Analysis of zz-www.sudokuoftheday.co.uk-20060808-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006
level: medium
position: ..6542.3.........49..3.........34.87.8..5...931..8.4.673........5..9.2.1......74. initial
Autosolve
position: 176542938.23.....494.3....2....34.87.8..5.3.931..8.4.673.4..895.5.793261...8.5743 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D4: 2,9 => CTR => D4: 1,6 * DIS # C6: 2,9 => CTR => C6: 5,7 * DIS # C6: 2,5 => CTR => C6: 7,9 * DIS # C6: 2,5 => CTR => C6: 7,9 * DIS # A4: 2,6 => CTR => A4: 5 * PRF # A4: 5 => SOL * PRF # A5: 2,6 => SOL * DIS # A5: 4 => CTR => A5: 2,6 * PRF # F2: 1,6 => SOL * DIS # F3: 1,6 => CTR => F3: 8 * PRF # F3: 8 => SOL * DIS # F5: 1,6 => CTR => F5: 7 * PRF # F5: 7 => SOL * CNT 13 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D4: 2,9 => CTR => D4: 1,6 * DIS D4: 1,6 # D5: 6 => CTR => D5: 1,2 * DIS D4: 1,6 + D5: 1,2 # C9: 1,2 => CTR => C9: 9 * PRF D4: 1,6 + D5: 1,2 + C9: 9 => SOL * STA D4: 1,6 + D5: 1,2 + C9: 9 * CNT 4 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..6542.3.........49..3.........34.87.8..5...931..8.4.673........5..9.2.1......74. | initial |
| 176542938.23.....494.3....2....34.87.8..5.3.931..8.4.673.4..895.5.793261...8.5743 | autosolve |
| 176542938823961574945378612592634187684157329317289456731426895458793261269815743 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) A2: 5,8 C3: 5,8 B4: 6,9 D6: 2,9 F6: 7,9 G4: 1,5 H5: 1,2 H6: 2,5 C7: 1,2 A8: 4,8 C8: 4,8 A9: 2,6 B9: 6,9 F7: 1,6 E9: 1,2 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G4,H5: 1.. / G4 = 1 => 19 pairs (_) / H5 = 1 => 0 pairs (X) C7,C9: 1.. / C7 = 1 => 18 pairs (_) / C9 = 1 => 15 pairs (_) D4,G4: 1.. / D4 = 1 => 0 pairs (X) / G4 = 1 => 19 pairs (_) C9,E9: 1.. / C9 = 1 => 15 pairs (_) / E9 = 1 => 18 pairs (_) H5,H6: 2.. / H5 = 2 => 19 pairs (_) / H6 = 2 => 0 pairs (X) E7,E9: 2.. / E7 = 2 => 18 pairs (_) / E9 = 2 => 15 pairs (_) C7,E7: 2.. / C7 = 2 => 15 pairs (_) / E7 = 2 => 18 pairs (_) A5,C5: 4.. / A5 = 4 => 0 pairs (X) / C5 = 4 => 0 pairs (_) A8,C8: 4.. / A8 = 4 => 0 pairs (*) / C8 = 4 => 0 pairs (X) A5,A8: 4.. / A5 = 4 => 0 pairs (X) / A8 = 4 => 0 pairs (_) C5,C8: 4.. / C5 = 4 => 0 pairs (*) / C8 = 4 => 0 pairs (X) A2,C3: 5.. / A2 = 5 => 0 pairs (X) / C3 = 5 => 0 pairs (_) G4,H6: 5.. / G4 = 5 => 0 pairs (X) / H6 = 5 => 19 pairs (_) C6,H6: 5.. / C6 = 5 => 0 pairs (X) / H6 = 5 => 19 pairs (_) A2,A4: 5.. / A2 = 5 => 0 pairs (X) / A4 = 5 => 0 pairs (_) G2,G3: 6.. / G2 = 6 => 19 pairs (_) / G3 = 6 => 18 pairs (_) A9,B9: 6.. / A9 = 6 => 17 pairs (_) / B9 = 6 => 17 pairs (_) E7,F7: 6.. / E7 = 6 => 18 pairs (_) / F7 = 6 => 20 pairs (_) B4,B9: 6.. / B4 = 6 => 17 pairs (_) / B9 = 6 => 17 pairs (_) E2,E3: 7.. / E2 = 7 => 17 pairs (_) / E3 = 7 => 17 pairs (_) H2,H3: 7.. / H2 = 7 => 17 pairs (_) / H3 = 7 => 17 pairs (_) C5,C6: 7.. / C5 = 7 => 0 pairs (X) / C6 = 7 => 0 pairs (_) F5,F6: 7.. / F5 = 7 => 0 pairs (*) / F6 = 7 => 0 pairs (X) E2,H2: 7.. / E2 = 7 => 17 pairs (_) / H2 = 7 => 17 pairs (_) E3,H3: 7.. / E3 = 7 => 17 pairs (_) / H3 = 7 => 17 pairs (_) C5,F5: 7.. / C5 = 7 => 0 pairs (X) / F5 = 7 => 0 pairs (_) C6,F6: 7.. / C6 = 7 => 0 pairs (*) / F6 = 7 => 0 pairs (X) A2,C3: 8.. / A2 = 8 => 0 pairs (*) / C3 = 8 => 0 pairs (X) F2,F3: 8.. / F2 = 8 => 0 pairs (X) / F3 = 8 => 0 pairs (_) A8,C8: 8.. / A8 = 8 => 0 pairs (X) / C8 = 8 => 0 pairs (_) A2,F2: 8.. / A2 = 8 => 0 pairs (*) / F2 = 8 => 0 pairs (X) C3,F3: 8.. / C3 = 8 => 0 pairs (X) / F3 = 8 => 0 pairs (_) A2,A8: 8.. / A2 = 8 => 0 pairs (*) / A8 = 8 => 0 pairs (X) C3,C8: 8.. / C3 = 8 => 0 pairs (X) / C8 = 8 => 0 pairs (_) D2,F2: 9.. / D2 = 9 => 0 pairs (*) / F2 = 9 => 0 pairs (X) B9,C9: 9.. / B9 = 9 => 17 pairs (_) / C9 = 9 => 17 pairs (_) B4,B9: 9.. / B4 = 9 => 17 pairs (_) / B9 = 9 => 17 pairs (_) F2,F6: 9.. / F2 = 9 => 0 pairs (X) / F6 = 9 => 0 pairs (_) * DURATION: 0:00:44.820532 START: 01:38:40.413554 END: 01:39:25.234086 2019-05-01 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,A9,B4,B9,C3,C7,C8,D6,E9,F6,F7,G4,H5,H6) * 176542938.23.....494.3....2....34.87.8..5.3.931..8.4.673.4..895.5.793261...8.5743 * PAIR B4: 6,9 ROW 4 D4: 6,9,1,2 # reduction candidate for 6,9 D4: 6,9 # 22 pairs D4: 1,2 # 17 pairs * PAIR D6: 2,9 BLK 5 D4: 2,9,1,6 # reduction candidate for 2,9 D4: 2,9 => CTR * 176542938.23.....494.3....2....34187487.5.32931..8745673.4..895854793261...8.5743 D4: 1,6 # 19 pairs * PAIR D6: 2,9 ROW 6 C6: 2,9,5,7 # reduction candidate for 2,9 C6: 2,9 => CTR * 176542938.23..9..49483..5.2..5.34187487.5.32931..8745673.4..895854793261...8.5743 C6: 5,7 # 16 pairs * PAIR F6: 7,9 ROW 6 C6: 7,9,2,5 # reduction candidate for 7,9 C6: 2,5 => CTR * 176542938.23..9..49483....2....34.87487.5.3.931.9874.673.4..895854793261...8.5743 C6: 7,9 # 22 pairs * PAIR G4: 1,5 COL G G2: 1,5,6 # reduction candidate for 1,5 G2: 1,5 # 18 pairs G3: 1,5,6 # reduction candidate for 1,5 G3: 1,5 # 19 pairs * PAIR H5: 1,2 ROW 5 D5: 1,2,6 # reduction candidate for 1,2 D5: 1,2 # 20 pairs D5: 6 # 18 pairs * PAIR H6: 2,5 ROW 6 C6: 2,5,7,9 # reduction candidate for 2,5 C6: 2,5 => CTR * 176542938.23..9..49483....2....34.87487.5.3.931.9874.673.4..895854793261...8.5743 C6: 7,9 # 22 pairs * PAIR C7: 1,2 BLK 7 C9: 1,2,9 # reduction candidate for 1,2 C9: 9 # 17 pairs C9: 1,2 # 17 pairs * PAIR C7: 1,2 ROW 7 E7: 1,2,6 # reduction candidate for 1,2 E7: 1,2 # 20 pairs E7: 6 # 18 pairs * PAIR A9: 2,6 COL A A4: 2,6,5 # reduction candidate for 2,6 A4: 2,6 => CTR * 1765429385239.8..49483..5.2..5.34187482.573.931728945673.4..895854793261...8.5743 A4: 5 => SOLVED * 176542938823961574945378612592634187684157329317289456731426895458793261269815743 A5: 2,6,4 # reduction candidate for 2,6 A5: 2,6 => SOLVED * 176542938823961574945378612592634187684157329317289456731426895458793261269815743 A5: 4 => CTR * 1765429385239.8..49483..5.2..5.34187482.573.931728945673.4..895854793261...8.5743 * PAIR F7: 1,6 BLK 8 E7: 1,6,2 # reduction candidate for 1,6 E7: 2 # 18 pairs E7: 1,6 # 15 pairs * PAIR F7: 1,6 COL F F2: 1,6,8,9 # reduction candidate for 1,6 F2: 1,6 => SOLVED * 176542938823961574945378612592634187684157329317289456731426895458793261269815743 F2: 8,9 # 16 pairs F3: 1,6,8 # reduction candidate for 1,6 F3: 1,6 => CTR * 1765429385239.8..49483..5.2..5.34187482.573.931728945673.4..895854793261...8.5743 F3: 8 => SOLVED * 176542938823961574945378612592634187684157329317289456731426895458793261269815743 F5: 1,6,7 # reduction candidate for 1,6 F5: 1,6 => CTR * 176542938.23..9..49483....2....34.87487.5.3.931..874.673.4..895854793261...8.5743 F5: 7 => SOLVED * 176542938823961574945378612592634187684157329317289456731426895458793261269815743 * PAIR E9: 1,2 BLK 8 E7: 1,2,6 # reduction candidate for 1,2 E7: 1,2 # 20 pairs E7: 6 # 18 pairs * PAIR E9: 1,2 ROW 9 C9: 1,2,9 # reduction candidate for 1,2 C9: 9 # 17 pairs C9: 1,2 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060808-absurd-base-pr-000.dot * REASONING * DIS # D4: 2,9 => CTR => D4: 1,6 * DIS # C6: 2,9 => CTR => C6: 5,7 * DIS # C6: 2,5 => CTR => C6: 7,9 * DIS # C6: 2,5 => CTR => C6: 7,9 * DIS # A4: 2,6 => CTR => A4: 5 * PRF # A4: 5 => SOL * PRF # A5: 2,6 => SOL * DIS # A5: 4 => CTR => A5: 2,6 * PRF # F2: 1,6 => SOL * DIS # F3: 1,6 => CTR => F3: 8 * PRF # F3: 8 => SOL * DIS # F5: 1,6 => CTR => F5: 7 * PRF # F5: 7 => SOL * CNT 13 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,A9,B4,B9,C3,C7,C8,D6,E9,F6,F7,G4,H5,H6) * 176542938.23.....494.3....2....34.87.8..5.3.931..8.4.673.4..895.5.793261...8.5743 * PAIR B4: 6,9 ROW 4 D4: 6,9,1,2 # reduction candidate for 6,9 D4: 6,9 # 22 pairs D4: 1,2 # 17 pairs * PAIR D6: 2,9 BLK 5 D4: 2,9,1,6 # reduction candidate for 2,9 D4: 2,9 => CTR * 176542938.23.....494.3....2....34187487.5.32931..8745673.4..895854793261...8.5743 * PAIR G4: 1,5 COL G G2: 1,5,6 # reduction candidate for 1,5 G2: 1,5 # 22 pairs G3: 1,5,6 # reduction candidate for 1,5 G3: 1,5 # 23 pairs * PAIR H5: 1,2 ROW 5 D5: 1,2,6 # reduction candidate for 1,2 D5: 6 => CTR * 176542938.23.....494.3....2....34.87.8.65.32931.28945673.4..895.5.793261...8.5743 * PAIR RESTART * PAIR C7: 1,2 BLK 7 C9: 1,2,9 # reduction candidate for 1,2 C9: 1,2 => CTR * 176542938.23.....494.3....226913458748725631931598742673.461895854793261691825743 C9: 9 => SOLVED * 176542938823961574945378612592634187684157329317289456731426895458793261269815743 * DURATION: 0:00:07.545234 START: 01:39:48.799272 END: 01:39:56.344506 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060808-absurd-base-pr-001.dot * REASONING * DIS # D4: 2,9 => CTR => D4: 1,6 * DIS D4: 1,6 # D5: 6 => CTR => D5: 1,2 * DIS D4: 1,6 + D5: 1,2 # C9: 1,2 => CTR => C9: 9 * PRF D4: 1,6 + D5: 1,2 + C9: 9 => SOL * STA D4: 1,6 + D5: 1,2 + C9: 9 * CNT 4 HDP CHAINS / 8 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060808, absurd
Solution
position: 176542938823961574945378612592634187684157329317289456731426895458793261269815743 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 # D4: 6,9 => UNS * INC # D4: 1,2 => UNS * DIS # D4: 2,9 => CTR => D4: 1,6 * INC # D4: 1,6 => UNS * DIS # C6: 2,9 => CTR => C6: 5,7 * INC # C6: 5,7 => UNS * INC # C6: 7,9 => UNS * DIS # C6: 2,5 => CTR => C6: 7,9 * INC # G2: 1,5 => UNS * INC # G3: 1,5 => UNS * INC # D5: 1,2 => UNS * INC # D5: 6 => UNS * DIS # C6: 2,5 => CTR => C6: 7,9 * INC # C6: 7,9 => UNS * INC # C9: 1,2 => UNS * INC # C9: 9 => UNS * INC # E7: 1,2 => UNS * INC # E7: 6 => UNS * DIS # A4: 2,6 => CTR => A4: 5 * PRF # A4: 5 => SOL * PRF # A5: 2,6 => SOL * DIS # A5: 4 => CTR => A5: 2,6 * INC # E7: 1,6 => UNS * INC # E7: 2 => UNS * PRF # F2: 1,6 => SOL * INC # F2: 8,9 => UNS * DIS # F3: 1,6 => CTR => F3: 8 * PRF # F3: 8 => SOL * DIS # F5: 1,6 => CTR => F5: 7 * PRF # F5: 7 => SOL * INC # E7: 1,2 => UNS * INC # E7: 6 => UNS * INC # C9: 1,2 => UNS * INC # C9: 9 => UNS * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D4: 6,9 => UNS * INC # D4: 1,2 => UNS * DIS # D4: 2,9 => CTR => D4: 1,6 * INC D4: 1,6 # G2: 1,5 => UNS * INC D4: 1,6 # G3: 1,5 => UNS * INC D4: 1,6 # D5: 1,2 => UNS * DIS D4: 1,6 # D5: 6 => CTR => D5: 1,2 * DIS D4: 1,6 + D5: 1,2 # C9: 1,2 => CTR => C9: 9 * PRF D4: 1,6 + D5: 1,2 + C9: 9 => SOL * STA D4: 1,6 + D5: 1,2 + C9: 9 * CNT 9 HDP CHAINS / 8 HYP OPENED