Analysis of zz-www.sudokuoftheday.co.uk-20060707-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006
level: medium
position: .6.73.1..9..1.4..57...5.9.....3......4......61.9..........8..51.3....26.45.6..8.9 initial
Autosolve
position: .6.7391..98312467571.8569.3...3.....34......61.9.6.3...9..83.5183....26.45.6..839 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 4 => CTR => C1: 2,5 * DIS # C1: 2,4 => CTR => C1: 5 * DIS # C4: 8 => CTR => C4: 5,6 * PRF # I4: 4,8 => SOL * DIS # C4: 5,8 => CTR => C4: 6 * PRF # D8: 4,5 => SOL * DIS # D8: 9 => CTR => D8: 4,5 * DIS # E4: 1,9 => CTR => E4: 4,7 * PRF # G4: 5,7 => SOL * DIS # G4: 4 => CTR => G4: 5,7 * DIS # E5: 1,9 => CTR => E5: 7 * DIS # C7: 2,6 => CTR => C7: 7 * PRF # C7: 7 => SOL * DIS # C9: 1,7 => CTR => C9: 2 * PRF # C9: 2 => SOL * DIS # E8: 1,7 => CTR => E8: 4,9 * DIS # F8: 1,7 => CTR => F8: 5 * PRF # F8: 5 => SOL * DIS # E8: 1,7 => CTR => E8: 4,9 * DIS # F8: 1,7 => CTR => F8: 5 * PRF # F8: 5 => SOL * PRF # F9: 1,7 => SOL * DIS # F9: 2 => CTR => F9: 1,7 * DIS # C9: 1,7 => CTR => C9: 2 * PRF # C9: 2 => SOL * DIS # E4: 1,7 => CTR => E4: 4,9 * DIS # G4: 5 => CTR => G4: 4,7 * DIS # E8: 4,7 => CTR => E8: 1,9 * PRF # E8: 1,9 => SOL * DIS # I4: 4,7 => CTR => I4: 2,8 * CNT 30 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 4 => CTR => C1: 2,5 * DIS C1: 2,5 # C4: 8 => CTR => C4: 5,6 * DIS C1: 2,5 + C4: 5,6 # I4: 2,7 => CTR => I4: 4,8 * PRF C1: 2,5 + C4: 5,6 + I4: 4,8 => SOL * STA C1: 2,5 + C4: 5,6 + I4: 4,8 * CNT 4 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .6.73.1..9..1.4..57...5.9.....3......4......61.9..........8..51.3....26.45.6..8.9 | initial |
| .6.7391..98312467571.8569.3...3.....34......61.9.6.3...9..83.5183....26.45.6..839 | autosolve |
| 265739184983124675714856923526341798348972516179568342697283451831495267452617839 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) A1: 2,5 C3: 2,4 H3: 2,4 A4: 5,6 B4: 2,7 C5: 5,8 B6: 2,7 D5: 2,9 D6: 4,5 H4: 1,9 G5: 5,7 H5: 1,9 A7: 2,6 C8: 1,7 D7: 2,4 E9: 1,7 G7: 4,7 I8: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H4,H5: 1.. / H4 = 1 => 0 pairs (X) / H5 = 1 => 17 pairs (_) C8,C9: 1.. / C8 = 1 => 19 pairs (_) / C9 = 1 => 0 pairs (X) B4,B6: 2.. / B4 = 2 => 17 pairs (_) / B6 = 2 => 21 pairs (_) D5,F5: 2.. / D5 = 2 => 0 pairs (X) / F5 = 2 => 0 pairs (_) D7,F9: 2.. / D7 = 2 => 0 pairs (*) / F9 = 2 => 0 pairs (X) C3,H3: 2.. / C3 = 2 => 0 pairs (X) / H3 = 2 => 20 pairs (_) B4,I4: 2.. / B4 = 2 => 17 pairs (_) / I4 = 2 => 21 pairs (_) C9,F9: 2.. / C9 = 2 => 0 pairs (*) / F9 = 2 => 0 pairs (X) A1,A7: 2.. / A1 = 2 => 19 pairs (_) / A7 = 2 => 0 pairs (X) D5,D7: 2.. / D5 = 2 => 0 pairs (X) / D7 = 2 => 0 pairs (_) F5,F9: 2.. / F5 = 2 => 0 pairs (*) / F9 = 2 => 0 pairs (X) C1,C3: 4.. / C1 = 4 => 0 pairs (X) / C3 = 4 => 20 pairs (_) E4,D6: 4.. / E4 = 4 => 0 pairs (*) / D6 = 4 => 0 pairs (X) G7,I8: 4.. / G7 = 4 => 0 pairs (*) / I8 = 4 => 0 pairs (X) C3,H3: 4.. / C3 = 4 => 20 pairs (_) / H3 = 4 => 0 pairs (X) D7,G7: 4.. / D7 = 4 => 0 pairs (X) / G7 = 4 => 0 pairs (_) E4,E8: 4.. / E4 = 4 => 0 pairs (*) / E8 = 4 => 0 pairs (X) G4,G7: 4.. / G4 = 4 => 0 pairs (X) / G7 = 4 => 0 pairs (_) A1,C1: 5.. / A1 = 5 => 0 pairs (X) / C1 = 5 => 19 pairs (_) D6,F6: 5.. / D6 = 5 => 0 pairs (*) / F6 = 5 => 0 pairs (X) G4,G5: 5.. / G4 = 5 => 0 pairs (X) / G5 = 5 => 20 pairs (_) D8,F8: 5.. / D8 = 5 => 0 pairs (X) / F8 = 5 => 0 pairs (_) C5,G5: 5.. / C5 = 5 => 0 pairs (X) / G5 = 5 => 20 pairs (_) A1,A4: 5.. / A1 = 5 => 0 pairs (X) / A4 = 5 => 19 pairs (_) D6,D8: 5.. / D6 = 5 => 0 pairs (*) / D8 = 5 => 0 pairs (X) F6,F8: 5.. / F6 = 5 => 0 pairs (X) / F8 = 5 => 0 pairs (_) A4,C4: 6.. / A4 = 6 => 0 pairs (X) / C4 = 6 => 19 pairs (_) A7,C7: 6.. / A7 = 6 => 19 pairs (_) / C7 = 6 => 0 pairs (X) A4,A7: 6.. / A4 = 6 => 0 pairs (X) / A7 = 6 => 19 pairs (_) C4,C7: 6.. / C4 = 6 => 19 pairs (_) / C7 = 6 => 0 pairs (X) B4,B6: 7.. / B4 = 7 => 21 pairs (_) / B6 = 7 => 17 pairs (_) G7,I8: 7.. / G7 = 7 => 0 pairs (X) / I8 = 7 => 0 pairs (_) C7,G7: 7.. / C7 = 7 => 0 pairs (*) / G7 = 7 => 0 pairs (X) H1,I1: 8.. / H1 = 8 => 20 pairs (_) / I1 = 8 => 20 pairs (_) C4,C5: 8.. / C4 = 8 => 0 pairs (X) / C5 = 8 => 20 pairs (_) C5,F5: 8.. / C5 = 8 => 20 pairs (_) / F5 = 8 => 0 pairs (X) H1,H6: 8.. / H1 = 8 => 20 pairs (_) / H6 = 8 => 20 pairs (_) H4,H5: 9.. / H4 = 9 => 17 pairs (_) / H5 = 9 => 0 pairs (X) D8,E8: 9.. / D8 = 9 => 0 pairs (X) / E8 = 9 => 0 pairs (_) E4,H4: 9.. / E4 = 9 => 0 pairs (X) / H4 = 9 => 17 pairs (_) D5,D8: 9.. / D5 = 9 => 0 pairs (*) / D8 = 9 => 0 pairs (X) * DURATION: 0:00:51.823018 START: 00:27:19.718720 END: 00:28:11.541738 2019-05-01 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,A7,B4,B6,C3,C5,C8,D5,D6,D7,E9,G5,G7,H3,H4,H5,I8) * .6.7391..98312467571.8569.3...3.....34......61.9.6.3...9..83.5183....26.45.6..839 * PAIR A1: 2,5 BLK 1 C1: 2,5,4 # reduction candidate for 2,5 C1: 4 => CTR * 5647391..9831246757128569436..3.....34......61.9.6.3..29648375183....26445.6.2839 C1: 2,5 # 20 pairs * PAIR C3: 2,4 BLK 1 C1: 2,4,5 # reduction candidate for 2,4 C1: 2,4 => CTR * 56.7391..98312467571.8569.36..34.5..34......61.9.6.3..29648375183....26445.6.2839 C1: 5 # 19 pairs * PAIR H3: 2,4 BLK 3 H1: 2,4,8 # reduction candidate for 2,4 H1: 2,4 # 20 pairs I1: 2,4,8 # reduction candidate for 2,4 I1: 2,4 # 20 pairs * PAIR H3: 2,4 COL H H6: 2,4,8 # reduction candidate for 2,4 H6: 8 # 20 pairs H6: 2,4 # 20 pairs * PAIR A4: 5,6 BLK 4 C4: 5,6,8 # reduction candidate for 5,6 C4: 8 => CTR * .6.7391..98312467571.8569.36.83..5..345..87.61.9.6.3..29..83.5183....26.45.6..839 C4: 5,6 # 20 pairs * PAIR B4: 2,7 ROW 4 I4: 2,7,4,8 # reduction candidate for 2,7 I4: 4,8 => SOLVED * 265739184983124675714856923526341798348972516179568342697283451831495267452617839 I4: 2,7 # 22 pairs * PAIR C5: 5,8 BLK 4 C4: 5,8,6 # reduction candidate for 5,8 C4: 5,8 => CTR * 56.7391..98312467571.8569.36..34.5..34......61.9.6.3..29648375183....26445.6.2839 C4: 6 # 19 pairs * PAIR B6: 2,7 ROW 6 I6: 2,7,4,8 # reduction candidate for 2,7 I6: 2,7 # 22 pairs I6: 4,8 # 19 pairs * PAIR D6: 4,5 COL D D8: 4,5,9 # reduction candidate for 4,5 D8: 4,5 => SOLVED * 265739184983124675714856923526341798348972516179568342697283451831495267452617839 D8: 9 => CTR * .6.7391..98312467571.8569.3...34.5..34......61.956.3...9.48375183.9.526445.6.2839 * PAIR H4: 1,9 ROW 4 E4: 1,9,4,7 # reduction candidate for 1,9 E4: 1,9 => CTR * .6.7391..98312467571.8569.3...3.....34......61.94653...9.28345183.5..26.45.6..839 E4: 4,7 # 20 pairs * PAIR G5: 5,7 BLK 6 G4: 5,7,4 # reduction candidate for 5,7 G4: 5,7 => SOLVED * 265739184983124675714856923526341798348972516179568342697283451831495267452617839 G4: 4 => CTR * .6.7391..98312467571.8569.3...3..4..34....5.61.94653...9.28375183.5..26.45.6..839 * PAIR H5: 1,9 ROW 5 E5: 1,9,7 # reduction candidate for 1,9 E5: 1,9 => CTR * .6.7391..98312467571.8569.3...3415..34.2....61.9.6.3...9.48375183.9.526445.6.2839 E5: 7 # 24 pairs * PAIR A7: 2,6 BLK 7 C7: 2,6,7 # reduction candidate for 2,6 C7: 2,6 => CTR * .6.7391..98312467571.8569.3...34.5..34......61.9.6.3...9..8375183....26445.6..839 C7: 7 => SOLVED * 265739184983124675714856923526341798348972516179568342697283451831495267452617839 * PAIR C8: 1,7 BLK 7 C9: 1,7,2 # reduction candidate for 1,7 C9: 1,7 => CTR * .6.7391..98312467571.8569.3...34.5..34.2....61.9.6.3...9.48375183.9.526445.6.2839 C9: 2 => SOLVED * 265739184983124675714856923526341798348972516179568342697283451831495267452617839 * PAIR C8: 1,7 ROW 8 E8: 1,7,4,9 # reduction candidate for 1,7 E8: 1,7 => CTR * .6.7391..98312467571.8569.3...34..9.34..9..161.956.3...9..8345183....26.45.6..839 E8: 4,9 # 19 pairs F8: 1,7,5 # reduction candidate for 1,7 F8: 1,7 => CTR * .6.7391..98312467571.8569.3...34....34......61.9.653...9..83.5183.59.26445.6..839 F8: 5 => SOLVED * 265739184983124675714856923526341798348972516179568342697283451831495267452617839 * PAIR E9: 1,7 BLK 8 E8: 1,7,4,9 # reduction candidate for 1,7 E8: 1,7 => CTR * .6.7391..98312467571.8569.3...34..9.34..9..161.956.3...9..8345183....26.45.6..839 E8: 4,9 # 19 pairs F8: 1,7,5 # reduction candidate for 1,7 F8: 1,7 => CTR * .6.7391..98312467571.8569.3...34....34......61.9.653...9..83.5183.59.26445.6..839 F8: 5 => SOLVED * 265739184983124675714856923526341798348972516179568342697283451831495267452617839 F9: 1,7,2 # reduction candidate for 1,7 F9: 1,7 => SOLVED * 265739184983124675714856923526341798348972516179568342697283451831495267452617839 F9: 2 => CTR * .6.7391..98312467571.8569.3...34.5..34.2....61.9.6.3...9.48375183.9.526445.6.2839 * PAIR E9: 1,7 ROW 9 C9: 1,7,2 # reduction candidate for 1,7 C9: 1,7 => CTR * .6.7391..98312467571.8569.3...34.5..34.2....61.9.6.3...9.48375183.9.526445.6.2839 C9: 2 => SOLVED * 265739184983124675714856923526341798348972516179568342697283451831495267452617839 * PAIR E9: 1,7 COL E E4: 1,7,4,9 # reduction candidate for 1,7 E4: 1,7 => CTR * .6.7391..98312467571.8569.3...3...9.34.....161.94653...9.28345183.5..26.45.6..839 E4: 4,9 # 19 pairs E5: 1,7,9 # reduction candidate for 1,7 E5: 1,7 # 21 pairs * PAIR G7: 4,7 COL G G4: 4,7,5 # reduction candidate for 4,7 G4: 5 => CTR * .6.7391..98312467571.8569.3...3..5..345..87.61.9.6.3...97.83451831...26.45.6..839 G4: 4,7 # 20 pairs * PAIR I8: 4,7 ROW 8 E8: 4,7,1,9 # reduction candidate for 4,7 E8: 4,7 => CTR * .6.7391..98312467571.8569.3...34.5..34.2....61.956.3...9.483751831975264457612839 E8: 1,9 => SOLVED * 265739184983124675714856923526341798348972516179568342697283451831495267452617839 * PAIR I8: 4,7 COL I I4: 4,7,2,8 # reduction candidate for 4,7 I4: 4,7 => CTR * .6.7391..98312467571.8569.3.2.34....34......6179.653...9..83.5183.59.26445.6..839 I4: 2,8 # 19 pairs I6: 4,7,2,8 # reduction candidate for 4,7 I6: 4,7 # 22 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060707-absurd-base-pr-000.dot * REASONING * DIS # C1: 4 => CTR => C1: 2,5 * DIS # C1: 2,4 => CTR => C1: 5 * DIS # C4: 8 => CTR => C4: 5,6 * PRF # I4: 4,8 => SOL * DIS # C4: 5,8 => CTR => C4: 6 * PRF # D8: 4,5 => SOL * DIS # D8: 9 => CTR => D8: 4,5 * DIS # E4: 1,9 => CTR => E4: 4,7 * PRF # G4: 5,7 => SOL * DIS # G4: 4 => CTR => G4: 5,7 * DIS # E5: 1,9 => CTR => E5: 7 * DIS # C7: 2,6 => CTR => C7: 7 * PRF # C7: 7 => SOL * DIS # C9: 1,7 => CTR => C9: 2 * PRF # C9: 2 => SOL * DIS # E8: 1,7 => CTR => E8: 4,9 * DIS # F8: 1,7 => CTR => F8: 5 * PRF # F8: 5 => SOL * DIS # E8: 1,7 => CTR => E8: 4,9 * DIS # F8: 1,7 => CTR => F8: 5 * PRF # F8: 5 => SOL * PRF # F9: 1,7 => SOL * DIS # F9: 2 => CTR => F9: 1,7 * DIS # C9: 1,7 => CTR => C9: 2 * PRF # C9: 2 => SOL * DIS # E4: 1,7 => CTR => E4: 4,9 * DIS # G4: 5 => CTR => G4: 4,7 * DIS # E8: 4,7 => CTR => E8: 1,9 * PRF # E8: 1,9 => SOL * DIS # I4: 4,7 => CTR => I4: 2,8 * CNT 30 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,A7,B4,B6,C3,C5,C8,D5,D6,D7,E9,G5,G7,H3,H4,H5,I8) * .6.7391..98312467571.8569.3...3.....34......61.9.6.3...9..83.5183....26.45.6..839 * PAIR A1: 2,5 BLK 1 C1: 2,5,4 # reduction candidate for 2,5 C1: 4 => CTR * 5647391..9831246757128569436..3.....34......61.9.6.3..29648375183....26445.6.2839 * PAIR A4: 5,6 BLK 4 C4: 5,6,8 # reduction candidate for 5,6 C4: 8 => CTR * .6.7391..9831246757148569236.83..5..345..87.61.9.6.3..29..83.5183....26.45.6..839 * PAIR B4: 2,7 ROW 4 I4: 2,7,4,8 # reduction candidate for 2,7 I4: 2,7 => CTR * .6.739148983124675714856923...348...348...5.61.9.6538..9..83.5183.59.26445.6..839 I4: 4,8 => SOLVED * 265739184983124675714856923526341798348972516179568342697283451831495267452617839 * DURATION: 0:00:05.628328 START: 00:28:48.679686 END: 00:28:54.308014 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060707-absurd-base-pr-001.dot * REASONING * DIS # C1: 4 => CTR => C1: 2,5 * DIS C1: 2,5 # C4: 8 => CTR => C4: 5,6 * DIS C1: 2,5 + C4: 5,6 # I4: 2,7 => CTR => I4: 4,8 * PRF C1: 2,5 + C4: 5,6 + I4: 4,8 => SOL * STA C1: 2,5 + C4: 5,6 + I4: 4,8 * CNT 4 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060707, absurd
Solution
position: 265739184983124675714856923526341798348972516179568342697283451831495267452617839 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 # C1: 2,5 => UNS * DIS # C1: 4 => CTR => C1: 2,5 * DIS # C1: 2,4 => CTR => C1: 5 * INC # C1: 5 => UNS * INC # H1: 2,4 => UNS * INC # I1: 2,4 => UNS * INC # H6: 2,4 => UNS * INC # H6: 8 => UNS * INC # C4: 5,6 => UNS * DIS # C4: 8 => CTR => C4: 5,6 * INC # I4: 2,7 => UNS * PRF # I4: 4,8 => SOL * DIS # C4: 5,8 => CTR => C4: 6 * INC # C4: 6 => UNS * INC # I6: 2,7 => UNS * INC # I6: 4,8 => UNS * PRF # D8: 4,5 => SOL * DIS # D8: 9 => CTR => D8: 4,5 * DIS # E4: 1,9 => CTR => E4: 4,7 * INC # E4: 4,7 => UNS * PRF # G4: 5,7 => SOL * DIS # G4: 4 => CTR => G4: 5,7 * DIS # E5: 1,9 => CTR => E5: 7 * INC # E5: 7 => UNS * DIS # C7: 2,6 => CTR => C7: 7 * PRF # C7: 7 => SOL * DIS # C9: 1,7 => CTR => C9: 2 * PRF # C9: 2 => SOL * DIS # E8: 1,7 => CTR => E8: 4,9 * INC # E8: 4,9 => UNS * DIS # F8: 1,7 => CTR => F8: 5 * PRF # F8: 5 => SOL * DIS # E8: 1,7 => CTR => E8: 4,9 * INC # E8: 4,9 => UNS * DIS # F8: 1,7 => CTR => F8: 5 * PRF # F8: 5 => SOL * PRF # F9: 1,7 => SOL * DIS # F9: 2 => CTR => F9: 1,7 * DIS # C9: 1,7 => CTR => C9: 2 * PRF # C9: 2 => SOL * DIS # E4: 1,7 => CTR => E4: 4,9 * INC # E4: 4,9 => UNS * INC # E5: 1,7 => UNS * INC # G4: 4,7 => UNS * DIS # G4: 5 => CTR => G4: 4,7 * DIS # E8: 4,7 => CTR => E8: 1,9 * PRF # E8: 1,9 => SOL * DIS # I4: 4,7 => CTR => I4: 2,8 * INC # I4: 2,8 => UNS * INC # I6: 4,7 => UNS * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 2,5 => UNS * DIS # C1: 4 => CTR => C1: 2,5 * INC C1: 2,5 # C4: 5,6 => UNS * DIS C1: 2,5 # C4: 8 => CTR => C4: 5,6 * DIS C1: 2,5 + C4: 5,6 # I4: 2,7 => CTR => I4: 4,8 * PRF C1: 2,5 + C4: 5,6 + I4: 4,8 => SOL * STA C1: 2,5 + C4: 5,6 + I4: 4,8 * CNT 6 HDP CHAINS / 5 HYP OPENED