Analysis of zz-www.sudokuoftheday.co.uk-20190410-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019
level: medium
position: 15837.........537..........8..5..9..5...3.....738.6......6.....6..9.1..4792.5...6 initial
Autosolve
position: 15837.......1.53783.72.8...8..5..9375..73.....738.6...481627593635981724792453..6 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B2: 4,6 => SOL * DIS # B2: 2 => CTR => B2: 4,6 * DIS # C2: 4,6 => CTR => C2: 9 * PRF # C2: 9 => SOL * DIS # E3: 4,6 => CTR => E3: 9 * PRF # E3: 9 => SOL * DIS # B4: 4,6 => CTR => B4: 1,2 * DIS # E3: 6 => CTR => E3: 4,9 * DIS # F5: 2 => CTR => F5: 4,9 * DIS # E3: 4,6 => CTR => E3: 9 * PRF # E3: 9 => SOL * PRF # B2: 4,6 => SOL * DIS # B2: 2 => CTR => B2: 4,6 * DIS # C2: 4,6 => CTR => C2: 9 * PRF # C2: 9 => SOL * DIS # G1: 4,6 => CTR => G1: 2 * PRF # G1: 2 => SOL * PRF # H3: 1,4 => SOL * PRF # G6: 1,4 => SOL * DIS # G6: 2 => CTR => G6: 1,4 * DIS # B4: 4,6 => CTR => B4: 1,2 * DIS # C2: 4,6 => CTR => C2: 9 * PRF # C2: 9 => SOL * DIS # F5: 2 => CTR => F5: 4,9 * DIS # C2: 6 => CTR => C2: 4,9 * DIS # B4: 2,6 => CTR => B4: 1,4 * DIS # F5: 2,4 => CTR => F5: 9 * PRF # F5: 9 => SOL * DIS # B4: 2,4 => CTR => B4: 1,6 * PRF # I6: 1,2 => SOL * DIS # B5: 4 => CTR => B5: 1,2 * CNT 31 HDP CHAINS / 43 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B2: 4,6 => SOL * STA B2: 4,6 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 15837.........537..........8..5..9..5...3.....738.6......6.....6..9.1..4792.5...6 | initial |
| 15837.......1.53783.72.8...8..5..9375..73.....738.6...481627593635981724792453..6 | autosolve |
| 158374269249165378367298145816542937524739681973816452481627593635981724792453816 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) A2: 2,9 B3: 4,6 F1: 4,9 E2: 4,6 H1: 4,6 I1: 2,9 G3: 1,4 C4: 4,6 C5: 4,9 A6: 2,9 E4: 1,4 F4: 2,4 E6: 1,9 G5: 6,8 H5: 6,8 I5: 1,2 G9: 1,8 H9: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B4,B5: 1.. / B4 = 1 => 0 pairs (*) / B5 = 1 => 0 pairs (X) E4,E6: 1.. / E4 = 1 => 0 pairs (X) / E6 = 1 => 0 pairs (_) G9,H9: 1.. / G9 = 1 => 0 pairs (X) / H9 = 1 => 16 pairs (_) B4,E4: 1.. / B4 = 1 => 0 pairs (*) / E4 = 1 => 0 pairs (X) B5,I5: 1.. / B5 = 1 => 0 pairs (X) / I5 = 1 => 0 pairs (_) A2,B2: 2.. / A2 = 2 => 0 pairs (*) / B2 = 2 => 0 pairs (X) G1,I1: 2.. / G1 = 2 => 0 pairs (*) / I1 = 2 => 0 pairs (X) F4,F5: 2.. / F4 = 2 => 19 pairs (_) / F5 = 2 => 0 pairs (X) B4,F4: 2.. / B4 = 2 => 0 pairs (X) / F4 = 2 => 19 pairs (_) A2,A6: 2.. / A2 = 2 => 0 pairs (*) / A6 = 2 => 0 pairs (X) G1,G6: 2.. / G1 = 2 => 0 pairs (*) / G6 = 2 => 0 pairs (X) G6,H6: 4.. / G6 = 4 => 0 pairs (*) / H6 = 4 => 0 pairs (X) H3,I3: 5.. / H3 = 5 => 20 pairs (_) / I3 = 5 => 0 pairs (*) H6,I6: 5.. / H6 = 5 => 0 pairs (*) / I6 = 5 => 0 pairs (X) H3,H6: 5.. / H3 = 5 => 20 pairs (_) / H6 = 5 => 0 pairs (*) I3,I6: 5.. / I3 = 5 => 0 pairs (*) / I6 = 5 => 0 pairs (X) E2,E3: 6.. / E2 = 6 => 18 pairs (_) / E3 = 6 => 0 pairs (X) G1,H1: 6.. / G1 = 6 => 0 pairs (X) / H1 = 6 => 16 pairs (_) B4,C4: 6.. / B4 = 6 => 0 pairs (X) / C4 = 6 => 18 pairs (_) G5,H5: 6.. / G5 = 6 => 16 pairs (_) / H5 = 6 => 0 pairs (X) B3,E3: 6.. / B3 = 6 => 18 pairs (_) / E3 = 6 => 0 pairs (X) C2,C4: 6.. / C2 = 6 => 0 pairs (X) / C4 = 6 => 18 pairs (_) G1,G5: 6.. / G1 = 6 => 0 pairs (X) / G5 = 6 => 16 pairs (_) H1,H5: 6.. / H1 = 6 => 16 pairs (_) / H5 = 6 => 0 pairs (X) G5,H5: 8.. / G5 = 8 => 0 pairs (X) / H5 = 8 => 16 pairs (_) G9,H9: 8.. / G9 = 8 => 16 pairs (_) / H9 = 8 => 0 pairs (X) G5,G9: 8.. / G5 = 8 => 0 pairs (X) / G9 = 8 => 16 pairs (_) H5,H9: 8.. / H5 = 8 => 16 pairs (_) / H9 = 8 => 0 pairs (X) A2,C2: 9.. / A2 = 9 => 0 pairs (X) / C2 = 9 => 0 pairs (_) F1,E3: 9.. / F1 = 9 => 0 pairs (X) / E3 = 9 => 0 pairs (_) I1,I3: 9.. / I1 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) C5,A6: 9.. / C5 = 9 => 0 pairs (X) / A6 = 9 => 0 pairs (_) F5,E6: 9.. / F5 = 9 => 0 pairs (*) / E6 = 9 => 0 pairs (X) F1,I1: 9.. / F1 = 9 => 0 pairs (X) / I1 = 9 => 0 pairs (_) E3,I3: 9.. / E3 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) C5,F5: 9.. / C5 = 9 => 0 pairs (X) / F5 = 9 => 0 pairs (_) A6,E6: 9.. / A6 = 9 => 0 pairs (*) / E6 = 9 => 0 pairs (X) A2,A6: 9.. / A2 = 9 => 0 pairs (X) / A6 = 9 => 0 pairs (_) C2,C5: 9.. / C2 = 9 => 0 pairs (*) / C5 = 9 => 0 pairs (X) E3,E6: 9.. / E3 = 9 => 0 pairs (*) / E6 = 9 => 0 pairs (X) F1,F5: 9.. / F1 = 9 => 0 pairs (X) / F5 = 9 => 0 pairs (_) * DURATION: 0:00:52.004313 START: 05:10:59.372942 END: 05:11:51.377255 2019-05-01 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,B3,C4,C5,E2,E4,E6,F1,F4,G3,G5,G9,H1,H5,H9,I1,I5) * 15837.......1.53783.72.8...8..5..9375..73.....738.6...481627593635981724792453..6 * PAIR B3: 4,6 BLK 1 B2: 4,6,2 # reduction candidate for 4,6 B2: 4,6 => SOLVED * 158374269249165378367298145816542937524739681973816452481627593635981724792453816 B2: 2 => CTR * 158379....2.1.53783.72.8...8..5.29375..73...2273896...481627593635981724792453..6 C2: 4,6,9 # reduction candidate for 4,6 C2: 4,6 => CTR * 15837....92.1.53783.72.8...8..5.29375.9734..2273896...481627593635981724792453..6 C2: 9 => SOLVED * 158374269249165378367298145816542937524739681973816452481627593635981724792453816 * PAIR B3: 4,6 ROW 3 E3: 4,6,9 # reduction candidate for 4,6 E3: 4,6 => CTR * 158379..2...1.53783.72.8..98..5..9375.973...12738.6...481627593635981724792453..6 E3: 9 => SOLVED * 158374269249165378367298145816542937524739681973816452481627593635981724792453816 * PAIR B3: 4,6 COL B B4: 4,6,1,2 # reduction candidate for 4,6 B4: 4,6 => CTR * 15837.......1.53783.72.8...8..51293751.734..2273896...481627593635981724792453..6 B4: 1,2 # 20 pairs * PAIR F1: 4,9 BLK 2 E3: 4,9,6 # reduction candidate for 4,9 E3: 6 => CTR * 158379..2...1453783472681598..51.93751.73.....738.6...481627593635981724792453..6 E3: 4,9 # 18 pairs * PAIR F1: 4,9 COL F F5: 4,9,2 # reduction candidate for 4,9 F5: 2 => CTR * 158379..2...1.53783.72.8..98..5.49375.9732..12738.6...481627593635981724792453..6 F5: 4,9 # 19 pairs * PAIR E2: 4,6 BLK 2 E3: 4,6,9 # reduction candidate for 4,6 E3: 4,6 => CTR * 158379..2...1.53783.72.8..98..5..9375.973...12738.6...481627593635981724792453..6 E3: 9 => SOLVED * 158374269249165378367298145816542937524739681973816452481627593635981724792453816 * PAIR E2: 4,6 ROW 2 B2: 4,6,2 # reduction candidate for 4,6 B2: 4,6 => SOLVED * 158374269249165378367298145816542937524739681973816452481627593635981724792453816 B2: 2 => CTR * 158379....2.1.53783.72.8...8..5.29375..73...2273896...481627593635981724792453..6 C2: 4,6,9 # reduction candidate for 4,6 C2: 4,6 => CTR * 15837....92.1.53783.72.8...8..5.29375.9734..2273896...481627593635981724792453..6 C2: 9 => SOLVED * 158374269249165378367298145816542937524739681973816452481627593635981724792453816 * PAIR H1: 4,6 BLK 3 G1: 4,6,2 # reduction candidate for 4,6 G1: 4,6 => CTR * 15837...2...1.53783.72.8..98..5..9375..73...1.738.6...481627593635981724792453..6 G1: 2 => SOLVED * 158374269249165378367298145816542937524739681973816452481627593635981724792453816 * PAIR G3: 1,4 BLK 3 H3: 1,4,5 # reduction candidate for 1,4 H3: 1,4 => SOLVED * 158374269249165378367298145816542937524739681973816452481627593635981724792453816 H3: 5 # 20 pairs * PAIR G3: 1,4 COL G G6: 1,4,2 # reduction candidate for 1,4 G6: 1,4 => SOLVED * 158374269249165378367298145816542937524739681973816452481627593635981724792453816 G6: 2 => CTR * 15837..622.91.53783.72.8.598.65..9375.4739....738.6245481627593635981724792453..6 * PAIR C4: 4,6 BLK 4 B4: 4,6,1,2 # reduction candidate for 4,6 B4: 4,6 => CTR * 15837.......1.53783.72.8...8..51293751.734..2273896...481627593635981724792453..6 B4: 1,2 # 20 pairs * PAIR C4: 4,6 COL C C2: 4,6,9 # reduction candidate for 4,6 C2: 4,6 => CTR * 15837....92.1.53783.72.8...8..5.29375.9734..2273896...481627593635981724792453..6 C2: 9 => SOLVED * 158374269249165378367298145816542937524739681973816452481627593635981724792453816 * PAIR C5: 4,9 ROW 5 F5: 4,9,2 # reduction candidate for 4,9 F5: 2 => CTR * 158379..2...1.53783.72.8..98..5.49375.9732..12738.6...481627593635981724792453..6 F5: 4,9 # 19 pairs * PAIR C5: 4,9 COL C C2: 4,9,6 # reduction candidate for 4,9 C2: 6 => CTR * 15837....926145378347268159864512937519734..2.738.6...481627593635981724792453..6 C2: 4,9 # 18 pairs * PAIR E4: 1,4 ROW 4 B4: 1,4,2,6 # reduction candidate for 1,4 B4: 2,6 => CTR * 158379......1.53783.72.8...8..51.93751.73...2273896...481627593635981724792453..6 B4: 1,4 # 20 pairs * PAIR F4: 2,4 BLK 5 F5: 2,4,9 # reduction candidate for 2,4 F5: 2,4 => CTR * 158379..2...1.53783.72.8..98..5..9375.973...12738.6...481627593635981724792453..6 F5: 9 => SOLVED * 158374269249165378367298145816542937524739681973816452481627593635981724792453816 * PAIR F4: 2,4 ROW 4 B4: 2,4,1,6 # reduction candidate for 2,4 B4: 2,4 => CTR * 158379......1.53783.72.8...8.651.93751.73...2273896...481627593635981724792453..6 B4: 1,6 # 21 pairs * PAIR I5: 1,2 BLK 6 G6: 1,2,4 # reduction candidate for 1,2 G6: 1,2 # 16 pairs I6: 1,2,5 # reduction candidate for 1,2 I6: 1,2 => SOLVED * 158374269249165378367298145816542937524739681973816452481627593635981724792453816 I6: 5 # 20 pairs * PAIR I5: 1,2 ROW 5 B5: 1,2,4 # reduction candidate for 1,2 B5: 4 => CTR * 15837.......1.53783.72.8...81654293754.73.....738.6...481627593635981724792453..6 B5: 1,2 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190410-absurd-base-pr-000.dot * REASONING * PRF # B2: 4,6 => SOL * DIS # B2: 2 => CTR => B2: 4,6 * DIS # C2: 4,6 => CTR => C2: 9 * PRF # C2: 9 => SOL * DIS # E3: 4,6 => CTR => E3: 9 * PRF # E3: 9 => SOL * DIS # B4: 4,6 => CTR => B4: 1,2 * DIS # E3: 6 => CTR => E3: 4,9 * DIS # F5: 2 => CTR => F5: 4,9 * DIS # E3: 4,6 => CTR => E3: 9 * PRF # E3: 9 => SOL * PRF # B2: 4,6 => SOL * DIS # B2: 2 => CTR => B2: 4,6 * DIS # C2: 4,6 => CTR => C2: 9 * PRF # C2: 9 => SOL * DIS # G1: 4,6 => CTR => G1: 2 * PRF # G1: 2 => SOL * PRF # H3: 1,4 => SOL * PRF # G6: 1,4 => SOL * DIS # G6: 2 => CTR => G6: 1,4 * DIS # B4: 4,6 => CTR => B4: 1,2 * DIS # C2: 4,6 => CTR => C2: 9 * PRF # C2: 9 => SOL * DIS # F5: 2 => CTR => F5: 4,9 * DIS # C2: 6 => CTR => C2: 4,9 * DIS # B4: 2,6 => CTR => B4: 1,4 * DIS # F5: 2,4 => CTR => F5: 9 * PRF # F5: 9 => SOL * DIS # B4: 2,4 => CTR => B4: 1,6 * PRF # I6: 1,2 => SOL * DIS # B5: 4 => CTR => B5: 1,2 * CNT 31 HDP CHAINS / 43 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,B3,C4,C5,E2,E4,E6,F1,F4,G3,G5,G9,H1,H5,H9,I1,I5) * 15837.......1.53783.72.8...8..5..9375..73.....738.6...481627593635981724792453..6 * PAIR B3: 4,6 BLK 1 B2: 4,6,2 # reduction candidate for 4,6 B2: 4,6 => SOLVED * 158374269249165378367298145816542937524739681973816452481627593635981724792453816 * DURATION: 0:00:01.689186 START: 05:12:25.834708 END: 05:12:27.523894 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190410-absurd-base-pr-001.dot * REASONING * PRF # B2: 4,6 => SOL * STA B2: 4,6 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190410, absurd
Solution
position: 158374269249165378367298145816542937524739681973816452481627593635981724792453816 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 # B2: 4,6 => SOL * DIS # B2: 2 => CTR => B2: 4,6 * DIS # C2: 4,6 => CTR => C2: 9 * PRF # C2: 9 => SOL * DIS # E3: 4,6 => CTR => E3: 9 * PRF # E3: 9 => SOL * DIS # B4: 4,6 => CTR => B4: 1,2 * INC # B4: 1,2 => UNS * INC # E3: 4,9 => UNS * DIS # E3: 6 => CTR => E3: 4,9 * INC # F5: 4,9 => UNS * DIS # F5: 2 => CTR => F5: 4,9 * DIS # E3: 4,6 => CTR => E3: 9 * PRF # E3: 9 => SOL * PRF # B2: 4,6 => SOL * DIS # B2: 2 => CTR => B2: 4,6 * DIS # C2: 4,6 => CTR => C2: 9 * PRF # C2: 9 => SOL * DIS # G1: 4,6 => CTR => G1: 2 * PRF # G1: 2 => SOL * PRF # H3: 1,4 => SOL * INC # H3: 5 => UNS * PRF # G6: 1,4 => SOL * DIS # G6: 2 => CTR => G6: 1,4 * DIS # B4: 4,6 => CTR => B4: 1,2 * INC # B4: 1,2 => UNS * DIS # C2: 4,6 => CTR => C2: 9 * PRF # C2: 9 => SOL * INC # F5: 4,9 => UNS * DIS # F5: 2 => CTR => F5: 4,9 * INC # C2: 4,9 => UNS * DIS # C2: 6 => CTR => C2: 4,9 * INC # B4: 1,4 => UNS * DIS # B4: 2,6 => CTR => B4: 1,4 * DIS # F5: 2,4 => CTR => F5: 9 * PRF # F5: 9 => SOL * DIS # B4: 2,4 => CTR => B4: 1,6 * INC # B4: 1,6 => UNS * INC # G6: 1,2 => UNS * PRF # I6: 1,2 => SOL * INC # I6: 5 => UNS * INC # B5: 1,2 => UNS * DIS # B5: 4 => CTR => B5: 1,2 * CNT 43 HDP CHAINS / 43 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # B2: 4,6 => SOL * STA B2: 4,6 * CNT 1 HDP CHAINS / 1 HYP OPENED