Contents
level: medium
The following important HDP chains were detected:
* DIS # B1: 1,8 => CTR => B1: 3,6 * DIS # F2: 3,6 => CTR => F2: 2 * DIS # A1: 6,8 => CTR => A1: 1 * DIS # B1: 6,8 => CTR => B1: 1,3 * PRF # A7: 6,8 => SOL * DIS # F2: 3,6 => CTR => F2: 2 * DIS # B1: 1,8 => CTR => B1: 3,6 * DIS # I1: 6 => CTR => I1: 2,8 * DIS # I1: 2 => CTR => I1: 6,8 * PRF # B5: 3,6 => SOL * DIS # D5: 3,6 => CTR => D5: 1,8 * DIS # D5: 1,3 => CTR => D5: 6,8 * DIS # I4: 1,3 => CTR => I4: 2,7 * DIS # E6: 1,2 => CTR => E6: 6 * DIS # I4: 1,2 => CTR => I4: 3,7 * PRF # F5: 3,4 => SOL * DIS # F5: 6,8 => CTR => F5: 3,4 * DIS # I4: 1,3 => CTR => I4: 2,7 * DIS # I5: 1,3 => CTR => I5: 2,9 * DIS # B5: 1,3 => CTR => B5: 2,6 * DIS # D5: 1,3 => CTR => D5: 6,8 * PRF # B7: 2,8 => SOL * DIS # D8: 8 => CTR => D8: 1,6 * DIS # E6: 2 => CTR => E6: 1,6 * DIS # F7: 6 => CTR => F7: 2,8 * PRF # G7: 7,8 => SOL * DIS # B8: 6 => CTR => B8: 7,8 * DIS # I4: 1,3 => CTR => I4: 2,7 * DIS # I5: 1,3 => CTR => I5: 2,9 * CNT 29 HDP CHAINS / 66 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
The following important HDP chains were detected:
* DIS # B1: 1,8 => CTR => B1: 3,6 * DIS B1: 3,6 # F2: 3,6 => CTR => F2: 2 * DIS B1: 3,6 + F2: 2 # F5: 3,6 => CTR => F5: 4,8 * PRF B1: 3,6 + F2: 2 + F5: 4,8 # B5: 3,6 => SOL * STA B1: 3,6 + F2: 2 + F5: 4,8 + B5: 3,6 * CNT 4 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
.......4.94..8...5.52..139..98....6.7...........9.75....143....3....9.24....756.. | initial |
..759..4.94..8.175.5274139.598....6.7...5......49.758...143..5.3.5..9.244.9.756.. | autosolve |
137596248946382175852741396598123467763854912214967583621438759375619824489275631 | solved |
level: medium
-------------------------------------------------- * PAIRS (16) C2: 3,6 A3: 6,8 F1: 3,6 G1: 2,8 I3: 6,8 C5: 3,6 D4: 1,3 E4: 1,2 F4: 3,4 H5: 1,3 B9: 2,8 E8: 1,6 D9: 2,8 G8: 7,8 H9: 1,3 I9: 1,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,B1: 1.. / A1 = 1 => 17 pairs (_) / B1 = 1 => 0 pairs (X) D8,E8: 1.. / D8 = 1 => 0 pairs (X) / E8 = 1 => 17 pairs (_) H9,I9: 1.. / H9 = 1 => 0 pairs (X) / I9 = 1 => 15 pairs (_) A1,A6: 1.. / A1 = 1 => 17 pairs (_) / A6 = 1 => 0 pairs (X) H5,H9: 1.. / H5 = 1 => 15 pairs (_) / H9 = 1 => 0 pairs (X) D2,F2: 2.. / D2 = 2 => 0 pairs (X) / F2 = 2 => 18 pairs (_) G1,I1: 2.. / G1 = 2 => 19 pairs (_) / I1 = 2 => 0 pairs (X) E4,E6: 2.. / E4 = 2 => 17 pairs (_) / E6 = 2 => 0 pairs (X) F7,D9: 2.. / F7 = 2 => 0 pairs (X) / D9 = 2 => 18 pairs (_) B9,D9: 2.. / B9 = 2 => 0 pairs (X) / D9 = 2 => 18 pairs (_) A6,A7: 2.. / A6 = 2 => 0 pairs (*) / A7 = 2 => 0 pairs (X) D2,D9: 2.. / D2 = 2 => 0 pairs (X) / D9 = 2 => 18 pairs (_) F2,F7: 2.. / F2 = 2 => 18 pairs (_) / F7 = 2 => 0 pairs (X) B1,C2: 3.. / B1 = 3 => 22 pairs (_) / C2 = 3 => 0 pairs (X) H9,I9: 3.. / H9 = 3 => 15 pairs (_) / I9 = 3 => 0 pairs (X) B1,F1: 3.. / B1 = 3 => 22 pairs (_) / F1 = 3 => 0 pairs (X) B6,I6: 3.. / B6 = 3 => 0 pairs (X) / I6 = 3 => 17 pairs (_) C2,C5: 3.. / C2 = 3 => 0 pairs (X) / C5 = 3 => 22 pairs (_) H5,H9: 3.. / H5 = 3 => 0 pairs (X) / H9 = 3 => 15 pairs (_) F4,F5: 4.. / F4 = 4 => 24 pairs (_) / F5 = 4 => 0 pairs (*) G4,G5: 4.. / G4 = 4 => 0 pairs (*) / G5 = 4 => 0 pairs (X) F4,G4: 4.. / F4 = 4 => 24 pairs (_) / G4 = 4 => 0 pairs (*) F5,G5: 4.. / F5 = 4 => 0 pairs (*) / G5 = 4 => 0 pairs (X) I1,I3: 6.. / I1 = 6 => 0 pairs (X) / I3 = 6 => 17 pairs (_) A3,I3: 6.. / A3 = 6 => 0 pairs (X) / I3 = 6 => 17 pairs (_) C2,C5: 6.. / C2 = 6 => 22 pairs (_) / C5 = 6 => 0 pairs (X) E6,E8: 6.. / E6 = 6 => 17 pairs (_) / E8 = 6 => 0 pairs (X) G4,I4: 7.. / G4 = 7 => 18 pairs (_) / I4 = 7 => 20 pairs (_) B7,B8: 7.. / B7 = 7 => 0 pairs (X) / B8 = 7 => 21 pairs (_) B8,G8: 7.. / B8 = 7 => 21 pairs (_) / G8 = 7 => 0 pairs (X) I4,I7: 7.. / I4 = 7 => 20 pairs (_) / I7 = 7 => 18 pairs (_) D5,F5: 8.. / D5 = 8 => 21 pairs (_) / F5 = 8 => 0 pairs (X) A3,I3: 8.. / A3 = 8 => 17 pairs (_) / I3 = 8 => 0 pairs (X) B9,D9: 8.. / B9 = 8 => 18 pairs (_) / D9 = 8 => 0 pairs (X) F5,F7: 8.. / F5 = 8 => 0 pairs (X) / F7 = 8 => 21 pairs (_) G5,I5: 9.. / G5 = 9 => 0 pairs (*) / I5 = 9 => 0 pairs (X) G7,I7: 9.. / G7 = 9 => 18 pairs (_) / I7 = 9 => 0 pairs (*) G5,G7: 9.. / G5 = 9 => 0 pairs (*) / G7 = 9 => 0 pairs (X) I5,I7: 9.. / I5 = 9 => 18 pairs (_) / I7 = 9 => 0 pairs (*) * DURATION: 0:00:49.738430 START: 00:46:32.995432 END: 00:47:22.733862 2019-05-01 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B9,C2,C5,D4,D9,E4,E8,F1,F4,G1,G8,H5,H9,I3,I9) * ..759..4.94..8.175.5274139.598....6.7...5......49.758...143..5.3.5..9.244.9.756.. * PAIR C2: 3,6 BLK 1 B1: 3,6,1,8 # reduction candidate for 3,6 B1: 1,8 => CTR * ..7593.4.943.8.175.5274139.598.2476.726.584.91349675822.14369573.5.19.244.9.756.. B1: 3,6 # 18 pairs * PAIR C2: 3,6 ROW 2 D2: 3,6,2 # reduction candidate for 3,6 D2: 3,6 # 18 pairs F2: 3,6,2 # reduction candidate for 3,6 F2: 3,6 => CTR * ..759..4.94.28.175.5274139.598....6.7...584....49.758...1432.5.3.5..9.244298756.. F2: 2 # 18 pairs * PAIR A3: 6,8 BLK 1 A1: 6,8,1 # reduction candidate for 6,8 A1: 6,8 => CTR * .17593.4.943.8.175.5274139.598..4.6.7.6.584.91.496758.2.143695.365.197244892756.. A1: 1 # 17 pairs B1: 6,8,1,3 # reduction candidate for 6,8 B1: 6,8 => CTR * 1.7593.4.943.8.175.5274139.598..4.6.7.6.584.92.496758...143.95.3.5.19.244.9.756.. B1: 1,3 # 18 pairs * PAIR A3: 6,8 COL A A7: 6,8,2 # reduction candidate for 6,8 A7: 6,8 => SOLVED * 137596248946382175852741396598123467763854912214967583621438759375619824489275631 A7: 2 # 20 pairs * PAIR F1: 3,6 BLK 2 D2: 3,6,2 # reduction candidate for 3,6 D2: 3,6 # 18 pairs F2: 3,6,2 # reduction candidate for 3,6 F2: 3,6 => CTR * ..759..4.94.28.175.5274139.598....6.7...584....49.758...1432.5.3.5..9.244298756.. F2: 2 # 18 pairs * PAIR F1: 3,6 ROW 1 B1: 3,6,1,8 # reduction candidate for 3,6 B1: 1,8 => CTR * ..7593.4.943.8.175.5274139.598.2476.726.584.91349675822.14369573.5.19.244.9.756.. B1: 3,6 # 18 pairs * PAIR F1: 3,6 COL F F5: 3,6,4,8 # reduction candidate for 3,6 F5: 3,6 # 18 pairs F5: 4,8 # 17 pairs * PAIR G1: 2,8 BLK 3 I1: 2,8,6 # reduction candidate for 2,8 I1: 6 => CTR * ..7593246943.8.175652741398598.2476.7.6.584.9..49675822.14369573.5.19.244.9.756.. I1: 2,8 # 17 pairs * PAIR I3: 6,8 BLK 3 I1: 6,8,2 # reduction candidate for 6,8 I1: 2 => CTR * ..759.84294..8.175852741396598..426772..584.9..492758.2714369583658197244.9.756.. I1: 6,8 # 19 pairs * PAIR C5: 3,6 BLK 4 B5: 3,6,1,2 # reduction candidate for 3,6 B5: 3,6 => SOLVED * 137596248946382175852741396598123467763854912214967583621438759375619824489275631 B5: 1,2 # 17 pairs B6: 3,6,1,2 # reduction candidate for 3,6 B6: 3,6 # 19 pairs * PAIR C5: 3,6 ROW 5 D5: 3,6,1,8 # reduction candidate for 3,6 D5: 3,6 => CTR * ..759..4.94..8.175.5274139.598..4.6.72..58419..49.758.2.143695.365.19724489275631 D5: 1,8 # 17 pairs F5: 3,6,4,8 # reduction candidate for 3,6 F5: 3,6 # 18 pairs * PAIR D4: 1,3 BLK 5 D5: 1,3,6,8 # reduction candidate for 1,3 D5: 1,3 => CTR * ..759..4.94..8.175.5274139.598.2476.726.584.91349675822.14369573.5.19.244.9.756.. D5: 6,8 # 17 pairs * PAIR D4: 1,3 ROW 4 I4: 1,3,2,7 # reduction candidate for 1,3 I4: 1,3 => CTR * .1759324.943682175.5274139.598.2476.72.85.419.349.7582261438957375..9824489275631 I4: 2,7 # 19 pairs * PAIR E4: 1,2 BLK 5 E6: 1,2,6 # reduction candidate for 1,2 E6: 1,2 => CTR * .37596.4.94..8.175.5274139.5983.4.6.72..5.419..49.7583261438957375169824489275631 E6: 6 # 17 pairs * PAIR E4: 1,2 ROW 4 I4: 1,2,3,7 # reduction candidate for 1,2 I4: 1,2 => CTR * ..759.24.94..82175.5274139.5983.476.72.856419614927583261438957375169824489275631 I4: 3,7 # 18 pairs * PAIR F4: 3,4 BLK 5 F5: 3,4,6,8 # reduction candidate for 3,4 F5: 3,4 => SOLVED * 137596248946382175852741396598123467763854912214967583621438759375619824489275631 F5: 6,8 => CTR * ..7593.4.943682175.5274139.598..4.6.726.584.91349675822.14369583658197244892756.. * PAIR H5: 1,3 BLK 6 I4: 1,3,2,7 # reduction candidate for 1,3 I4: 1,3 => CTR * .1759324.943682175.5274139.598.2476.72.85.419.349.7582261438957375..9824489275631 I4: 2,7 # 19 pairs I5: 1,3,2,9 # reduction candidate for 1,3 I5: 1,3 => CTR * ..759.24.94..82175.5274139.598.2346772.8549...349675822614387593756198244892756.. I5: 2,9 # 17 pairs I6: 1,3,2 # reduction candidate for 1,3 I6: 1,3 # 21 pairs * PAIR H5: 1,3 ROW 5 B5: 1,3,2,6 # reduction candidate for 1,3 B5: 1,3 => CTR * ..759..4.943.8.175.5274139.598.2..6.7...5......49.758...143..5.3.5..9.244.9.756.. B5: 2,6 # 22 pairs D5: 1,3,6,8 # reduction candidate for 1,3 D5: 1,3 => CTR * ..759..4.94..8.175.5274139.598.2476.726.584.91349675822.14369573.5.19.244.9.756.. D5: 6,8 # 17 pairs * PAIR B9: 2,8 BLK 7 A7: 2,8,6 # reduction candidate for 2,8 A7: 2,8 # 19 pairs B7: 2,8,6,7 # reduction candidate for 2,8 B7: 2,8 => SOLVED * 137596248946382175852741396598123467763854912214967583621438759375619824489275631 B7: 6,7 # 17 pairs * PAIR E8: 1,6 BLK 8 D8: 1,6,8 # reduction candidate for 1,6 D8: 8 => CTR * ..759..4.94..82175.5274139.598.2.4677...5......49.758...143..5.3.58197244892756.. D8: 1,6 # 19 pairs * PAIR E8: 1,6 COL E E6: 1,6,2 # reduction candidate for 1,6 E6: 2 => CTR * ..759.24.94..82175.5274139.59831476272.8564.9614927583261438957375169824489275631 E6: 1,6 # 17 pairs * PAIR D9: 2,8 BLK 8 F7: 2,8,6 # reduction candidate for 2,8 F7: 6 => CTR * ..759..4.94..82175.5274139.598....6.7...584.9..49.758...143695.365.197244.92756.. F7: 2,8 # 19 pairs * PAIR G8: 7,8 BLK 9 G7: 7,8,9 # reduction candidate for 7,8 G7: 7,8 => SOLVED * 137596248946382175852741396598123467763854912214967583621438759375619824489275631 G7: 9 # 18 pairs I7: 7,8,9 # reduction candidate for 7,8 I7: 7,8 # 18 pairs * PAIR G8: 7,8 ROW 8 B8: 7,8,6 # reduction candidate for 7,8 B8: 6 => CTR * ..759..4.94..8.175.5274139.598.2.4677...54.....496758..7143..5.365.197244.9.756.. B8: 7,8 # 19 pairs * PAIR I9: 1,3 COL I I4: 1,3,2,7 # reduction candidate for 1,3 I4: 1,3 => CTR * .1759324.943682175.5274139.598.2476.72.85.419.349.7582261438957375..9824489275631 I4: 2,7 # 19 pairs I5: 1,3,2,9 # reduction candidate for 1,3 I5: 1,3 => CTR * ..759.24.94..82175.5274139.598.2346772.8549...349675822614387593756198244892756.. I5: 2,9 # 17 pairs I6: 1,3,2 # reduction candidate for 1,3 I6: 1,3 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060718-absurd-base-pr-000.dot * REASONING * DIS # B1: 1,8 => CTR => B1: 3,6 * DIS # F2: 3,6 => CTR => F2: 2 * DIS # A1: 6,8 => CTR => A1: 1 * DIS # B1: 6,8 => CTR => B1: 1,3 * PRF # A7: 6,8 => SOL * DIS # F2: 3,6 => CTR => F2: 2 * DIS # B1: 1,8 => CTR => B1: 3,6 * DIS # I1: 6 => CTR => I1: 2,8 * DIS # I1: 2 => CTR => I1: 6,8 * PRF # B5: 3,6 => SOL * DIS # D5: 3,6 => CTR => D5: 1,8 * DIS # D5: 1,3 => CTR => D5: 6,8 * DIS # I4: 1,3 => CTR => I4: 2,7 * DIS # E6: 1,2 => CTR => E6: 6 * DIS # I4: 1,2 => CTR => I4: 3,7 * PRF # F5: 3,4 => SOL * DIS # F5: 6,8 => CTR => F5: 3,4 * DIS # I4: 1,3 => CTR => I4: 2,7 * DIS # I5: 1,3 => CTR => I5: 2,9 * DIS # B5: 1,3 => CTR => B5: 2,6 * DIS # D5: 1,3 => CTR => D5: 6,8 * PRF # B7: 2,8 => SOL * DIS # D8: 8 => CTR => D8: 1,6 * DIS # E6: 2 => CTR => E6: 1,6 * DIS # F7: 6 => CTR => F7: 2,8 * PRF # G7: 7,8 => SOL * DIS # B8: 6 => CTR => B8: 7,8 * DIS # I4: 1,3 => CTR => I4: 2,7 * DIS # I5: 1,3 => CTR => I5: 2,9 * CNT 29 HDP CHAINS / 66 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B9,C2,C5,D4,D9,E4,E8,F1,F4,G1,G8,H5,H9,I3,I9) * ..759..4.94..8.175.5274139.598....6.7...5......49.758...143..5.3.5..9.244.9.756.. * PAIR C2: 3,6 BLK 1 B1: 3,6,1,8 # reduction candidate for 3,6 B1: 1,8 => CTR * ..7593.4.943.8.175.5274139.598.2476.726.584.91349675822.14369573.5.19.244.9.756.. * PAIR C2: 3,6 ROW 2 D2: 3,6,2 # reduction candidate for 3,6 D2: 3,6 # 19 pairs F2: 3,6,2 # reduction candidate for 3,6 F2: 3,6 => CTR * 1.759..4.94.28.175852741396598....6.7...584....49.758...1432.5.3.5..9.244298756.. * RESTART * PAIR RESTART * PAIR F1: 3,6 COL F F5: 3,6,4,8 # reduction candidate for 3,6 F5: 3,6 => CTR * 13759624894..82175852741396598..476.72.85.419614927583261438957375.69824489275631 * PAIR RESTART * PAIR C5: 3,6 BLK 4 B5: 3,6,1,2 # reduction candidate for 3,6 B5: 3,6 => SOLVED * 137596248946382175852741396598123467763854912214967583621438759375619824489275631 * DURATION: 0:00:06.443487 START: 00:48:09.067178 END: 00:48:15.510665 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060718-absurd-base-pr-001.dot * REASONING * DIS # B1: 1,8 => CTR => B1: 3,6 * DIS B1: 3,6 # F2: 3,6 => CTR => F2: 2 * DIS B1: 3,6 + F2: 2 # F5: 3,6 => CTR => F5: 4,8 * PRF B1: 3,6 + F2: 2 + F5: 4,8 # B5: 3,6 => SOL * STA B1: 3,6 + F2: 2 + F5: 4,8 + B5: 3,6 * CNT 4 HDP CHAINS / 6 HYP OPENED
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060718, absurd
See section Pair Reduction for the HDP chains leading to this result.
Full list of HDP chains traversed:
* INC # B1: 3,6 => UNS * DIS # B1: 1,8 => CTR => B1: 3,6 * INC # D2: 3,6 => UNS * DIS # F2: 3,6 => CTR => F2: 2 * INC # F2: 2 => UNS * DIS # A1: 6,8 => CTR => A1: 1 * INC # A1: 1 => UNS * DIS # B1: 6,8 => CTR => B1: 1,3 * INC # B1: 1,3 => UNS * PRF # A7: 6,8 => SOL * INC # A7: 2 => UNS * INC # D2: 3,6 => UNS * DIS # F2: 3,6 => CTR => F2: 2 * INC # F2: 2 => UNS * INC # B1: 3,6 => UNS * DIS # B1: 1,8 => CTR => B1: 3,6 * INC # F5: 3,6 => UNS * INC # F5: 4,8 => UNS * INC # I1: 2,8 => UNS * DIS # I1: 6 => CTR => I1: 2,8 * INC # I1: 6,8 => UNS * DIS # I1: 2 => CTR => I1: 6,8 * PRF # B5: 3,6 => SOL * INC # B5: 1,2 => UNS * INC # B6: 3,6 => UNS * DIS # D5: 3,6 => CTR => D5: 1,8 * INC # D5: 1,8 => UNS * INC # F5: 3,6 => UNS * DIS # D5: 1,3 => CTR => D5: 6,8 * INC # D5: 6,8 => UNS * DIS # I4: 1,3 => CTR => I4: 2,7 * INC # I4: 2,7 => UNS * DIS # E6: 1,2 => CTR => E6: 6 * INC # E6: 6 => UNS * DIS # I4: 1,2 => CTR => I4: 3,7 * INC # I4: 3,7 => UNS * PRF # F5: 3,4 => SOL * DIS # F5: 6,8 => CTR => F5: 3,4 * DIS # I4: 1,3 => CTR => I4: 2,7 * INC # I4: 2,7 => UNS * DIS # I5: 1,3 => CTR => I5: 2,9 * INC # I5: 2,9 => UNS * INC # I6: 1,3 => UNS * DIS # B5: 1,3 => CTR => B5: 2,6 * INC # B5: 2,6 => UNS * DIS # D5: 1,3 => CTR => D5: 6,8 * INC # D5: 6,8 => UNS * INC # A7: 2,8 => UNS * PRF # B7: 2,8 => SOL * INC # B7: 6,7 => UNS * INC # D8: 1,6 => UNS * DIS # D8: 8 => CTR => D8: 1,6 * INC # E6: 1,6 => UNS * DIS # E6: 2 => CTR => E6: 1,6 * INC # F7: 2,8 => UNS * DIS # F7: 6 => CTR => F7: 2,8 * PRF # G7: 7,8 => SOL * INC # G7: 9 => UNS * INC # I7: 7,8 => UNS * INC # B8: 7,8 => UNS * DIS # B8: 6 => CTR => B8: 7,8 * DIS # I4: 1,3 => CTR => I4: 2,7 * INC # I4: 2,7 => UNS * DIS # I5: 1,3 => CTR => I5: 2,9 * INC # I5: 2,9 => UNS * INC # I6: 1,3 => UNS * CNT 66 HDP CHAINS / 66 HYP OPENED
Full list of HDP chains traversed:
* INC # B1: 3,6 => UNS * DIS # B1: 1,8 => CTR => B1: 3,6 * INC B1: 3,6 # D2: 3,6 => UNS * DIS B1: 3,6 # F2: 3,6 => CTR => F2: 2 * DIS B1: 3,6 + F2: 2 # F5: 3,6 => CTR => F5: 4,8 * PRF B1: 3,6 + F2: 2 + F5: 4,8 # B5: 3,6 => SOL * STA B1: 3,6 + F2: 2 + F5: 4,8 + B5: 3,6 * CNT 6 HDP CHAINS / 6 HYP OPENED