Analysis of zz-www.sudokuoftheday.co.uk-20190119-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019
level: medium
position: .......2....14958...7.25..98.2..7.4.94.2......56...........3164....9......5...2.. initial
Autosolve
position: 5......2.623149587..7.25..9832..7.4.9412.....756.....22....3164....92.....5...29. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A8: 3 => CTR => A8: 1,4 * DIS # B8: 1,8 => CTR => B8: 6 * DIS # D1: 6,8 => CTR => D1: 3,7 * PRF # E1: 6,8 => SOL * DIS # I1: 6 => CTR => I1: 1,3 * DIS # B7: 7 => CTR => B7: 8,9 * DIS # C1: 4 => CTR => C1: 8,9 * DIS # D8: 6 => CTR => D8: 4,8 * DIS # A8: 3,4 => CTR => A8: 1 * CNT 9 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A8: 3 => CTR => A8: 1,4 * DIS A8: 1,4 # B1: 9 => CTR => B1: 1,8 * PRF A8: 1,4 + B1: 1,8 # E1: 6,8 => SOL * STA A8: 1,4 + B1: 1,8 + E1: 6,8 * CNT 3 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .......2....14958...7.25..98.2..7.4.94.2......56...........3164....9......5...2.. | initial |
| 5......2.623149587..7.25..9832..7.4.9412.....756.....22....3164....92.....5...29. | autosolve |
| 519786423623149587487325619832657941941238756756914832298573164164892375375461298 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) A3: 1,4 B3: 1,8 F1: 6,8 H3: 1,3 F5: 6,8 F6: 1,4 G4: 6,9 H5: 5,7 H6: 1,3 C7: 8,9 C8: 4,8 A9: 3,4 F9: 1,4 H8: 5,7 I9: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I1,H3: 1.. / I1 = 1 => 20 pairs (_) / H3 = 1 => 21 pairs (_) I4,H6: 1.. / I4 = 1 => 21 pairs (_) / H6 = 1 => 20 pairs (_) A8,B8: 1.. / A8 = 1 => 18 pairs (_) / B8 = 1 => 0 pairs (X) E9,F9: 1.. / E9 = 1 => 0 pairs (X) / F9 = 1 => 13 pairs (_) B1,I1: 1.. / B1 = 1 => 21 pairs (_) / I1 = 1 => 20 pairs (_) E4,I4: 1.. / E4 = 1 => 20 pairs (_) / I4 = 1 => 21 pairs (_) A3,A8: 1.. / A3 = 1 => 0 pairs (X) / A8 = 1 => 18 pairs (_) F6,F9: 1.. / F6 = 1 => 0 pairs (X) / F9 = 1 => 13 pairs (_) H3,H6: 1.. / H3 = 1 => 21 pairs (_) / H6 = 1 => 20 pairs (_) I1,I4: 1.. / I1 = 1 => 20 pairs (_) / I4 = 1 => 21 pairs (_) A8,A9: 3.. / A8 = 3 => 0 pairs (X) / A9 = 3 => 18 pairs (_) A9,I9: 3.. / A9 = 3 => 18 pairs (_) / I9 = 3 => 0 pairs (X) H3,H6: 3.. / H3 = 3 => 20 pairs (_) / H6 = 3 => 21 pairs (_) C1,A3: 4.. / C1 = 4 => 0 pairs (X) / A3 = 4 => 18 pairs (_) G1,G3: 4.. / G1 = 4 => 18 pairs (_) / G3 = 4 => 0 pairs (X) D6,F6: 4.. / D6 = 4 => 0 pairs (X) / F6 = 4 => 13 pairs (_) C1,G1: 4.. / C1 = 4 => 0 pairs (X) / G1 = 4 => 18 pairs (_) A3,G3: 4.. / A3 = 4 => 18 pairs (_) / G3 = 4 => 0 pairs (X) C1,C8: 4.. / C1 = 4 => 0 pairs (X) / C8 = 4 => 18 pairs (_) F6,F9: 4.. / F6 = 4 => 13 pairs (_) / F9 = 4 => 0 pairs (X) D7,E7: 5.. / D7 = 5 => 19 pairs (_) / E7 = 5 => 16 pairs (_) H8,I8: 5.. / H8 = 5 => 16 pairs (_) / I8 = 5 => 15 pairs (_) D4,D7: 5.. / D4 = 5 => 16 pairs (_) / D7 = 5 => 19 pairs (_) H5,H8: 5.. / H5 = 5 => 15 pairs (_) / H8 = 5 => 16 pairs (_) B8,B9: 6.. / B8 = 6 => 21 pairs (_) / B9 = 6 => 0 pairs (X) D3,G3: 6.. / D3 = 6 => 0 pairs (X) / G3 = 6 => 19 pairs (_) B8,D8: 6.. / B8 = 6 => 21 pairs (_) / D8 = 6 => 0 pairs (X) F1,F5: 6.. / F1 = 6 => 19 pairs (_) / F5 = 6 => 23 pairs (_) D1,E1: 7.. / D1 = 7 => 16 pairs (_) / E1 = 7 => 16 pairs (_) G5,H5: 7.. / G5 = 7 => 15 pairs (_) / H5 = 7 => 16 pairs (_) B7,B9: 7.. / B7 = 7 => 0 pairs (X) / B9 = 7 => 21 pairs (_) G8,H8: 7.. / G8 = 7 => 16 pairs (_) / H8 = 7 => 15 pairs (_) G5,G8: 7.. / G5 = 7 => 15 pairs (_) / G8 = 7 => 16 pairs (_) H5,H8: 7.. / H5 = 7 => 16 pairs (_) / H8 = 7 => 15 pairs (_) B3,D3: 8.. / B3 = 8 => 20 pairs (_) / D3 = 8 => 0 pairs (X) F1,F5: 8.. / F1 = 8 => 23 pairs (_) / F5 = 8 => 19 pairs (_) B1,C1: 9.. / B1 = 9 => 20 pairs (_) / C1 = 9 => 21 pairs (_) D4,D6: 9.. / D4 = 9 => 0 pairs (X) / D6 = 9 => 14 pairs (_) G4,G6: 9.. / G4 = 9 => 14 pairs (_) / G6 = 9 => 0 pairs (X) B7,C7: 9.. / B7 = 9 => 21 pairs (_) / C7 = 9 => 20 pairs (_) D4,G4: 9.. / D4 = 9 => 0 pairs (X) / G4 = 9 => 14 pairs (_) D6,G6: 9.. / D6 = 9 => 14 pairs (_) / G6 = 9 => 0 pairs (X) B1,B7: 9.. / B1 = 9 => 20 pairs (_) / B7 = 9 => 21 pairs (_) C1,C7: 9.. / C1 = 9 => 21 pairs (_) / C7 = 9 => 20 pairs (_) * DURATION: 0:00:49.795396 START: 03:03:57.019272 END: 03:04:46.814668 2019-05-01 * CP COUNT: (44) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A9,B3,C7,C8,F1,F5,F6,F9,G4,H3,H5,H6,H8,I9) * 5......2.623149587..7.25..9832..7.4.9412.....756.....22....3164....92.....5...29. * PAIR A3: 1,4 COL A A8: 1,4,3 # reduction candidate for 1,4 A8: 3 => CTR * 5......2.623149587187.25439832..7.4.9412.....756....122....316431.692.....5...29. A8: 1,4 # 18 pairs * PAIR B3: 1,8 BLK 1 B1: 1,8,9 # reduction candidate for 1,8 B1: 1,8 # 21 pairs B1: 9 # 20 pairs * PAIR B3: 1,8 COL B B8: 1,8,6 # reduction candidate for 1,8 B8: 1,8 => CTR * 59.7..421623149587417.256.9832..794.9412.....7569.4..2279..3164...692....65471298 B8: 6 # 21 pairs * PAIR F1: 6,8 BLK 2 D1: 6,8,3,7 # reduction candidate for 6,8 D1: 6,8 => CTR * 519.76423623149587487325619832..7941941238756756914832298753164164892..53.54.1298 D1: 3,7 # 16 pairs E1: 6,8,3,7 # reduction candidate for 6,8 E1: 6,8 => SOLVED * 519786423623149587487325619832657941941238756756914832298573164164892375375461298 E1: 3,7 # 16 pairs D3: 6,8,3 # reduction candidate for 6,8 D3: 6,8 # 20 pairs * PAIR H3: 1,3 BLK 3 I1: 1,3,6 # reduction candidate for 1,3 I1: 6 => CTR * 519378426623149587487625319832.57.419412.6...756....32298..3164164892753375461298 I1: 1,3 # 17 pairs * PAIR F5: 6,8 BLK 5 E5: 6,8,3,5 # reduction candidate for 6,8 E5: 6,8 # 20 pairs E5: 3,5 # 16 pairs * PAIR F5: 6,8 ROW 5 G5: 6,8,3,7 # reduction candidate for 6,8 G5: 6,8 # 18 pairs I5: 6,8,3,5 # reduction candidate for 6,8 I5: 6,8 # 18 pairs * PAIR G4: 6,9 ROW 4 D4: 6,9,5 # reduction candidate for 6,9 D4: 6,9 # 19 pairs D4: 5 # 16 pairs * PAIR H6: 1,3 ROW 6 E6: 1,3,8 # reduction candidate for 1,3 E6: 8 # 29 pairs E6: 1,3 # 16 pairs * PAIR C7: 8,9 BLK 7 B7: 8,9,7 # reduction candidate for 8,9 B7: 7 => CTR * 59.37..21623149587..7.25.39832.1794.9412.....7569.4.12279..3164.6.492...48576129. B7: 8,9 # 21 pairs * PAIR C7: 8,9 COL C C1: 8,9,4 # reduction candidate for 8,9 C1: 4 => CTR * 594....21623149587187.25439832.17.4.9412.....756..4.12279..3164.18692.....5...29. C1: 8,9 # 18 pairs * PAIR C8: 4,8 ROW 8 D8: 4,8,6 # reduction candidate for 4,8 D8: 6 => CTR * 59.7..421623149587417.256.9832..794.9412.....7569.4..2279..3164...692....65471298 D8: 4,8 # 21 pairs * PAIR C8: 4,8 COL C C1: 4,8,9 # reduction candidate for 4,8 C1: 9 # 21 pairs C1: 4,8 # 20 pairs * PAIR A9: 3,4 BLK 7 A8: 3,4,1 # reduction candidate for 3,4 A8: 3,4 => CTR * 5......2.623149587187.25439832..7.4.9412.....756....122....3164.1.692.....5...29. A8: 1 # 18 pairs * PAIR I9: 3,8 BLK 9 G8: 3,8,7 # reduction candidate for 3,8 G8: 3,8 # 15 pairs I8: 3,8,5 # reduction candidate for 3,8 I8: 3,8 # 16 pairs * PAIR I9: 3,8 COL I I5: 3,8,5,6 # reduction candidate for 3,8 I5: 3,8 # 19 pairs I5: 5,6 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190119-absurd-base-pr-000.dot * REASONING * DIS # A8: 3 => CTR => A8: 1,4 * DIS # B8: 1,8 => CTR => B8: 6 * DIS # D1: 6,8 => CTR => D1: 3,7 * PRF # E1: 6,8 => SOL * DIS # I1: 6 => CTR => I1: 1,3 * DIS # B7: 7 => CTR => B7: 8,9 * DIS # C1: 4 => CTR => C1: 8,9 * DIS # D8: 6 => CTR => D8: 4,8 * DIS # A8: 3,4 => CTR => A8: 1 * CNT 9 HDP CHAINS / 35 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A9,B3,C7,C8,F1,F5,F6,F9,G4,H3,H5,H6,H8,I9) * 5......2.623149587..7.25..9832..7.4.9412.....756.....22....3164....92.....5...29. * PAIR A3: 1,4 COL A A8: 1,4,3 # reduction candidate for 1,4 A8: 3 => CTR * 5......2.623149587187.25439832..7.4.9412.....756....122....316431.692.....5...29. * PAIR RESTART * PAIR B3: 1,8 BLK 1 B1: 1,8,9 # reduction candidate for 1,8 B1: 9 => CTR * 598376.21623149587..7.25.39832.1794.9412.....7569.4.122.9753164...892...375461298 * PAIR F1: 6,8 BLK 2 E1: 6,8,7 # reduction candidate for 6,8 E1: 6,8 => SOLVED * 519786423623149587487325619832657941941238756756914832298573164164892375375461298 * DURATION: 0:00:04.320465 START: 03:05:08.791513 END: 03:05:13.111978 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190119-absurd-base-pr-001.dot * REASONING * DIS # A8: 3 => CTR => A8: 1,4 * DIS A8: 1,4 # B1: 9 => CTR => B1: 1,8 * PRF A8: 1,4 + B1: 1,8 # E1: 6,8 => SOL * STA A8: 1,4 + B1: 1,8 + E1: 6,8 * CNT 3 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190119, absurd
Solution
position: 519786423623149587487325619832657941941238756756914832298573164164892375375461298 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 # A8: 1,4 => UNS * DIS # A8: 3 => CTR => A8: 1,4 * INC # B1: 1,8 => UNS * INC # B1: 9 => UNS * DIS # B8: 1,8 => CTR => B8: 6 * INC # B8: 6 => UNS * DIS # D1: 6,8 => CTR => D1: 3,7 * INC # D1: 3,7 => UNS * PRF # E1: 6,8 => SOL * INC # E1: 3,7 => UNS * INC # D3: 6,8 => UNS * INC # I1: 1,3 => UNS * DIS # I1: 6 => CTR => I1: 1,3 * INC # E5: 6,8 => UNS * INC # E5: 3,5 => UNS * INC # G5: 6,8 => UNS * INC # I5: 6,8 => UNS * INC # D4: 6,9 => UNS * INC # D4: 5 => UNS * INC # E6: 1,3 => UNS * INC # E6: 8 => UNS * INC # B7: 8,9 => UNS * DIS # B7: 7 => CTR => B7: 8,9 * INC # C1: 8,9 => UNS * DIS # C1: 4 => CTR => C1: 8,9 * INC # D8: 4,8 => UNS * DIS # D8: 6 => CTR => D8: 4,8 * INC # C1: 4,8 => UNS * INC # C1: 9 => UNS * DIS # A8: 3,4 => CTR => A8: 1 * INC # A8: 1 => UNS * INC # G8: 3,8 => UNS * INC # I8: 3,8 => UNS * INC # I5: 3,8 => UNS * INC # I5: 5,6 => UNS * CNT 35 HDP CHAINS / 35 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A8: 1,4 => UNS * DIS # A8: 3 => CTR => A8: 1,4 * INC A8: 1,4 # B1: 1,8 => UNS * DIS A8: 1,4 # B1: 9 => CTR => B1: 1,8 * PRF A8: 1,4 + B1: 1,8 # E1: 6,8 => SOL * STA A8: 1,4 + B1: 1,8 + E1: 6,8 * CNT 5 HDP CHAINS / 5 HYP OPENED