Analysis of zz-www.sudokuoftheday.co.uk-20060503-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006
level: medium
position: 4.59....2.32.1.4............9...6..4367..92.8..1.8...397.........38..7...2...3... initial
Autosolve
position: 4.59....2.32.1.4....9.......98..6.74367..92.8.41.8...3974..1...1538.472.826..3.4. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G1: 1,8 => CTR => G1: 3,6 * DIS # H1: 1,8 => CTR => H1: 3,6 * DIS # E3: 5,6 => CTR => E3: 2,3,4 * DIS # H2: 5,6 => CTR => H2: 8,9 * DIS # D7: 5,6 => CTR => D7: 2 * DIS # F3: 5,8 => CTR => F3: 2 * DIS # H2: 6,9 => CTR => H2: 5,8 * DIS # E3: 2,5,6 => CTR => E3: 3,4 * DIS # E4: 3 => CTR => E4: 2,5 * PRF # D6: 2,5 => SOL * DIS # D6: 7 => CTR => D6: 2,5 * DIS # F6: 2,5 => CTR => F6: 7 * PRF # F6: 7 => SOL * DIS # G9: 1,5 => CTR => G9: 9 * DIS # H2: 6,9 => CTR => H2: 5,8 * DIS # E9: 9 => CTR => E9: 5,7 * DIS # D6: 2 => CTR => D6: 5,7 * DIS # H1: 3,8 => CTR => H1: 1,6 * DIS # H3: 3,8 => CTR => H3: 1,5,6 * DIS # D7: 5,6 => CTR => D7: 2 * CNT 20 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 # G1: 1,8 => CTR => G1: 3,6 * DIS G1: 3,6 # H1: 1,8 => CTR => H1: 3,6 * PRF G1: 3,6 + H1: 3,6 => SOL * STA G1: 3,6 + H1: 3,6 * CNT 3 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 4.59....2.32.1.4............9...6..4367..92.8..1.8...397.........38..7...2...3... | initial |
| 4.59....2.32.1.4....9.......98..6.74367..92.8.41.8...3974..1...1538.472.826..3.4. | autosolve |
| 415978362732615489689432517598326174367149258241587693974261835153894726826753941 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (23) B1: 1,8 A2: 6,7 A3: 6,7 B3: 1,8 F1: 7,8 D2: 5,6 F2: 5,8 D3: 3,4 A4: 2,5 A6: 2,5 D4: 1,3 D5: 1,4 E5: 4,5 G4: 1,5 H5: 1,5 G6: 6,9 H6: 6,9 E8: 6,9 D9: 5,7 G7: 3,8 H7: 3,8 I7: 5,6 I8: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,B3: 1.. / B1 = 1 => 22 pairs (_) / B3 = 1 => 0 pairs (X) D4,D5: 1.. / D4 = 1 => 0 pairs (X) / D5 = 1 => 20 pairs (_) G4,H5: 1.. / G4 = 1 => 20 pairs (_) / H5 = 1 => 0 pairs (X) G9,I9: 1.. / G9 = 1 => 0 pairs (X) / I9 = 1 => 25 pairs (_) D4,G4: 1.. / D4 = 1 => 0 pairs (X) / G4 = 1 => 20 pairs (_) D5,H5: 1.. / D5 = 1 => 20 pairs (_) / H5 = 1 => 0 pairs (X) I3,I9: 1.. / I3 = 1 => 0 pairs (X) / I9 = 1 => 25 pairs (_) E3,F3: 2.. / E3 = 2 => 0 pairs (X) / F3 = 2 => 24 pairs (_) A4,A6: 2.. / A4 = 2 => 27 pairs (_) / A6 = 2 => 20 pairs (_) D7,E7: 2.. / D7 = 2 => 25 pairs (_) / E7 = 2 => 0 pairs (X) A4,E4: 2.. / A4 = 2 => 27 pairs (_) / E4 = 2 => 20 pairs (_) D6,D7: 2.. / D6 = 2 => 0 pairs (X) / D7 = 2 => 25 pairs (_) F3,F6: 2.. / F3 = 2 => 24 pairs (_) / F6 = 2 => 0 pairs (X) D4,E4: 3.. / D4 = 3 => 20 pairs (_) / E4 = 3 => 0 pairs (X) G7,H7: 3.. / G7 = 3 => 0 pairs (X) / H7 = 3 => 21 pairs (_) D3,D4: 3.. / D3 = 3 => 0 pairs (X) / D4 = 3 => 20 pairs (_) D3,E3: 4.. / D3 = 4 => 20 pairs (_) / E3 = 4 => 0 pairs (X) D5,E5: 4.. / D5 = 4 => 0 pairs (X) / E5 = 4 => 20 pairs (_) D3,D5: 4.. / D3 = 4 => 20 pairs (_) / D5 = 4 => 0 pairs (X) E3,E5: 4.. / E3 = 4 => 0 pairs (X) / E5 = 4 => 20 pairs (_) A4,A6: 5.. / A4 = 5 => 20 pairs (_) / A6 = 5 => 27 pairs (_) G4,H5: 5.. / G4 = 5 => 0 pairs (X) / H5 = 5 => 20 pairs (_) E5,H5: 5.. / E5 = 5 => 0 pairs (X) / H5 = 5 => 20 pairs (_) A2,A3: 6.. / A2 = 6 => 0 pairs (X) / A3 = 6 => 23 pairs (_) G6,H6: 6.. / G6 = 6 => 19 pairs (_) / H6 = 6 => 0 pairs (X) I7,I8: 6.. / I7 = 6 => 0 pairs (X) / I8 = 6 => 27 pairs (_) E8,I8: 6.. / E8 = 6 => 0 pairs (X) / I8 = 6 => 27 pairs (_) D2,D7: 6.. / D2 = 6 => 24 pairs (_) / D7 = 6 => 0 pairs (X) A2,A3: 7.. / A2 = 7 => 23 pairs (_) / A3 = 7 => 0 pairs (X) E1,F1: 7.. / E1 = 7 => 0 pairs (*) / F1 = 7 => 0 pairs (X) I2,I3: 7.. / I2 = 7 => 0 pairs (X) / I3 = 7 => 23 pairs (_) D6,F6: 7.. / D6 = 7 => 0 pairs (X) / F6 = 7 => 0 pairs (_) D9,E9: 7.. / D9 = 7 => 0 pairs (*) / E9 = 7 => 0 pairs (X) A2,I2: 7.. / A2 = 7 => 23 pairs (_) / I2 = 7 => 0 pairs (X) A3,I3: 7.. / A3 = 7 => 0 pairs (X) / I3 = 7 => 23 pairs (_) D6,D9: 7.. / D6 = 7 => 0 pairs (X) / D9 = 7 => 0 pairs (_) E1,E9: 7.. / E1 = 7 => 0 pairs (*) / E9 = 7 => 0 pairs (X) F1,F6: 7.. / F1 = 7 => 0 pairs (X) / F6 = 7 => 0 pairs (_) B1,B3: 8.. / B1 = 8 => 0 pairs (X) / B3 = 8 => 22 pairs (_) G7,H7: 8.. / G7 = 8 => 21 pairs (_) / H7 = 8 => 0 pairs (X) F2,H2: 8.. / F2 = 8 => 0 pairs (X) / H2 = 8 => 19 pairs (_) H2,I2: 9.. / H2 = 9 => 0 pairs (X) / I2 = 9 => 19 pairs (_) G6,H6: 9.. / G6 = 9 => 0 pairs (X) / H6 = 9 => 19 pairs (_) E8,E9: 9.. / E8 = 9 => 27 pairs (_) / E9 = 9 => 0 pairs (X) E8,I8: 9.. / E8 = 9 => 27 pairs (_) / I8 = 9 => 0 pairs (X) G6,G9: 9.. / G6 = 9 => 0 pairs (X) / G9 = 9 => 19 pairs (_) H2,H6: 9.. / H2 = 9 => 0 pairs (X) / H6 = 9 => 19 pairs (_) * DURATION: 0:01:18.051834 START: 22:51:08.424203 END: 22:52:26.476037 2019-04-30 * CP COUNT: (47) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A4,A6,B1,B3,D2,D3,D4,D5,D9,E5,E8,F1,F2,G4,G6,G7,H5,H6,H7,I7,I8) * 4.59....2.32.1.4....9.......98..6.74367..92.8.41.8...3974..1...1538.472.826..3.4. * PAIR B1: 1,8 ROW 1 G1: 1,8,3,6 # reduction candidate for 1,8 G1: 1,8 => CTR * 4.5937.6273261.4.96.94....7.983.6174367149258.4178.693974261..5153894726826573941 G1: 3,6 # 24 pairs H1: 1,8,3,6 # reduction candidate for 1,8 H1: 1,8 => CTR * 4.59.7..2.3261.4..6.9.....7.98..6.74367..92.8.4178..63974261..5153894726826573.41 H1: 3,6 # 24 pairs * PAIR B3: 1,8 ROW 3 G3: 1,8,3,5,6 # reduction candidate for 1,8 G3: 1,8 # 27 pairs H3: 1,8,3,5,6 # reduction candidate for 1,8 H3: 1,8 # 27 pairs * PAIR D2: 5,6 BLK 2 E3: 5,6,2,3,4 # reduction candidate for 5,6 E3: 5,6 => CTR * 4.5937..2.32.184....94.2....983.6174367149258.41785..39742.1...1538.472.826573941 E3: 2,3,4 # 23 pairs * PAIR D2: 5,6 ROW 2 H2: 5,6,8,9 # reduction candidate for 5,6 H2: 5,6 => CTR * 4.5937.627326184596.94....7.983.6.74367..92.8.4178.693974261..5153894726826573941 H2: 8,9 # 24 pairs * PAIR D2: 5,6 COL D D7: 5,6,2 # reduction candidate for 5,6 D7: 5,6 => CTR * 4.5978..2.32.15489.89..2..7298..6.74367..92.8541287.939745218..1538.472.8267.3.4. D7: 2 # 25 pairs * PAIR F2: 5,8 BLK 2 F3: 5,8,2 # reduction candidate for 5,8 F3: 5,8 => CTR * 4.5937..27326154896.9428537298356174367149258541782..3974261..5153894726826573941 F3: 2 # 24 pairs * PAIR F2: 5,8 ROW 2 H2: 5,8,6,9 # reduction candidate for 5,8 H2: 6,9 => CTR * 4.59.7..2.326184956.9.....7.98..6574367.59218541782963974261...1538.472.826573.4. H2: 5,8 # 19 pairs * PAIR D3: 3,4 BLK 2 E3: 3,4,2,5,6 # reduction candidate for 3,4 E3: 2,5,6 => CTR * 4.5937..2.3261.4.96.94..537.983561743671492585417826939742.1...1538.472.826573941 E3: 3,4 # 27 pairs * PAIR A4: 2,5 ROW 4 E4: 2,5,3 # reduction candidate for 2,5 E4: 3 => CTR * 415978..2.326154896.9342...298136574367459218541287..3974.21...1538.472.826793145 E4: 2,5 # 20 pairs * PAIR A6: 2,5 ROW 6 D6: 2,5,7 # reduction candidate for 2,5 D6: 2,5 => SOLVED * 415978362732615489689432517598326174367149258241587693974261835153894726826753941 D6: 7 => CTR * 4.5937.627326154896.94....7.983.6174367149258.4178..93974261..5153894726826573941 F6: 2,5,7 # reduction candidate for 2,5 F6: 2,5 => CTR * 4.5937.627326154896.94....7.983.6174367149258.4178..93974261..5153894726826573941 F6: 7 => SOLVED * 415978362732615489689432517598326174367149258241587693974261835153894726826753941 * PAIR E5: 4,5 COL E E3: 4,5,2,3,6 # reduction candidate for 4,5 E3: 4,5 # 30 pairs E3: 2,3,6 # 20 pairs * PAIR G4: 1,5 COL G G3: 1,5,3,6,8 # reduction candidate for 1,5 G3: 1,5 # 21 pairs G9: 1,5,9 # reduction candidate for 1,5 G9: 1,5 => CTR * 4.59.7..2.326184956.9.......98..6.74367..92.8.4178.9639742.1...1538.472.826573149 G9: 9 # 19 pairs * PAIR H5: 1,5 COL H H3: 1,5,3,6,8 # reduction candidate for 1,5 H3: 1,5 # 24 pairs H3: 3,6,8 # 23 pairs * PAIR H6: 6,9 COL H H2: 6,9,5,8 # reduction candidate for 6,9 H2: 6,9 => CTR * 4.59.7..2.326184956.9.....7.98..6574367.59218541782963974261...1538.472.826573.4. H2: 5,8 # 19 pairs * PAIR D9: 5,7 BLK 8 E9: 5,7,9 # reduction candidate for 5,7 E9: 9 => CTR * 4.5978..2.32.15489.89..2..7.98..6.74367..92.8.41.87.93974..183.15389472.826..3.4. E9: 5,7 # 27 pairs * PAIR D9: 5,7 COL D D6: 5,7,2 # reduction candidate for 5,7 D6: 2 => CTR * 4.5978..2.32.15489.89..2..7298..6.74367..92.8541287.939745218..1538.472.8267.3.4. D6: 5,7 # 25 pairs * PAIR G7: 3,8 COL G G1: 3,8,1,6 # reduction candidate for 3,8 G1: 3,8 # 24 pairs G3: 3,8,1,5,6 # reduction candidate for 3,8 G3: 3,8 # 25 pairs * PAIR H7: 3,8 COL H H1: 3,8,1,6 # reduction candidate for 3,8 H1: 3,8 => CTR * 4.59.7..2.326184..6.9.....7.98..6.74367..92.8.4178..63974261..5153894726826573.41 H1: 1,6 # 24 pairs H3: 3,8,1,5,6 # reduction candidate for 3,8 H3: 3,8 => CTR * 4.5937..27326184596.94....7.983.6.74367..92.8.4178...3974261..5153894726826573.41 H3: 1,5,6 # 23 pairs * PAIR I7: 5,6 ROW 7 D7: 5,6,2 # reduction candidate for 5,6 D7: 5,6 => CTR * 4.5978..2.32.15489.89..2..7298..6.74367..92.8541287.939745218..1538.472.8267.3.4. D7: 2 # 25 pairs E7: 5,6,2 # reduction candidate for 5,6 E7: 5,6 # 25 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060503-absurd-base-pr-000.dot * REASONING * DIS # G1: 1,8 => CTR => G1: 3,6 * DIS # H1: 1,8 => CTR => H1: 3,6 * DIS # E3: 5,6 => CTR => E3: 2,3,4 * DIS # H2: 5,6 => CTR => H2: 8,9 * DIS # D7: 5,6 => CTR => D7: 2 * DIS # F3: 5,8 => CTR => F3: 2 * DIS # H2: 6,9 => CTR => H2: 5,8 * DIS # E3: 2,5,6 => CTR => E3: 3,4 * DIS # E4: 3 => CTR => E4: 2,5 * PRF # D6: 2,5 => SOL * DIS # D6: 7 => CTR => D6: 2,5 * DIS # F6: 2,5 => CTR => F6: 7 * PRF # F6: 7 => SOL * DIS # G9: 1,5 => CTR => G9: 9 * DIS # H2: 6,9 => CTR => H2: 5,8 * DIS # E9: 9 => CTR => E9: 5,7 * DIS # D6: 2 => CTR => D6: 5,7 * DIS # H1: 3,8 => CTR => H1: 1,6 * DIS # H3: 3,8 => CTR => H3: 1,5,6 * DIS # D7: 5,6 => CTR => D7: 2 * CNT 20 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A4,A6,B1,B3,D2,D3,D4,D5,D9,E5,E8,F1,F2,G4,G6,G7,H5,H6,H7,I7,I8) * 4.59....2.32.1.4....9.......98..6.74367..92.8.41.8...3974..1...1538.472.826..3.4. * PAIR B1: 1,8 ROW 1 G1: 1,8,3,6 # reduction candidate for 1,8 G1: 1,8 => CTR * 4.5937.6273261.4.96.94....7.983.6174367149258.4178.693974261..5153894726826573941 H1: 1,8,3,6 # reduction candidate for 1,8 H1: 1,8 => CTR * 4.59.7..2.3261.4..6.9.....7.98..6.74367..92.8.4178..63974261..5153894726826573.41 H1: 3,6 => SOLVED * 415978362732615489689432517598326174367149258241587693974261835153894726826753941 * DURATION: 0:00:02.747501 START: 22:53:08.487742 END: 22:53:11.235243 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060503-absurd-base-pr-001.dot * REASONING * DIS # G1: 1,8 => CTR => G1: 3,6 * DIS G1: 3,6 # H1: 1,8 => CTR => H1: 3,6 * PRF G1: 3,6 + H1: 3,6 => SOL * STA G1: 3,6 + H1: 3,6 * CNT 3 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060503, absurd
Solution
position: 415978362732615489689432517598326174367149258241587693974261835153894726826753941 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:
* DIS # G1: 1,8 => CTR => G1: 3,6 * INC # G1: 3,6 => UNS * DIS # H1: 1,8 => CTR => H1: 3,6 * INC # H1: 3,6 => UNS * INC # G3: 1,8 => UNS * INC # H3: 1,8 => UNS * DIS # E3: 5,6 => CTR => E3: 2,3,4 * INC # E3: 2,3,4 => UNS * DIS # H2: 5,6 => CTR => H2: 8,9 * INC # H2: 8,9 => UNS * DIS # D7: 5,6 => CTR => D7: 2 * INC # D7: 2 => UNS * DIS # F3: 5,8 => CTR => F3: 2 * INC # F3: 2 => UNS * INC # H2: 5,8 => UNS * DIS # H2: 6,9 => CTR => H2: 5,8 * INC # E3: 3,4 => UNS * DIS # E3: 2,5,6 => CTR => E3: 3,4 * INC # E4: 2,5 => UNS * DIS # E4: 3 => CTR => E4: 2,5 * PRF # D6: 2,5 => SOL * DIS # D6: 7 => CTR => D6: 2,5 * DIS # F6: 2,5 => CTR => F6: 7 * PRF # F6: 7 => SOL * INC # E3: 4,5 => UNS * INC # E3: 2,3,6 => UNS * INC # G3: 1,5 => UNS * DIS # G9: 1,5 => CTR => G9: 9 * INC # G9: 9 => UNS * INC # H3: 1,5 => UNS * INC # H3: 3,6,8 => UNS * DIS # H2: 6,9 => CTR => H2: 5,8 * INC # H2: 5,8 => UNS * INC # E9: 5,7 => UNS * DIS # E9: 9 => CTR => E9: 5,7 * INC # D6: 5,7 => UNS * DIS # D6: 2 => CTR => D6: 5,7 * INC # G1: 3,8 => UNS * INC # G3: 3,8 => UNS * DIS # H1: 3,8 => CTR => H1: 1,6 * INC # H1: 1,6 => UNS * DIS # H3: 3,8 => CTR => H3: 1,5,6 * INC # H3: 1,5,6 => UNS * DIS # D7: 5,6 => CTR => D7: 2 * INC # D7: 2 => UNS * INC # E7: 5,6 => UNS * CNT 46 HDP CHAINS / 46 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # G1: 1,8 => CTR => G1: 3,6 * DIS G1: 3,6 # H1: 1,8 => CTR => H1: 3,6 * PRF G1: 3,6 + H1: 3,6 => SOL * STA G1: 3,6 + H1: 3,6 * CNT 3 HDP CHAINS / 2 HYP OPENED