Analysis of zz-www.sudokuoftheday.co.uk-20060825-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: 43...57.29...634....7.............1....39...8.59....6.....2.8..14.6...2....8....9 initial
Autosolve
position: 436..57.29..7634....7............91....39...8.59....6..9..2.8..1486.9.2....8....9 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H3: 5,8 => CTR => H3: 3,9 * DIS # B2: 1,8 => CTR => B2: 2 * DIS # F3: 4,8 => CTR => F3: 2 * DIS # E4: 4,8 => CTR => E4: 5,7 * DIS # E6: 4,8 => CTR => E6: 1,7 * DIS # H3: 8,9 => CTR => H3: 3,5 * DIS # H3: 5,8 => CTR => H3: 3,9 * DIS # C2: 2 => CTR => C2: 1,5 * DIS # I3: 3,5 => CTR => I3: 1,6 * DIS # H9: 5,7 => CTR => H9: 3,4 * DIS # A7: 3,5 => CTR => A7: 6,7 * DIS # H7: 3,5 => CTR => H7: 4,7 * DIS # I3: 3,5 => CTR => I3: 1,6 * DIS # H7: 3,5 => CTR => H7: 4,7 * PRF # I8: 3,5 => SOL * DIS # I8: 7 => CTR => I8: 3,5 * DIS # H9: 3,5 => CTR => H9: 4,7 * DIS # E8: 3,5 => CTR => E8: 7 * PRF # E8: 7 => SOL * CNT 19 HDP CHAINS / 43 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H3: 5,8 => CTR => H3: 3,9 * DIS H3: 3,9 # B2: 1,8 => CTR => B2: 2 * PRF H3: 3,9 + B2: 2 # I3: 6 => SOL * STA H3: 3,9 + B2: 2 + I3: 6 * CNT 3 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 43...57.29...634....7.............1....39...8.59....6.....2.8..14.6...2....8....9 | initial |
| 436..57.29..7634....7............91....39...8.59....6..9..2.8..1486.9.2....8....9 | autosolve |
| 436185792921763485587942136362458917714396258859217364693524871148679523275831649 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) A3: 5,8 B3: 1,8 D1: 1,9 E1: 1,8 E3: 4,8 H1: 8,9 H2: 5,8 I2: 1,5 G3: 1,6 G5: 2,5 H5: 5,7 G6: 2,3 C7: 3,5 I7: 1,6 G8: 3,5 G9: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,E1: 1.. / D1 = 1 => 16 pairs (_) / E1 = 1 => 0 pairs (X) B5,C5: 1.. / B5 = 1 => 18 pairs (_) / C5 = 1 => 0 pairs (X) I7,G9: 1.. / I7 = 1 => 22 pairs (_) / G9 = 1 => 14 pairs (_) C2,C5: 1.. / C2 = 1 => 18 pairs (_) / C5 = 1 => 0 pairs (X) G3,G9: 1.. / G3 = 1 => 22 pairs (_) / G9 = 1 => 14 pairs (_) B2,C2: 2.. / B2 = 2 => 18 pairs (_) / C2 = 2 => 0 pairs (X) D3,F3: 2.. / D3 = 2 => 0 pairs (X) / F3 = 2 => 17 pairs (_) G5,G6: 2.. / G5 = 2 => 0 pairs (*) / G6 = 2 => 0 pairs (X) H3,I3: 3.. / H3 = 3 => 18 pairs (_) / I3 = 3 => 0 pairs (X) E8,E9: 3.. / E8 = 3 => 0 pairs (X) / E9 = 3 => 18 pairs (_) G6,G8: 3.. / G6 = 3 => 0 pairs (*) / G8 = 3 => 0 pairs (X) C4,C5: 4.. / C4 = 4 => 0 pairs (X) / C5 = 4 => 19 pairs (_) I4,I6: 4.. / I4 = 4 => 21 pairs (_) / I6 = 4 => 18 pairs (_) H7,H9: 4.. / H7 = 4 => 19 pairs (_) / H9 = 4 => 17 pairs (_) C5,F5: 4.. / C5 = 4 => 19 pairs (_) / F5 = 4 => 0 pairs (X) C2,A3: 5.. / C2 = 5 => 0 pairs (X) / A3 = 5 => 16 pairs (_) D4,E4: 5.. / D4 = 5 => 0 pairs (X) / E4 = 5 => 23 pairs (_) G5,H5: 5.. / G5 = 5 => 0 pairs (X) / H5 = 5 => 0 pairs (_) D4,D7: 5.. / D4 = 5 => 0 pairs (X) / D7 = 5 => 23 pairs (_) G5,G8: 5.. / G5 = 5 => 0 pairs (X) / G8 = 5 => 0 pairs (_) G3,I3: 6.. / G3 = 6 => 14 pairs (_) / I3 = 6 => 22 pairs (_) F4,F5: 6.. / F4 = 6 => 16 pairs (_) / F5 = 6 => 19 pairs (_) I7,G9: 6.. / I7 = 6 => 14 pairs (_) / G9 = 6 => 22 pairs (_) A7,I7: 6.. / A7 = 6 => 22 pairs (_) / I7 = 6 => 14 pairs (_) G3,G9: 6.. / G3 = 6 => 14 pairs (_) / G9 = 6 => 22 pairs (_) I3,I7: 6.. / I3 = 6 => 22 pairs (_) / I7 = 6 => 14 pairs (_) E8,I8: 7.. / E8 = 7 => 0 pairs (*) / I8 = 7 => 0 pairs (X) E1,H1: 8.. / E1 = 8 => 16 pairs (_) / H1 = 8 => 0 pairs (X) B2,H2: 8.. / B2 = 8 => 0 pairs (X) / H2 = 8 => 17 pairs (_) D1,D3: 9.. / D1 = 9 => 0 pairs (X) / D3 = 9 => 16 pairs (_) H1,H3: 9.. / H1 = 9 => 16 pairs (_) / H3 = 9 => 0 pairs (X) D1,H1: 9.. / D1 = 9 => 0 pairs (X) / H1 = 9 => 16 pairs (_) D3,H3: 9.. / D3 = 9 => 16 pairs (_) / H3 = 9 => 0 pairs (X) * DURATION: 0:00:37.398474 START: 02:04:03.912128 END: 02:04:41.310602 2019-05-01 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B3,C7,D1,E1,E3,G3,G5,G6,G8,G9,H1,H2,H5,I2,I7) * 436..57.29..7634....7............91....39...8.59....6..9..2.8..1486.9.2....8....9 * PAIR A3: 5,8 ROW 3 H3: 5,8,3,9 # reduction candidate for 5,8 H3: 5,8 => CTR * 436..57929..7634....79.2..3......91....39...8.59...36..9..2.8.6148639527...8....9 H3: 3,9 # 17 pairs * PAIR B3: 1,8 BLK 1 B2: 1,8,2 # reduction candidate for 1,8 B2: 1,8 => CTR * 436.157829.27634.55.7........4..691...1394..8.59.7..64.9..2.8..1486.9.27...8....9 B2: 2 # 18 pairs * PAIR E1: 1,8 COL E E6: 1,8,4,7 # reduction candidate for 1,8 E6: 1,8 # 19 pairs E6: 4,7 # 17 pairs * PAIR E3: 4,8 BLK 2 F3: 4,8,2 # reduction candidate for 4,8 F3: 4,8 => CTR * 436..57.29..7634....72...93......91....39...8.59...36..9..2.8.6148639527...8....9 F3: 2 # 17 pairs * PAIR E3: 4,8 COL E E4: 4,8,5,7 # reduction candidate for 4,8 E4: 4,8 => CTR * 436.15782982763451517...693...5..91...1394578.59....6..9..2.8..1486.9.2....8....9 E4: 5,7 # 17 pairs E6: 4,8,1,7 # reduction candidate for 4,8 E6: 4,8 => CTR * 436.15782982763451517...693......91...1394578.59....6..9..2.8..1486.9.2....8....9 E6: 1,7 # 17 pairs * PAIR H1: 8,9 BLK 3 H3: 8,9,3,5 # reduction candidate for 8,9 H3: 8,9 => CTR * 436..57.29..7634....7.....3......91....39...8.59...36..9..2.8.6148639527...8....9 H3: 3,5 # 17 pairs * PAIR H2: 5,8 BLK 3 H3: 5,8,3,9 # reduction candidate for 5,8 H3: 5,8 => CTR * 436..57929..7634....79.2..3......91....39...8.59...36..9..2.8.6148639527...8....9 H3: 3,9 # 17 pairs * PAIR I2: 1,5 BLK 3 I3: 1,5,3,6 # reduction candidate for 1,5 I3: 3,6 # 17 pairs I3: 1,5 # 17 pairs * PAIR I2: 1,5 ROW 2 C2: 1,5,2 # reduction candidate for 1,5 C2: 2 => CTR * 436.157829.27634.55.7........4..691...1394..8.59.7..64.9..2.8..1486.9.27...8....9 C2: 1,5 # 18 pairs * PAIR G3: 1,6 BLK 3 I3: 1,6,3,5 # reduction candidate for 1,6 I3: 3,5 => CTR * 436..57.29..7634.1.17...6.5..4..6913..1394.78359.7826479..218.61486.9327562837149 I3: 1,6 # 17 pairs * PAIR H5: 5,7 COL H H7: 5,7,3,4 # reduction candidate for 5,7 H7: 5,7 # 21 pairs H9: 5,7,3,4 # reduction candidate for 5,7 H9: 5,7 => CTR * 4361857929.1763485587942631..245.91..1439.258.5921.364.93521846148679523265834179 H9: 3,4 # 17 pairs * PAIR G6: 2,3 ROW 6 A6: 2,3,7,8 # reduction candidate for 2,3 A6: 2,3 # 19 pairs A6: 7,8 # 18 pairs * PAIR C7: 3,5 BLK 7 A7: 3,5,6,7 # reduction candidate for 3,5 A7: 3,5 => CTR * 436..57.29.17634.5587.426.1......91..1439..78.59....6.3951278461486.9.27..28.4159 A7: 6,7 # 17 pairs A9: 3,5,2,6,7 # reduction candidate for 3,5 A9: 3,5 # 22 pairs C9: 3,5,2 # reduction candidate for 3,5 C9: 3,5 # 21 pairs * PAIR C7: 3,5 ROW 7 H7: 3,5,4,7 # reduction candidate for 3,5 H7: 3,5 => CTR * 436..57.29..76348...7....3....5..91....39.578.59...26..93.2.85.148659327...83..49 H7: 4,7 # 18 pairs * PAIR I7: 1,6 COL I I3: 1,6,3,5 # reduction candidate for 1,6 I3: 3,5 => CTR * 436..57.29..7634.1.17...6.5..4..6913..1394.78359.7826479..218.61486.9327562837149 I3: 1,6 # 17 pairs * PAIR G8: 3,5 BLK 9 H7: 3,5,4,7 # reduction candidate for 3,5 H7: 3,5 => CTR * 436..57.29..76348...7....3....5..91....39.578.59...26..93.2.85.148659327...83..49 H7: 4,7 # 18 pairs I8: 3,5,7 # reduction candidate for 3,5 I8: 3,5 => SOLVED * 436185792921763485587942136362458917714396258859217364693524871148679523275831649 I8: 7 => CTR * 436..57.29..7634....7....3....5..91....39.578.59...26..9..2.8..148659327...83...9 H9: 3,5,4,7 # reduction candidate for 3,5 H9: 3,5 => CTR * 436..57.29..76348...7...63....5..91...439.578.59...26..9.12.84.148659327...834159 H9: 4,7 # 17 pairs * PAIR G8: 3,5 ROW 8 E8: 3,5,7 # reduction candidate for 3,5 E8: 3,5 => CTR * 436..57.29..7634....7....3....5..91....39.578.59...26..9..2.8..148659327...83...9 E8: 7 => SOLVED * 436185792921763485587942136362458917714396258859217364693524871148679523275831649 * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060825-absurd-base-pr-000.dot * REASONING * DIS # H3: 5,8 => CTR => H3: 3,9 * DIS # B2: 1,8 => CTR => B2: 2 * DIS # F3: 4,8 => CTR => F3: 2 * DIS # E4: 4,8 => CTR => E4: 5,7 * DIS # E6: 4,8 => CTR => E6: 1,7 * DIS # H3: 8,9 => CTR => H3: 3,5 * DIS # H3: 5,8 => CTR => H3: 3,9 * DIS # C2: 2 => CTR => C2: 1,5 * DIS # I3: 3,5 => CTR => I3: 1,6 * DIS # H9: 5,7 => CTR => H9: 3,4 * DIS # A7: 3,5 => CTR => A7: 6,7 * DIS # H7: 3,5 => CTR => H7: 4,7 * DIS # I3: 3,5 => CTR => I3: 1,6 * DIS # H7: 3,5 => CTR => H7: 4,7 * PRF # I8: 3,5 => SOL * DIS # I8: 7 => CTR => I8: 3,5 * DIS # H9: 3,5 => CTR => H9: 4,7 * DIS # E8: 3,5 => CTR => E8: 7 * PRF # E8: 7 => SOL * CNT 19 HDP CHAINS / 43 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B3,C7,D1,E1,E3,G3,G5,G6,G8,G9,H1,H2,H5,I2,I7) * 436..57.29..7634....7............91....39...8.59....6..9..2.8..1486.9.2....8....9 * PAIR A3: 5,8 ROW 3 H3: 5,8,3,9 # reduction candidate for 5,8 H3: 5,8 => CTR * 436..57929..7634....79.2..3......91....39...8.59...36..9..2.8.6148639527...8....9 * PAIR RESTART * PAIR B3: 1,8 BLK 1 B2: 1,8,2 # reduction candidate for 1,8 B2: 1,8 => CTR * 436.157829.27634.55.7........4..691...1394..8.59.7..64.9..2.8..1486.9.27...8....9 * PAIR I2: 1,5 BLK 3 I3: 1,5,6 # reduction candidate for 1,5 I3: 6 => SOLVED * 436185792921763485587942136362458917714396258859217364693524871148679523275831649 * DURATION: 0:00:05.245983 START: 02:05:07.248326 END: 02:05:12.494309 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060825-absurd-base-pr-001.dot * REASONING * DIS # H3: 5,8 => CTR => H3: 3,9 * DIS H3: 3,9 # B2: 1,8 => CTR => B2: 2 * PRF H3: 3,9 + B2: 2 # I3: 6 => SOL * STA H3: 3,9 + B2: 2 + I3: 6 * CNT 3 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060825, absurd
Solution
position: 436185792921763485587942136362458917714396258859217364693524871148679523275831649 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 # H3: 5,8 => CTR => H3: 3,9 * INC # H3: 3,9 => UNS * DIS # B2: 1,8 => CTR => B2: 2 * INC # B2: 2 => UNS * INC # E6: 1,8 => UNS * INC # E6: 4,7 => UNS * DIS # F3: 4,8 => CTR => F3: 2 * INC # F3: 2 => UNS * DIS # E4: 4,8 => CTR => E4: 5,7 * INC # E4: 5,7 => UNS * DIS # E6: 4,8 => CTR => E6: 1,7 * INC # E6: 1,7 => UNS * DIS # H3: 8,9 => CTR => H3: 3,5 * INC # H3: 3,5 => UNS * DIS # H3: 5,8 => CTR => H3: 3,9 * INC # H3: 3,9 => UNS * INC # I3: 1,5 => UNS * INC # I3: 3,6 => UNS * INC # C2: 1,5 => UNS * DIS # C2: 2 => CTR => C2: 1,5 * INC # I3: 1,6 => UNS * DIS # I3: 3,5 => CTR => I3: 1,6 * INC # H7: 5,7 => UNS * DIS # H9: 5,7 => CTR => H9: 3,4 * INC # H9: 3,4 => UNS * INC # A6: 2,3 => UNS * INC # A6: 7,8 => UNS * DIS # A7: 3,5 => CTR => A7: 6,7 * INC # A7: 6,7 => UNS * INC # A9: 3,5 => UNS * INC # C9: 3,5 => UNS * DIS # H7: 3,5 => CTR => H7: 4,7 * INC # H7: 4,7 => UNS * INC # I3: 1,6 => UNS * DIS # I3: 3,5 => CTR => I3: 1,6 * DIS # H7: 3,5 => CTR => H7: 4,7 * INC # H7: 4,7 => UNS * PRF # I8: 3,5 => SOL * DIS # I8: 7 => CTR => I8: 3,5 * DIS # H9: 3,5 => CTR => H9: 4,7 * INC # H9: 4,7 => UNS * DIS # E8: 3,5 => CTR => E8: 7 * PRF # E8: 7 => SOL * CNT 43 HDP CHAINS / 43 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # H3: 5,8 => CTR => H3: 3,9 * DIS H3: 3,9 # B2: 1,8 => CTR => B2: 2 * INC H3: 3,9 + B2: 2 # I3: 1,5 => UNS * PRF H3: 3,9 + B2: 2 # I3: 6 => SOL * STA H3: 3,9 + B2: 2 + I3: 6 * CNT 4 HDP CHAINS / 4 HYP OPENED