Analysis of zz-www.sudokuoftheday.co.uk-20060318-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006
level: medium
position: 29.1.....1.8.....46..8.2...8....3.6..3..194....97....3....7...69.........4..2.79. initial
Autosolve
position: 29.1.....1.8.9...46..8.2..98....396773..194..4.97....3...97...69.7.......4..2.79. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E1: 3,4 => CTR => E1: 5,6 * DIS # H2: 5,7 => CTR => H2: 2,3 * DIS # H1: 5,8 => CTR => H1: 3,7 * DIS # I5: 5,8 => CTR => I5: 2 * DIS # I8: 5,8 => CTR => I8: 1,2 * DIS # C4: 1,2 => CTR => C4: 5 * DIS # B7: 1,2 => CTR => B7: 8 * DIS # B8: 1,2 => CTR => B8: 6,8 * DIS # C5: 5 => CTR => C5: 2,6 * DIS # B8: 1,8 => CTR => B8: 2,6 * DIS # D4: 4,5 => CTR => D4: 2 * DIS # E1: 4,5 => CTR => E1: 3,6 * DIS # E8: 4,5 => CTR => E8: 3,6,8 * DIS # H7: 3,5 => CTR => H7: 2,4,8 * DIS # B7: 1,2 => CTR => B7: 8 * DIS # B8: 1,2 => CTR => B8: 6,8 * DIS # C4: 1,2 => CTR => C4: 5 * PRF # D9: 6 => SOL * DIS # B8: 2,8 => CTR => B8: 1,6 * DIS # F9: 1,6 => CTR => F9: 5,8 * CNT 20 HDP CHAINS / 49 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E1: 3,4 => CTR => E1: 5,6 * DIS E1: 5,6 # H2: 5,7 => CTR => H2: 2,3 * DIS E1: 5,6 + H2: 2,3 # F2: 6 => CTR => F2: 5,7 * DIS E1: 5,6 + H2: 2,3 + F2: 5,7 # H1: 5,8 => CTR => H1: 3,7 * DIS E1: 5,6 + H2: 2,3 + F2: 5,7 + H1: 3,7 # I5: 5,8 => CTR => I5: 2 * PRF E1: 5,6 + H2: 2,3 + F2: 5,7 + H1: 3,7 + I5: 2 # H3: 3,5 => SOL * STA E1: 5,6 + H2: 2,3 + F2: 5,7 + H1: 3,7 + I5: 2 + H3: 3,5 * CNT 6 HDP CHAINS / 16 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 29.1.....1.8.....46..8.2...8....3.6..3..194....97....3....7...69.........4..2.79. | initial |
| 29.1.....1.8.9...46..8.2..98....396773..194..4.97....3...97...69.7.......4..2.79. | autosolve |
| 293164875158397624674852139815243967736519482429786513582971346967438251341625798 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) C1: 3,4 B2: 5,7 B3: 5,7 C3: 3,4 I1: 5,8 B4: 1,2 B6: 2,6 E4: 4,5 A7: 3,5 C7: 1,2 A9: 3,5 C9: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G3,H3: 1.. / G3 = 1 => 13 pairs (_) / H3 = 1 => 14 pairs (_) B4,C4: 1.. / B4 = 1 => 13 pairs (_) / C4 = 1 => 0 pairs (X) G6,H6: 1.. / G6 = 1 => 14 pairs (_) / H6 = 1 => 13 pairs (_) I8,I9: 1.. / I8 = 1 => 19 pairs (_) / I9 = 1 => 0 pairs (X) G3,G6: 1.. / G3 = 1 => 13 pairs (_) / G6 = 1 => 14 pairs (_) H3,H6: 1.. / H3 = 1 => 14 pairs (_) / H6 = 1 => 13 pairs (_) G2,H2: 2.. / G2 = 2 => 0 pairs (X) / H2 = 2 => 14 pairs (_) D4,D5: 2.. / D4 = 2 => 14 pairs (_) / D5 = 2 => 0 pairs (X) I5,I8: 2.. / I5 = 2 => 19 pairs (_) / I8 = 2 => 0 pairs (X) C1,C3: 3.. / C1 = 3 => 11 pairs (_) / C3 = 3 => 0 pairs (X) A7,A9: 3.. / A7 = 3 => 0 pairs (X) / A9 = 3 => 11 pairs (_) A9,D9: 3.. / A9 = 3 => 11 pairs (_) / D9 = 3 => 0 pairs (X) C1,C3: 4.. / C1 = 4 => 0 pairs (X) / C3 = 4 => 11 pairs (_) D4,E4: 4.. / D4 = 4 => 0 pairs (X) / E4 = 4 => 13 pairs (_) H7,H8: 4.. / H7 = 4 => 12 pairs (_) / H8 = 4 => 0 pairs (X) C3,E3: 4.. / C3 = 4 => 11 pairs (_) / E3 = 4 => 0 pairs (X) F7,H7: 4.. / F7 = 4 => 0 pairs (X) / H7 = 4 => 12 pairs (_) D4,D8: 4.. / D4 = 4 => 0 pairs (X) / D8 = 4 => 13 pairs (_) B2,B3: 5.. / B2 = 5 => 12 pairs (_) / B3 = 5 => 0 pairs (X) C4,C5: 5.. / C4 = 5 => 14 pairs (_) / C5 = 5 => 0 pairs (X) A7,A9: 5.. / A7 = 5 => 11 pairs (_) / A9 = 5 => 0 pairs (X) G1,G2: 6.. / G1 = 6 => 0 pairs (X) / G2 = 6 => 16 pairs (_) C5,B6: 6.. / C5 = 6 => 19 pairs (_) / B6 = 6 => 0 pairs (X) B8,C9: 6.. / B8 = 6 => 19 pairs (_) / C9 = 6 => 0 pairs (X) C5,D5: 6.. / C5 = 6 => 19 pairs (_) / D5 = 6 => 0 pairs (X) B6,B8: 6.. / B6 = 6 => 0 pairs (X) / B8 = 6 => 19 pairs (_) C5,C9: 6.. / C5 = 6 => 19 pairs (_) / C9 = 6 => 0 pairs (X) B2,B3: 7.. / B2 = 7 => 0 pairs (X) / B3 = 7 => 12 pairs (_) F1,F2: 7.. / F1 = 7 => 0 pairs (X) / F2 = 7 => 12 pairs (_) F1,H1: 7.. / F1 = 7 => 0 pairs (X) / H1 = 7 => 12 pairs (_) B3,H3: 7.. / B3 = 7 => 12 pairs (_) / H3 = 7 => 0 pairs (X) E6,F6: 8.. / E6 = 8 => 13 pairs (_) / F6 = 8 => 0 pairs (X) H5,I5: 8.. / H5 = 8 => 13 pairs (_) / I5 = 8 => 0 pairs (X) B7,B8: 8.. / B7 = 8 => 12 pairs (_) / B8 = 8 => 0 pairs (X) F9,I9: 8.. / F9 = 8 => 14 pairs (_) / I9 = 8 => 0 pairs (*) E6,E8: 8.. / E6 = 8 => 13 pairs (_) / E8 = 8 => 0 pairs (X) * DURATION: 0:00:43.490804 START: 19:56:55.358429 END: 19:57:38.849233 2019-04-30 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,B2,B3,B4,B6,C1,C3,C7,C9,E4,I1) * 29.1.....1.8.9...46..8.2..98....396773..194..4.97....3...97...69.7.......4..2.79. * PAIR C1: 3,4 ROW 1 E1: 3,4,5,6 # reduction candidate for 3,4 E1: 3,4 => CTR * 29.1.....1.8.9...46..8.2..98..453967735.194..4.97....3...97...69.7.......4..2.79. E1: 5,6 # 13 pairs * PAIR B2: 5,7 ROW 2 F2: 5,7,6 # reduction candidate for 5,7 F2: 5,7 # 15 pairs H2: 5,7,2,3 # reduction candidate for 5,7 H2: 5,7 => CTR * 29.1..6..1.83962.46..8.2..98....396773..194..4.97....3...97...69.7.3....34..2.79. H2: 2,3 # 13 pairs * PAIR B3: 5,7 ROW 3 H3: 5,7,1,3 # reduction candidate for 5,7 H3: 5,7 # 15 pairs H3: 1,3 # 13 pairs * PAIR C3: 3,4 ROW 3 E3: 3,4,5 # reduction candidate for 3,4 E3: 3,4 # 14 pairs E3: 5 # 13 pairs * PAIR I1: 5,8 BLK 3 G1: 5,8,3,6 # reduction candidate for 5,8 G1: 5,8 # 20 pairs H1: 5,8,3,7 # reduction candidate for 5,8 H1: 5,8 => CTR * 29.1.7...1.8.9...46..8.2..98..453967735.194..4.97....3...97...69.7.......4..2.79. H1: 3,7 # 13 pairs * PAIR I1: 5,8 COL I I5: 5,8,2 # reduction candidate for 5,8 I5: 5,8 => CTR * 29.1.....1.8.9...46..8.2..98.52439677326194..469785..3.21974..6987..1.42.46.28791 I5: 2 # 19 pairs I8: 5,8,1,2 # reduction candidate for 5,8 I8: 5,8 => CTR * 29.1.....1.8.9...46..8.2..98....396773..194.24297....3..297...6967..1....41.2.79. I8: 1,2 # 13 pairs I9: 5,8,1 # reduction candidate for 5,8 I9: 5,8 # 19 pairs * PAIR B4: 1,2 BLK 4 C4: 1,2,5 # reduction candidate for 1,2 C4: 1,2 => CTR * 29.1.....1.8.9...46..8.2..98..2.39677356194..4697....3...97...69.7.......46.2.79. C4: 5 # 14 pairs * PAIR B4: 1,2 COL B B7: 1,2,8 # reduction candidate for 1,2 B7: 1,2 => CTR * 29.1.....1.8.9...46..8.2..98.52439677326194..469785..3.2197...69874....2.46.2.791 B7: 8 # 12 pairs B8: 1,2,6,8 # reduction candidate for 1,2 B8: 1,2 => CTR * 29.1.....1.8.9...46..8.2..98..2439677326194..4697....3.8197...69274......46.2.79. B8: 6,8 # 13 pairs * PAIR B6: 2,6 BLK 4 C5: 2,6,5 # reduction candidate for 2,6 C5: 5 => CTR * 29.1.....1.8.9...46..8.2..98..2.39677356194..4697....3...97...69.7.......46.2.79. C5: 2,6 # 14 pairs * PAIR B6: 2,6 COL B B8: 2,6,1,8 # reduction candidate for 2,6 B8: 1,8 => CTR * 29.1.4.7.1.8.976246748.2..98152439677326194..469785..3.2197...69874....2.46.2.791 B8: 2,6 # 13 pairs * PAIR E4: 4,5 BLK 5 D4: 4,5,2 # reduction candidate for 4,5 D4: 4,5 => CTR * 29.1.....1.8.9...46..8.2..98....39677362194..4.97....3...97...69.7.....2.4..2.791 D4: 2 # 14 pairs * PAIR E4: 4,5 COL E E1: 4,5,3,6 # reduction candidate for 4,5 E1: 4,5 => CTR * 29315.6..1.8.9...46.4832..98....396773.6194..469785..3...97...69.7.6.....46.28791 E1: 3,6 # 13 pairs E3: 4,5,3 # reduction candidate for 4,5 E3: 4,5 # 15 pairs E8: 4,5,3,6,8 # reduction candidate for 4,5 E8: 4,5 => CTR * 29.16....1.8.9.6246..832..98....396773..194..4.978...3...97...69.7.......4..2.79. E8: 3,6,8 # 12 pairs * PAIR A7: 3,5 ROW 7 G7: 3,5,2,8 # reduction candidate for 3,5 G7: 3,5 # 13 pairs H7: 3,5,2,4,8 # reduction candidate for 3,5 H7: 3,5 => CTR * 29.1.....1.8.9...46..8.2..98..453967735.194..4.97....3...974..69.7....4..4..2.79. H7: 2,4,8 # 12 pairs * PAIR C7: 1,2 BLK 7 B7: 1,2,8 # reduction candidate for 1,2 B7: 1,2 => CTR * 29.1.....1.8.9...46..8.2..98.52439677326194..469785..3.2197...69874....2.46.2.791 B7: 8 # 12 pairs B8: 1,2,6,8 # reduction candidate for 1,2 B8: 1,2 => CTR * 29.1.....1.8.9...46..8.2..98..2439677326194..4697....3.8197...69274......46.2.79. B8: 6,8 # 13 pairs * PAIR C7: 1,2 COL C C4: 1,2,5 # reduction candidate for 1,2 C4: 1,2 => CTR * 29.1.....1.8.9...46..8.2..98..2.39677356194..4697....3...97...69.7.......46.2.79. C4: 5 # 14 pairs * PAIR A9: 3,5 ROW 9 D9: 3,5,6 # reduction candidate for 3,5 D9: 6 => SOLVED * 293164875158397624674852139815243967736519482429786513582971346967438251341625798 D9: 3,5 # 14 pairs * PAIR C9: 1,6 BLK 7 B8: 1,6,2,8 # reduction candidate for 1,6 B8: 2,8 => CTR * 29.1.4.7.1.8.976246748.2..98152439677326194..4697..213.2197..469874....2.46.2.791 B8: 1,6 # 15 pairs * PAIR C9: 1,6 ROW 9 F9: 1,6,5,8 # reduction candidate for 1,6 F9: 1,6 => CTR * 29.16.8.51.839.6246..8.2..98152.396773..194824297....3..297...6967...2.1.41.26798 F9: 5,8 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060318-absurd-base-pr-000.dot * REASONING * DIS # E1: 3,4 => CTR => E1: 5,6 * DIS # H2: 5,7 => CTR => H2: 2,3 * DIS # H1: 5,8 => CTR => H1: 3,7 * DIS # I5: 5,8 => CTR => I5: 2 * DIS # I8: 5,8 => CTR => I8: 1,2 * DIS # C4: 1,2 => CTR => C4: 5 * DIS # B7: 1,2 => CTR => B7: 8 * DIS # B8: 1,2 => CTR => B8: 6,8 * DIS # C5: 5 => CTR => C5: 2,6 * DIS # B8: 1,8 => CTR => B8: 2,6 * DIS # D4: 4,5 => CTR => D4: 2 * DIS # E1: 4,5 => CTR => E1: 3,6 * DIS # E8: 4,5 => CTR => E8: 3,6,8 * DIS # H7: 3,5 => CTR => H7: 2,4,8 * DIS # B7: 1,2 => CTR => B7: 8 * DIS # B8: 1,2 => CTR => B8: 6,8 * DIS # C4: 1,2 => CTR => C4: 5 * PRF # D9: 6 => SOL * DIS # B8: 2,8 => CTR => B8: 1,6 * DIS # F9: 1,6 => CTR => F9: 5,8 * CNT 20 HDP CHAINS / 49 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,B2,B3,B4,B6,C1,C3,C7,C9,E4,I1) * 29.1.....1.8.9...46..8.2..98....396773..194..4.97....3...97...69.7.......4..2.79. * PAIR C1: 3,4 ROW 1 E1: 3,4,5,6 # reduction candidate for 3,4 E1: 3,4 => CTR * 29.1.....1.8.9...46..8.2..98..453967735.194..4.97....3...97...69.7.......4..2.79. * PAIR RESTART * PAIR B2: 5,7 ROW 2 F2: 5,7,6 # reduction candidate for 5,7 F2: 5,7 # 16 pairs H2: 5,7,2,3 # reduction candidate for 5,7 H2: 5,7 => CTR * 29.1..6..1.83962.46..8.2..98....396773..194..4.97....3...97...69.7.3....34..2.79. * RESTART * PAIR B2: 5,7 ROW 2 F2: 5,7,6 # reduction candidate for 5,7 F2: 6 => CTR * 29.1.7...178.96..465.842.798..45396773..194..4.97....3...97...69.7.......4..2.79. * PAIR RESTART * PAIR B3: 5,7 ROW 3 H3: 5,7,1,3 # reduction candidate for 5,7 H3: 5,7 # 19 pairs H3: 1,3 # 14 pairs * PAIR C3: 3,4 ROW 3 E3: 3,4,5 # reduction candidate for 3,4 E3: 3,4 # 18 pairs E3: 5 # 13 pairs * PAIR I1: 5,8 BLK 3 G1: 5,8,3,6 # reduction candidate for 5,8 G1: 5,8 # 20 pairs H1: 5,8,3,7 # reduction candidate for 5,8 H1: 5,8 => CTR * 29.1.7...178.95..465.842.798..453967735.194..4.97....3...97...69.7.......4..2.79. * RESTART * PAIR I1: 5,8 BLK 3 G1: 5,8,3,6 # reduction candidate for 5,8 G1: 5,8 # 20 pairs G1: 3,6 # 19 pairs * PAIR I1: 5,8 COL I I5: 5,8,2 # reduction candidate for 5,8 I5: 5,8 => CTR * 29.1.....15839762467.8.2..98.52439677326194..469785213.21974..69875....2.46.28791 * RESTART * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A7,A9,D2,D9,E1,E3,E6,E8,F6,F8,G1,G2,G6,G7,G8,H2,H6,I1,I9) * 2931.4.7.158.97..46748.2..98152439677365194824297....3.82971.469674....1.41.2.79. * PAIR E3: 3,5 ROW 3 G3: 3,5,1 # reduction candidate for 3,5 G3: 3,5 # 19 pairs H3: 3,5,1 # reduction candidate for 3,5 H3: 3,5 => SOLVED * 293164875158397624674852139815243967736519482429786513582971346967438251341625798 * DURATION: 0:01:45.312854 START: 19:58:09.757444 END: 19:59:55.070298 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060318-absurd-base-pr-001.dot * REASONING * DIS # E1: 3,4 => CTR => E1: 5,6 * DIS E1: 5,6 # H2: 5,7 => CTR => H2: 2,3 * DIS E1: 5,6 + H2: 2,3 # F2: 6 => CTR => F2: 5,7 * DIS E1: 5,6 + H2: 2,3 + F2: 5,7 # H1: 5,8 => CTR => H1: 3,7 * DIS E1: 5,6 + H2: 2,3 + F2: 5,7 + H1: 3,7 # I5: 5,8 => CTR => I5: 2 * PRF E1: 5,6 + H2: 2,3 + F2: 5,7 + H1: 3,7 + I5: 2 # H3: 3,5 => SOL * STA E1: 5,6 + H2: 2,3 + F2: 5,7 + H1: 3,7 + I5: 2 + H3: 3,5 * CNT 6 HDP CHAINS / 16 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060318, absurd
Solution
position: 293164875158397624674852139815243967736519482429786513582971346967438251341625798 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 # E1: 3,4 => CTR => E1: 5,6 * INC # E1: 5,6 => UNS * INC # F2: 5,7 => UNS * DIS # H2: 5,7 => CTR => H2: 2,3 * INC # H2: 2,3 => UNS * INC # H3: 5,7 => UNS * INC # H3: 1,3 => UNS * INC # E3: 3,4 => UNS * INC # E3: 5 => UNS * INC # G1: 5,8 => UNS * DIS # H1: 5,8 => CTR => H1: 3,7 * INC # H1: 3,7 => UNS * DIS # I5: 5,8 => CTR => I5: 2 * INC # I5: 2 => UNS * DIS # I8: 5,8 => CTR => I8: 1,2 * INC # I8: 1,2 => UNS * INC # I9: 5,8 => UNS * DIS # C4: 1,2 => CTR => C4: 5 * INC # C4: 5 => UNS * DIS # B7: 1,2 => CTR => B7: 8 * INC # B7: 8 => UNS * DIS # B8: 1,2 => CTR => B8: 6,8 * INC # B8: 6,8 => UNS * INC # C5: 2,6 => UNS * DIS # C5: 5 => CTR => C5: 2,6 * INC # B8: 2,6 => UNS * DIS # B8: 1,8 => CTR => B8: 2,6 * DIS # D4: 4,5 => CTR => D4: 2 * INC # D4: 2 => UNS * DIS # E1: 4,5 => CTR => E1: 3,6 * INC # E1: 3,6 => UNS * INC # E3: 4,5 => UNS * DIS # E8: 4,5 => CTR => E8: 3,6,8 * INC # E8: 3,6,8 => UNS * INC # G7: 3,5 => UNS * DIS # H7: 3,5 => CTR => H7: 2,4,8 * INC # H7: 2,4,8 => UNS * DIS # B7: 1,2 => CTR => B7: 8 * INC # B7: 8 => UNS * DIS # B8: 1,2 => CTR => B8: 6,8 * INC # B8: 6,8 => UNS * DIS # C4: 1,2 => CTR => C4: 5 * INC # C4: 5 => UNS * INC # D9: 3,5 => UNS * PRF # D9: 6 => SOL * INC # B8: 1,6 => UNS * DIS # B8: 2,8 => CTR => B8: 1,6 * DIS # F9: 1,6 => CTR => F9: 5,8 * INC # F9: 5,8 => UNS * CNT 49 HDP CHAINS / 49 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # E1: 3,4 => CTR => E1: 5,6 * INC E1: 5,6 # F2: 5,7 => UNS * DIS E1: 5,6 # H2: 5,7 => CTR => H2: 2,3 * INC E1: 5,6 + H2: 2,3 # F2: 5,7 => UNS * DIS E1: 5,6 + H2: 2,3 # F2: 6 => CTR => F2: 5,7 * INC E1: 5,6 + H2: 2,3 + F2: 5,7 # H3: 5,7 => UNS * INC E1: 5,6 + H2: 2,3 + F2: 5,7 # H3: 1,3 => UNS * INC E1: 5,6 + H2: 2,3 + F2: 5,7 # E3: 3,4 => UNS * INC E1: 5,6 + H2: 2,3 + F2: 5,7 # E3: 5 => UNS * INC E1: 5,6 + H2: 2,3 + F2: 5,7 # G1: 5,8 => UNS * DIS E1: 5,6 + H2: 2,3 + F2: 5,7 # H1: 5,8 => CTR => H1: 3,7 * INC E1: 5,6 + H2: 2,3 + F2: 5,7 + H1: 3,7 # G1: 5,8 => UNS * INC E1: 5,6 + H2: 2,3 + F2: 5,7 + H1: 3,7 # G1: 3,6 => UNS * DIS E1: 5,6 + H2: 2,3 + F2: 5,7 + H1: 3,7 # I5: 5,8 => CTR => I5: 2 * INC E1: 5,6 + H2: 2,3 + F2: 5,7 + H1: 3,7 + I5: 2 # G3: 3,5 => UNS * PRF E1: 5,6 + H2: 2,3 + F2: 5,7 + H1: 3,7 + I5: 2 # H3: 3,5 => SOL * STA E1: 5,6 + H2: 2,3 + F2: 5,7 + H1: 3,7 + I5: 2 + H3: 3,5 * CNT 16 HDP CHAINS / 16 HYP OPENED