Analysis of zz-www.sudokuoftheday.co.uk-20060715-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: 4.3..65.2..53.8...9....27..3....4.2....7....626.........1983.6.......9.......5..4 initial
Autosolve
position: 4.31.65.2.253.864.9.6..27..3....4.2....72...626..3.....4198326......79.......5..4 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I3: 1,8 => CTR => I3: 3 * DIS # H6: 8,9 => CTR => H6: 1,5,7 * DIS # B5: 1,9 => CTR => B5: 5 * DIS # H5: 1,9 => CTR => H5: 3,5,8 * DIS # H6: 5,8 => CTR => H6: 1,7,9 * DIS # H6: 1,9 => CTR => H6: 5,7,8 * DIS # I4: 1,8 => CTR => I4: 5,7,9 * PRF # G5: 1,8 => SOL * DIS # H5: 1,8 => CTR => H5: 3,5,9 * DIS # G6: 1,8 => CTR => G6: 4 * DIS # H6: 1,8 => CTR => H6: 5,7,9 * DIS # I6: 1,8 => CTR => I6: 5,7,9 * PRF # G9: 3 => SOL * DIS # C9: 2,8 => CTR => C9: 7,9 * PRF # C9: 7,9 => SOL * CNT 15 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I3: 1,8 => CTR => I3: 3 * DIS I3: 3 # B5: 1,9 => CTR => B5: 5 * DIS I3: 3 + B5: 5 # H5: 1,9 => CTR => H5: 3 * PRF I3: 3 + B5: 5 + H5: 3 => SOL * STA I3: 3 + B5: 5 + H5: 3 * CNT 4 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 4.3..65.2..53.8...9....27..3....4.2....7....626.........1983.6.......9.......5..4 | initial |
| 4.31.65.2.253.864.9.6..27..3....4.2....72...626..3.....4198326......79.......5..4 | autosolve |
| 483176592725398641916542783378654129154729836269831475541983267632417958897265314 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) B1: 7,8 A2: 1,7 B3: 1,8 E1: 7,9 E2: 7,9 D3: 4,5 E3: 4,5 H1: 8,9 I2: 1,9 E4: 5,6 F5: 1,9 D6: 5,8 F6: 1,9 G4: 1,8 A7: 5,7 B8: 3,5 C8: 2,8 D9: 2,6 E9: 1,6 I7: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,B3: 1.. / A2 = 1 => 19 pairs (_) / B3 = 1 => 0 pairs (*) F5,F6: 1.. / F5 = 1 => 0 pairs (X) / F6 = 1 => 21 pairs (_) E8,E9: 1.. / E8 = 1 => 18 pairs (_) / E9 = 1 => 21 pairs (_) A2,I2: 1.. / A2 = 1 => 19 pairs (_) / I2 = 1 => 0 pairs (*) A2,A5: 1.. / A2 = 1 => 19 pairs (_) / A5 = 1 => 0 pairs (*) C8,C9: 2.. / C8 = 2 => 19 pairs (_) / C9 = 2 => 0 pairs (X) D8,D9: 2.. / D8 = 2 => 0 pairs (X) / D9 = 2 => 19 pairs (_) C8,D8: 2.. / C8 = 2 => 19 pairs (_) / D8 = 2 => 0 pairs (X) C9,D9: 2.. / C9 = 2 => 0 pairs (X) / D9 = 2 => 19 pairs (_) H3,I3: 3.. / H3 = 3 => 0 pairs (X) / I3 = 3 => 21 pairs (_) G5,H5: 3.. / G5 = 3 => 21 pairs (_) / H5 = 3 => 0 pairs (*) B8,B9: 3.. / B8 = 3 => 23 pairs (_) / B9 = 3 => 0 pairs (X) G5,G9: 3.. / G5 = 3 => 21 pairs (_) / G9 = 3 => 0 pairs (*) I3,I8: 3.. / I3 = 3 => 21 pairs (_) / I8 = 3 => 0 pairs (X) D3,E3: 4.. / D3 = 4 => 19 pairs (_) / E3 = 4 => 16 pairs (_) C5,C6: 4.. / C5 = 4 => 20 pairs (_) / C6 = 4 => 0 pairs (X) G5,G6: 4.. / G5 = 4 => 0 pairs (X) / G6 = 4 => 20 pairs (_) D8,E8: 4.. / D8 = 4 => 16 pairs (_) / E8 = 4 => 19 pairs (_) C5,G5: 4.. / C5 = 4 => 20 pairs (_) / G5 = 4 => 0 pairs (X) C6,G6: 4.. / C6 = 4 => 0 pairs (X) / G6 = 4 => 20 pairs (_) D3,D8: 4.. / D3 = 4 => 19 pairs (_) / D8 = 4 => 16 pairs (_) E3,E8: 4.. / E3 = 4 => 16 pairs (_) / E8 = 4 => 19 pairs (_) D3,E3: 5.. / D3 = 5 => 16 pairs (_) / E3 = 5 => 19 pairs (_) A7,I7: 5.. / A7 = 5 => 23 pairs (_) / I7 = 5 => 0 pairs (X) E3,E4: 5.. / E3 = 5 => 19 pairs (_) / E4 = 5 => 16 pairs (_) D4,E4: 6.. / D4 = 6 => 16 pairs (_) / E4 = 6 => 19 pairs (_) A8,A9: 6.. / A8 = 6 => 23 pairs (_) / A9 = 6 => 21 pairs (_) B1,A2: 7.. / B1 = 7 => 19 pairs (_) / A2 = 7 => 0 pairs (*) E1,E2: 7.. / E1 = 7 => 0 pairs (*) / E2 = 7 => 0 pairs (X) I7,H9: 7.. / I7 = 7 => 23 pairs (_) / H9 = 7 => 0 pairs (X) B1,E1: 7.. / B1 = 7 => 19 pairs (_) / E1 = 7 => 0 pairs (*) A2,E2: 7.. / A2 = 7 => 0 pairs (*) / E2 = 7 => 0 pairs (X) A7,I7: 7.. / A7 = 7 => 0 pairs (X) / I7 = 7 => 23 pairs (_) H6,H9: 7.. / H6 = 7 => 23 pairs (_) / H9 = 7 => 0 pairs (X) B1,B3: 8.. / B1 = 8 => 0 pairs (*) / B3 = 8 => 0 pairs (X) D4,D6: 8.. / D4 = 8 => 18 pairs (_) / D6 = 8 => 21 pairs (_) B1,H1: 8.. / B1 = 8 => 0 pairs (*) / H1 = 8 => 0 pairs (X) E1,E2: 9.. / E1 = 9 => 19 pairs (_) / E2 = 9 => 0 pairs (*) H1,I2: 9.. / H1 = 9 => 0 pairs (*) / I2 = 9 => 0 pairs (X) F5,F6: 9.. / F5 = 9 => 21 pairs (_) / F6 = 9 => 0 pairs (X) B9,C9: 9.. / B9 = 9 => 23 pairs (_) / C9 = 9 => 0 pairs (X) E1,H1: 9.. / E1 = 9 => 19 pairs (_) / H1 = 9 => 0 pairs (*) E2,I2: 9.. / E2 = 9 => 0 pairs (*) / I2 = 9 => 0 pairs (X) * DURATION: 0:00:51.793842 START: 00:42:02.576868 END: 00:42:54.370710 2019-05-01 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,B1,B3,B8,C8,D3,D6,D9,E1,E2,E3,E4,E9,F5,F6,G4,H1,I2,I7) * 4.31.65.2.253.864.9.6..27..3....4.2....72...626..3.....4198326......79.......5..4 * PAIR B3: 1,8 ROW 3 H3: 1,8,3 # reduction candidate for 1,8 H3: 1,8 # 21 pairs I3: 1,8,3 # reduction candidate for 1,8 I3: 1,8 => CTR * 4.31.65.2.253.864.9.6..273.3....4.2.5.472.38626..3.45.741983265852..7913639215874 I3: 3 # 21 pairs * PAIR H1: 8,9 COL H H5: 8,9,1,3,5 # reduction candidate for 8,9 H5: 8,9 # 23 pairs H6: 8,9,1,5,7 # reduction candidate for 8,9 H6: 8,9 => CTR * 473196582125378649986..27..3....4.2....72..5626.53..9.74198326553...7918.....5.74 H6: 1,5,7 # 20 pairs * PAIR I2: 1,9 COL I I4: 1,9,5,7,8 # reduction candidate for 1,9 I4: 1,9 # 22 pairs I6: 1,9,5,7,8 # reduction candidate for 1,9 I6: 1,9 # 25 pairs * PAIR E4: 5,6 BLK 5 D4: 5,6,8 # reduction candidate for 5,6 D4: 5,6 # 21 pairs D4: 8 # 18 pairs * PAIR F5: 1,9 ROW 5 B5: 1,9,5 # reduction candidate for 1,9 B5: 1,9 => CTR * 473196582125378649986..27..3....4.2..1.729.5626.531.9.74198326553...7918.....5.74 B5: 5 # 23 pairs H5: 1,9,3,5,8 # reduction candidate for 1,9 H5: 1,9 => CTR * 4.31.65.2125378649986..2713319..482785472139626783945174198326553..1798......5.34 H5: 3,5,8 # 20 pairs * PAIR D6: 5,8 BLK 5 D4: 5,8,6 # reduction candidate for 5,8 D4: 5,8 # 19 pairs D4: 6 # 16 pairs * PAIR D6: 5,8 ROW 6 H6: 5,8,1,7,9 # reduction candidate for 5,8 H6: 5,8 => CTR * 473196582125378649986..27..3....4.2....72139626.839451741983265.....79...392.5174 H6: 1,7,9 # 20 pairs I6: 5,8,1,7,9 # reduction candidate for 5,8 I6: 5,8 # 22 pairs * PAIR F6: 1,9 ROW 6 H6: 1,9,5,7,8 # reduction candidate for 1,9 H6: 1,9 => CTR * 473196582125378649986..27..3....4.2....72..5626.53..9.74198326553...7918.....5.74 H6: 5,7,8 # 20 pairs I6: 1,9,5,7,8 # reduction candidate for 1,9 I6: 1,9 # 25 pairs * PAIR G4: 1,8 BLK 6 I4: 1,8,5,7,9 # reduction candidate for 1,8 I4: 1,8 => CTR * 4.31.65.2.253.864.9.6..27..3....4.2....72...626..3.....4198326......79.......5..4 I4: 5,7,9 # 20 pairs G5: 1,8,3,4 # reduction candidate for 1,8 G5: 1,8 => SOLVED * 483176592725398641916542783378654129154729836269831475541983267632417958897265314 G5: 3,4 # 21 pairs H5: 1,8,3,5,9 # reduction candidate for 1,8 H5: 1,8 => CTR * 4.31.6592.25398641916..27..3....412.15472938626..314...4198326..3...79.8.....5..4 H5: 3,5,9 # 20 pairs G6: 1,8,4 # reduction candidate for 1,8 G6: 1,8 => CTR * 4.31.65.2.253.8641916..27833....412.158729436264.318...4198326..32..79.88..265314 G6: 4 # 20 pairs H6: 1,8,5,7,9 # reduction candidate for 1,8 H6: 1,8 => CTR * 473196582.253.864.9.6..27..3....4.2....72...626..3....741983265.....79.......5.74 H6: 5,7,9 # 20 pairs I6: 1,8,5,7,9 # reduction candidate for 1,8 I6: 1,8 => CTR * 473196582125378649986..27..3....4.2.8.472.3.6267.3.4...4198326..3...79...9...5..4 I6: 5,7,9 # 20 pairs * PAIR G4: 1,8 COL G G9: 1,8,3 # reduction candidate for 1,8 G9: 3 => SOLVED * 483176592725398641916542783378654129154729836269831475541983267632417958897265314 G9: 1,8 # 21 pairs * PAIR B8: 3,5 ROW 8 H8: 3,5,1,8 # reduction candidate for 3,5 H8: 3,5 # 24 pairs I8: 3,5,1,8 # reduction candidate for 3,5 I8: 3,5 # 23 pairs * PAIR C8: 2,8 BLK 7 C9: 2,8,7,9 # reduction candidate for 2,8 C9: 2,8 => CTR * 473196582125378649986..27133.9..4.278.472...6267.3.4..741983265.3...79...9...5..4 C9: 7,9 => SOLVED * 483176592725398641916542783378654129154729836269831475541983267632417958897265314 * PAIR D9: 2,6 BLK 8 D8: 2,6,4 # reduction candidate for 2,6 D8: 2,6 # 19 pairs D8: 4 # 16 pairs * PAIR E9: 1,6 BLK 8 E8: 1,6,4 # reduction candidate for 1,6 E8: 4 # 19 pairs E8: 1,6 # 16 pairs * PAIR I7: 5,7 COL I I4: 5,7,1,8,9 # reduction candidate for 5,7 I4: 5,7 # 23 pairs I6: 5,7,1,8,9 # reduction candidate for 5,7 I6: 5,7 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060715-absurd-base-pr-000.dot * REASONING * DIS # I3: 1,8 => CTR => I3: 3 * DIS # H6: 8,9 => CTR => H6: 1,5,7 * DIS # B5: 1,9 => CTR => B5: 5 * DIS # H5: 1,9 => CTR => H5: 3,5,8 * DIS # H6: 5,8 => CTR => H6: 1,7,9 * DIS # H6: 1,9 => CTR => H6: 5,7,8 * DIS # I4: 1,8 => CTR => I4: 5,7,9 * PRF # G5: 1,8 => SOL * DIS # H5: 1,8 => CTR => H5: 3,5,9 * DIS # G6: 1,8 => CTR => G6: 4 * DIS # H6: 1,8 => CTR => H6: 5,7,9 * DIS # I6: 1,8 => CTR => I6: 5,7,9 * PRF # G9: 3 => SOL * DIS # C9: 2,8 => CTR => C9: 7,9 * PRF # C9: 7,9 => SOL * CNT 15 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,B1,B3,B8,C8,D3,D6,D9,E1,E2,E3,E4,E9,F5,F6,G4,H1,I2,I7) * 4.31.65.2.253.864.9.6..27..3....4.2....72...626..3.....4198326......79.......5..4 * PAIR B3: 1,8 ROW 3 H3: 1,8,3 # reduction candidate for 1,8 H3: 1,8 # 21 pairs I3: 1,8,3 # reduction candidate for 1,8 I3: 1,8 => CTR * 4.31.65.2.253.864.9.6..273.3....4.2.5.472.38626..3.45.741983265852..7913639215874 * RESTART * PAIR RESTART * PAIR I2: 1,9 COL I I4: 1,9,5,7,8 # reduction candidate for 1,9 I4: 1,9 # 23 pairs I6: 1,9,5,7,8 # reduction candidate for 1,9 I6: 1,9 # 27 pairs * PAIR E4: 5,6 BLK 5 D4: 5,6,8 # reduction candidate for 5,6 D4: 8 # 22 pairs D4: 5,6 # 22 pairs * PAIR F5: 1,9 ROW 5 B5: 1,9,5 # reduction candidate for 1,9 B5: 1,9 => CTR * 473196582125378649986..271339...4.2.5..729..626..31.9.741983265.....793..392.5.74 H5: 1,9,3 # reduction candidate for 1,9 H5: 1,9 => CTR * 473196582.253.864.9.6..27.33....4.2.85472.3.6269.3147.54198326763...795.79...5.34 H5: 3 => SOLVED * 483176592725398641916542783378654129154729836269831475541983267632417958897265314 * DURATION: 0:00:06.570908 START: 00:43:22.972162 END: 00:43:29.543070 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060715-absurd-base-pr-001.dot * REASONING * DIS # I3: 1,8 => CTR => I3: 3 * DIS I3: 3 # B5: 1,9 => CTR => B5: 5 * DIS I3: 3 + B5: 5 # H5: 1,9 => CTR => H5: 3 * PRF I3: 3 + B5: 5 + H5: 3 => SOL * STA I3: 3 + B5: 5 + H5: 3 * CNT 4 HDP CHAINS / 8 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060715, absurd
Solution
position: 483176592725398641916542783378654129154729836269831475541983267632417958897265314 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 # H3: 1,8 => UNS * DIS # I3: 1,8 => CTR => I3: 3 * INC # I3: 3 => UNS * INC # H5: 8,9 => UNS * DIS # H6: 8,9 => CTR => H6: 1,5,7 * INC # H6: 1,5,7 => UNS * INC # I4: 1,9 => UNS * INC # I6: 1,9 => UNS * INC # D4: 5,6 => UNS * INC # D4: 8 => UNS * DIS # B5: 1,9 => CTR => B5: 5 * INC # B5: 5 => UNS * DIS # H5: 1,9 => CTR => H5: 3,5,8 * INC # H5: 3,5,8 => UNS * INC # D4: 5,8 => UNS * INC # D4: 6 => UNS * DIS # H6: 5,8 => CTR => H6: 1,7,9 * INC # H6: 1,7,9 => UNS * INC # I6: 5,8 => UNS * DIS # H6: 1,9 => CTR => H6: 5,7,8 * INC # H6: 5,7,8 => UNS * INC # I6: 1,9 => UNS * DIS # I4: 1,8 => CTR => I4: 5,7,9 * INC # I4: 5,7,9 => UNS * PRF # G5: 1,8 => SOL * INC # G5: 3,4 => UNS * DIS # H5: 1,8 => CTR => H5: 3,5,9 * INC # H5: 3,5,9 => UNS * DIS # G6: 1,8 => CTR => G6: 4 * INC # G6: 4 => UNS * DIS # H6: 1,8 => CTR => H6: 5,7,9 * INC # H6: 5,7,9 => UNS * DIS # I6: 1,8 => CTR => I6: 5,7,9 * INC # I6: 5,7,9 => UNS * INC # G9: 1,8 => UNS * PRF # G9: 3 => SOL * INC # H8: 3,5 => UNS * INC # I8: 3,5 => UNS * DIS # C9: 2,8 => CTR => C9: 7,9 * PRF # C9: 7,9 => SOL * INC # D8: 2,6 => UNS * INC # D8: 4 => UNS * INC # E8: 1,6 => UNS * INC # E8: 4 => UNS * INC # I4: 5,7 => UNS * INC # I6: 5,7 => UNS * CNT 46 HDP CHAINS / 46 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # H3: 1,8 => UNS * DIS # I3: 1,8 => CTR => I3: 3 * INC I3: 3 # I4: 1,9 => UNS * INC I3: 3 # I6: 1,9 => UNS * INC I3: 3 # D4: 5,6 => UNS * INC I3: 3 # D4: 8 => UNS * DIS I3: 3 # B5: 1,9 => CTR => B5: 5 * DIS I3: 3 + B5: 5 # H5: 1,9 => CTR => H5: 3 * PRF I3: 3 + B5: 5 + H5: 3 => SOL * STA I3: 3 + B5: 5 + H5: 3 * CNT 9 HDP CHAINS / 8 HYP OPENED