678359589342167736915824958421673147563298362789415294137586873256941615894732 F9: 2,9 # 18 pairs * PAIR D8: 2,9 COL D D3: 2,9,4 # reduction candidate for 2,9 D3: 2,9 => SOLVED * 421678359589342167736915824958421673147563298362789415294137586873256941615894732 D3: 4 => CTR * .2167835.58.3.21.773.4158..4589216731975634283627849152..137586873.56.416158..73. * PAIR E9: 4,9 BLK 8 F9: 4,9,2 # reduction candidate for 4,9 F9: 4,9 => SOLVED * 421678359589342167736915824958421673147563298362789415294137586873256941615894732 F9: 2 => CTR * 92167835458.39412773..158...58.216731.7563..836278..152..137586873.56.41615842739 * PAIR G8: 2,9 COL G G5: 2,9,4 # reduction candidate for 2,9 G5: 2,9 => SOLVED * 421678359589342167736915824958421673147563298362789415294137586873256941615894732 G5: 4 => CTR * .2167835.58.3..1.773..158...58.216731.7563428362784915249137586873956.416158..73. * PAIR I9: 2,9 ROW 9 F9: 2,9,4 # reduction candidate for 2,9 F9: 4 => SOLVED * 421678359589342167736915824958421673147563298362789415294137586873256941615894732 F9: 2,9 # 18 pairs * PAIR I9: 2,9 COL I I3: 2,9,4 # reduction candidate for 2,9 I3: 2,9 => CTR * .2167835458.3..1.773..158..4589216731975634283627849152..137586873.56.416158..73. I3: 4 => SOLVED * 421678359589342167736915824958421673147563298362789415294137586873256941615894732 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-119-base-pr-000.dot * REASONING * PRF # C2: 4,9 => SOL * DIS # C2: 6 => CTR => C2: 4,9 * DIS # C3: 4,9 => CTR => C3: 6 * PRF # C3: 6 => SOL * DIS # F2: 4,9 => CTR => F2: 2 * PRF # F2: 2 => SOL * PRF # D3: 4,9 => SOL * DIS # D3: 2 => CTR => D3: 4,9 * PRF # C2: 4,9 => SOL * DIS # C2: 6 => CTR => C2: 4,9 * PRF # I3: 4,9 => SOL * DIS # I3: 2 => CTR => I3: 4,9 * DIS # G5: 4,9 => CTR => G5: 2 * PRF # G5: 2 => SOL * PRF # D3: 4,9 => SOL * DIS # D3: 2 => CTR => D3: 4,9 * DIS # F2: 4,9 => CTR => F2: 2 * PRF # F2: 2 => SOL * PRF # F9: 4,9 => SOL * DIS # F9: 2 => CTR => F9: 4,9 * PRF # G5: 2,9 => SOL * DIS # G5: 4 => CTR => G5: 2,9 * DIS # H2: 2,9 => CTR => H2: 6 * PRF # H2: 6 => SOL * PRF # H3: 2,9 => SOL * DIS # H3: 6 => CTR => H3: 2,9 * DIS # G5: 4,9 => CTR => G5: 2 * PRF # G5: 2 => SOL * PRF # C2: 4,9 => SOL * DIS # C2: 6 => CTR => C2: 4,9 * DIS # C3: 4,9 => CTR => C3: 6 * PRF # C3: 6 => SOL * PRF # F9: 4 => SOL * PRF # D3: 2,9 => SOL * DIS # D3: 4 => CTR => D3: 2,9 * PRF # F9: 4,9 => SOL * DIS # F9: 2 => CTR => F9: 4,9 * PRF # G5: 2,9 => SOL * DIS # G5: 4 => CTR => G5: 2,9 * PRF # F9: 4 => SOL * DIS # I3: 2,9 => CTR => I3: 4 * PRF # I3: 4 => SOL * CNT 42 HDP CHAINS / 44 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B5,B7,C7,D4,D8,E2,E9,F6,G6,G8,H5,I1,I9) * .2167835.58.3..1.773..158...58.216731.7563..836278..152..137586873.56.416158..73. * PAIR A1: 4,9 BLK 1 C2: 4,9,6 # reduction candidate for 4,9 C2: 4,9 => SOLVED * 421678359589342167736915824958421673147563298362789415294137586873256941615894732 * DURATION: 0:00:01.884913 START: 06:52:49.058828 END: 06:52:50.943741 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-119-base-pr-001.dot * REASONING * PRF # C2: 4,9 => SOL * STA C2: 4,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 119 solution: 421678359589342167736915824958421673147563298362789415294137586873256941615894732 info: 1802 FNWX S8.f 16629 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 421678359589342167736915824958421673147563298362789415294137586873256941615894732 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 # C2: 4,9 => SOL * DIS # C2: 6 => CTR => C2: 4,9 * DIS # C3: 4,9 => CTR => C3: 6 * PRF # C3: 6 => SOL * DIS # F2: 4,9 => CTR => F2: 2 * PRF # F2: 2 => SOL * PRF # D3: 4,9 => SOL * DIS # D3: 2 => CTR => D3: 4,9 * PRF # C2: 4,9 => SOL * DIS # C2: 6 => CTR => C2: 4,9 * PRF # I3: 4,9 => SOL * DIS # I3: 2 => CTR => I3: 4,9 * DIS # G5: 4,9 => CTR => G5: 2 * PRF # G5: 2 => SOL * PRF # D3: 4,9 => SOL * DIS # D3: 2 => CTR => D3: 4,9 * DIS # F2: 4,9 => CTR => F2: 2 * PRF # F2: 2 => SOL * PRF # F9: 4,9 => SOL * DIS # F9: 2 => CTR => F9: 4,9 * PRF # G5: 2,9 => SOL * DIS # G5: 4 => CTR => G5: 2,9 * DIS # H2: 2,9 => CTR => H2: 6 * PRF # H2: 6 => SOL * PRF # H3: 2,9 => SOL * DIS # H3: 6 => CTR => H3: 2,9 * DIS # G5: 4,9 => CTR => G5: 2 * PRF # G5: 2 => SOL * PRF # C2: 4,9 => SOL * DIS # C2: 6 => CTR => C2: 4,9 * DIS # C3: 4,9 => CTR => C3: 6 * PRF # C3: 6 => SOL * INC # F9: 2,9 => UNS * PRF # F9: 4 => SOL * PRF # D3: 2,9 => SOL * DIS # D3: 4 => CTR => D3: 2,9 * PRF # F9: 4,9 => SOL * DIS # F9: 2 => CTR => F9: 4,9 * PRF # G5: 2,9 => SOL * DIS # G5: 4 => CTR => G5: 2,9 * INC # F9: 2,9 => UNS * PRF # F9: 4 => SOL * DIS # I3: 2,9 => CTR => I3: 4 * PRF # I3: 4 => SOL * CNT 44 HDP CHAINS / 44 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C2: 4,9 => SOL * STA C2: 4,9 * CNT 1 HDP CHAINS / 1 HYP OPENED