Analysis of zz-www.sudokuoftheday.co.uk-20060716-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: ..7619..........6...1....3.6.....1.5.4.8.69......2...3.3.1..8......7.3..7...83.16 initial
Autosolve
position: 3.76194.8.......61.61..8.396...9.1.514.8.69......216.3.3.16.8..816.7.3..7...83.16 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 2,5 => CTR => A2: 4,9 * DIS # B2: 2,5 => CTR => B2: 8,9 * DIS # C2: 2,5 => CTR => C2: 4,8,9 * DIS # E2: 4,5 => CTR => E2: 3 * PRF # A3: 2 => SOL * PRF # A7: 5,9 => SOL * DIS # D4: 4,7 => CTR => D4: 3 * DIS # E2: 4 => CTR => E2: 3,5 * DIS # H7: 2,7 => CTR => H7: 5,9 * DIS # I7: 4 => CTR => I7: 2,7 * DIS # I7: 2,4 => CTR => I7: 7 * CNT 11 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 2,5 => CTR => A2: 4,9 * DIS A2: 4,9 # B2: 2,5 => CTR => B2: 8,9 * DIS A2: 4,9 + B2: 8,9 # C2: 2,5 => CTR => C2: 4,8,9 * PRF A2: 4,9 + B2: 8,9 + C2: 4,8,9 # A7: 5,9 => SOL * STA A2: 4,9 + B2: 8,9 + C2: 4,8,9 + A7: 5,9 * CNT 4 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..7619..........6...1....3.6.....1.5.4.8.69......2...3.3.1..8......7.3..7...83.16 | initial |
| 3.76194.8.......61.61..8.396...9.1.514.8.69......216.3.3.16.8..816.7.3..7...83.16 | autosolve |
| 357619428489235761261748539628397145143856972975421683532164897816972354794583216 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) B1: 2,5 E3: 4,5 H1: 2,5 C5: 3,5 A6: 5,9 F4: 4,7 E5: 3,5 H4: 4,8 H5: 2,7 I5: 2,7 H6: 4,8 I8: 2,4 G9: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B4,C4: 2.. / B4 = 2 => 20 pairs (_) / C4 = 2 => 15 pairs (_) H5,I5: 2.. / H5 = 2 => 0 pairs (X) / I5 = 2 => 11 pairs (_) B1,H1: 2.. / B1 = 2 => 0 pairs (X) / H1 = 2 => 18 pairs (_) D2,E2: 3.. / D2 = 3 => 0 pairs (X) / E2 = 3 => 15 pairs (_) C4,C5: 3.. / C4 = 3 => 0 pairs (X) / C5 = 3 => 15 pairs (_) D4,E5: 3.. / D4 = 3 => 15 pairs (_) / E5 = 3 => 0 pairs (X) C4,D4: 3.. / C4 = 3 => 0 pairs (X) / D4 = 3 => 15 pairs (_) C5,E5: 3.. / C5 = 3 => 15 pairs (_) / E5 = 3 => 0 pairs (X) D2,D4: 3.. / D2 = 3 => 0 pairs (X) / D4 = 3 => 15 pairs (_) E2,E5: 3.. / E2 = 3 => 15 pairs (_) / E5 = 3 => 0 pairs (X) E2,E3: 4.. / E2 = 4 => 0 pairs (X) / E3 = 4 => 16 pairs (_) H4,H6: 4.. / H4 = 4 => 14 pairs (_) / H6 = 4 => 14 pairs (_) I7,I8: 4.. / I7 = 4 => 0 pairs (X) / I8 = 4 => 14 pairs (_) A3,E3: 4.. / A3 = 4 => 0 pairs (X) / E3 = 4 => 16 pairs (_) D6,H6: 4.. / D6 = 4 => 14 pairs (_) / H6 = 4 => 14 pairs (_) C9,D9: 4.. / C9 = 4 => 13 pairs (_) / D9 = 4 => 16 pairs (_) E5,D6: 5.. / E5 = 5 => 15 pairs (_) / D6 = 5 => 0 pairs (X) B1,H1: 5.. / B1 = 5 => 18 pairs (_) / H1 = 5 => 0 pairs (X) C5,E5: 5.. / C5 = 5 => 0 pairs (X) / E5 = 5 => 15 pairs (_) G2,G3: 7.. / G2 = 7 => 17 pairs (_) / G3 = 7 => 15 pairs (_) B4,B6: 7.. / B4 = 7 => 17 pairs (_) / B6 = 7 => 15 pairs (_) H5,I5: 7.. / H5 = 7 => 11 pairs (_) / I5 = 7 => 0 pairs (X) H7,I7: 7.. / H7 = 7 => 0 pairs (X) / I7 = 7 => 11 pairs (_) D3,G3: 7.. / D3 = 7 => 17 pairs (_) / G3 = 7 => 15 pairs (_) B6,D6: 7.. / B6 = 7 => 15 pairs (_) / D6 = 7 => 17 pairs (_) F2,F4: 7.. / F2 = 7 => 20 pairs (_) / F4 = 7 => 16 pairs (_) H5,H7: 7.. / H5 = 7 => 11 pairs (_) / H7 = 7 => 0 pairs (X) I5,I7: 7.. / I5 = 7 => 0 pairs (X) / I7 = 7 => 11 pairs (_) B2,C2: 8.. / B2 = 8 => 14 pairs (_) / C2 = 8 => 18 pairs (_) H4,H6: 8.. / H4 = 8 => 14 pairs (_) / H6 = 8 => 14 pairs (_) D8,D9: 9.. / D8 = 9 => 12 pairs (_) / D9 = 9 => 18 pairs (_) H7,H8: 9.. / H7 = 9 => 12 pairs (_) / H8 = 9 => 18 pairs (_) D8,H8: 9.. / D8 = 9 => 12 pairs (_) / H8 = 9 => 18 pairs (_) * DURATION: 0:00:40.754808 START: 00:43:38.889847 END: 00:44:19.644655 2019-05-01 * CP COUNT: (33) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B1,C5,E3,E5,F4,G9,H1,H4,H5,H6,I5,I8) * 3.76194.8.......61.61..8.396...9.1.514.8.69......216.3.3.16.8..816.7.3..7...83.16 * PAIR B1: 2,5 BLK 1 A2: 2,5,4,9 # reduction candidate for 2,5 A2: 2,5 => CTR * 357619428.8934..61461.58.396.3.9.1851458369..978521643.3.16.89781697.3.479..83516 A2: 4,9 # 14 pairs B2: 2,5,8,9 # reduction candidate for 2,5 B2: 2,5 => CTR * 3.76194.89.8.4..61461.58.396...9.1.51458.69......216.3.3.16.8..816.7.3..7...83.16 B2: 8,9 # 14 pairs C2: 2,5,4,8,9 # reduction candidate for 2,5 C2: 2,5 => CTR * 3.76194.898..4..61461.58.396...9.1.51458.69......216.3.3.16.8..816.7.3..7...83.16 C2: 4,8,9 # 13 pairs A3: 2,5,4 # reduction candidate for 2,5 A3: 2,5 # 16 pairs * PAIR B1: 2,5 COL B B9: 2,5,9 # reduction candidate for 2,5 B9: 2,5 # 18 pairs B9: 9 # 12 pairs * PAIR E3: 4,5 BLK 2 E2: 4,5,3 # reduction candidate for 4,5 E2: 4,5 => CTR * 3.76194.8.893...61.61..8.39623.9.1851458369..978521643.3.16.89781697.3.479..83516 E2: 3 # 15 pairs * PAIR E3: 4,5 ROW 3 A3: 4,5,2 # reduction candidate for 4,5 A3: 2 => SOLVED * 357619428489235761261748539628397145143856972975421683532164897816972354794583216 A3: 4,5 # 16 pairs * PAIR H1: 2,5 BLK 3 G2: 2,5,7 # reduction candidate for 2,5 G2: 2,5 # 15 pairs G3: 2,5,7 # reduction candidate for 2,5 G3: 2,5 # 17 pairs * PAIR H1: 2,5 COL H H7: 2,5,7,9 # reduction candidate for 2,5 H7: 2,5 # 12 pairs H8: 2,5,9 # reduction candidate for 2,5 H8: 2,5 # 12 pairs * PAIR A6: 5,9 BLK 4 B6: 5,9,7,8 # reduction candidate for 5,9 B6: 5,9 # 19 pairs C6: 5,9,8 # reduction candidate for 5,9 C6: 5,9 # 17 pairs * PAIR A6: 5,9 COL A A2: 5,9,2,4 # reduction candidate for 5,9 A2: 5,9 # 16 pairs A7: 5,9,2,4 # reduction candidate for 5,9 A7: 5,9 => SOLVED * 357619428489235761261748539628397145143856972975421683532164897816972354794583216 A7: 2,4 # 14 pairs * PAIR F4: 4,7 BLK 5 D4: 4,7,3 # reduction candidate for 4,7 D4: 4,7 => CTR * 3.76194.8.893...61.61..8.39623.9.1851458369..978521643.3.16.89781697.3.479..83516 D4: 3 # 15 pairs D6: 4,7,5 # reduction candidate for 4,7 D6: 4,7 # 15 pairs * PAIR E5: 3,5 COL E E2: 3,5,4 # reduction candidate for 3,5 E2: 4 => CTR * 3.76194.8.8934..61461.58.39623.9.1851458369..978521643.3.16.89781697.3.479..83516 E2: 3,5 # 16 pairs * PAIR H5: 2,7 COL H H7: 2,7,5,9 # reduction candidate for 2,7 H7: 2,7 => CTR * 3.7619458.......61.61..8.396...9.1.514.8.69......216.3.3.16.8..816.7.39.72.983516 H7: 5,9 # 12 pairs * PAIR I5: 2,7 COL I I7: 2,7,4 # reduction candidate for 2,7 I7: 4 => CTR * 3.7619458.......61.61..8.396...9.1.514.8.6927....216.3.3.162874816.7.392724983516 I7: 2,7 # 14 pairs * PAIR I8: 2,4 BLK 9 I7: 2,4,7 # reduction candidate for 2,4 I7: 2,4 => CTR * 3.7619458.......61.61..8.396...9.1.514.8.6927....216.3.3.16.87.816.7.39.72.983516 I7: 7 # 11 pairs * PAIR I8: 2,4 ROW 8 D8: 2,4,5,9 # reduction candidate for 2,4 D8: 2,4 # 20 pairs F8: 2,4,5 # reduction candidate for 2,4 F8: 2,4 # 16 pairs * PAIR G9: 2,5 BLK 9 H7: 2,5,7,9 # reduction candidate for 2,5 H7: 2,5 # 12 pairs H8: 2,5,9 # reduction candidate for 2,5 H8: 2,5 # 12 pairs * PAIR G9: 2,5 ROW 9 B9: 2,5,9 # reduction candidate for 2,5 B9: 2,5 # 18 pairs C9: 2,5,4,9 # reduction candidate for 2,5 C9: 2,5 # 20 pairs D9: 2,5,4,9 # reduction candidate for 2,5 D9: 2,5 # 19 pairs * PAIR G9: 2,5 COL G G2: 2,5,7 # reduction candidate for 2,5 G2: 2,5 # 15 pairs G3: 2,5,7 # reduction candidate for 2,5 G3: 2,5 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060716-absurd-base-pr-000.dot * REASONING * DIS # A2: 2,5 => CTR => A2: 4,9 * DIS # B2: 2,5 => CTR => B2: 8,9 * DIS # C2: 2,5 => CTR => C2: 4,8,9 * DIS # E2: 4,5 => CTR => E2: 3 * PRF # A3: 2 => SOL * PRF # A7: 5,9 => SOL * DIS # D4: 4,7 => CTR => D4: 3 * DIS # E2: 4 => CTR => E2: 3,5 * DIS # H7: 2,7 => CTR => H7: 5,9 * DIS # I7: 4 => CTR => I7: 2,7 * DIS # I7: 2,4 => CTR => I7: 7 * CNT 11 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B1,C5,E3,E5,F4,G9,H1,H4,H5,H6,I5,I8) * 3.76194.8.......61.61..8.396...9.1.514.8.69......216.3.3.16.8..816.7.3..7...83.16 * PAIR B1: 2,5 BLK 1 A2: 2,5,4,9 # reduction candidate for 2,5 A2: 2,5 => CTR * 357619428.8934..61461.58.396.3.9.1851458369..978521643.3.16.89781697.3.479..83516 B2: 2,5,8,9 # reduction candidate for 2,5 B2: 2,5 => CTR * 3.76194.89.8.4..61461.58.396...9.1.51458.69......216.3.3.16.8..816.7.3..7...83.16 C2: 2,5,4,8,9 # reduction candidate for 2,5 C2: 2,5 => CTR * 3.76194.898..4..61461.58.396...9.1.51458.69......216.3.3.16.8..816.7.3..7...83.16 * RESTART * PAIR B1: 2,5 COL B B9: 2,5,9 # reduction candidate for 2,5 B9: 2,5 # 18 pairs B9: 9 # 17 pairs * PAIR H1: 2,5 BLK 3 G2: 2,5,7 # reduction candidate for 2,5 G2: 2,5 # 18 pairs G3: 2,5,7 # reduction candidate for 2,5 G3: 2,5 # 20 pairs * PAIR H1: 2,5 COL H H7: 2,5,7,9 # reduction candidate for 2,5 H7: 2,5 # 12 pairs H8: 2,5,9 # reduction candidate for 2,5 H8: 2,5 # 15 pairs * PAIR A6: 5,9 BLK 4 B6: 5,9,7,8 # reduction candidate for 5,9 B6: 5,9 # 19 pairs C6: 5,9,8 # reduction candidate for 5,9 C6: 5,9 # 17 pairs * PAIR A6: 5,9 COL A A7: 5,9,2,4 # reduction candidate for 5,9 A7: 5,9 => SOLVED * 357619428489235761261748539628397145143856972975421683532164897816972354794583216 * DURATION: 0:00:09.943230 START: 00:44:48.265271 END: 00:44:58.208501 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060716-absurd-base-pr-001.dot * REASONING * DIS # A2: 2,5 => CTR => A2: 4,9 * DIS A2: 4,9 # B2: 2,5 => CTR => B2: 8,9 * DIS A2: 4,9 + B2: 8,9 # C2: 2,5 => CTR => C2: 4,8,9 * PRF A2: 4,9 + B2: 8,9 + C2: 4,8,9 # A7: 5,9 => SOL * STA A2: 4,9 + B2: 8,9 + C2: 4,8,9 + A7: 5,9 * CNT 4 HDP CHAINS / 12 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060716, absurd
Solution
position: 357619428489235761261748539628397145143856972975421683532164897816972354794583216 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 # A2: 2,5 => CTR => A2: 4,9 * INC # A2: 4,9 => UNS * DIS # B2: 2,5 => CTR => B2: 8,9 * INC # B2: 8,9 => UNS * DIS # C2: 2,5 => CTR => C2: 4,8,9 * INC # C2: 4,8,9 => UNS * INC # A3: 2,5 => UNS * INC # B9: 2,5 => UNS * INC # B9: 9 => UNS * DIS # E2: 4,5 => CTR => E2: 3 * INC # E2: 3 => UNS * INC # A3: 4,5 => UNS * PRF # A3: 2 => SOL * INC # G2: 2,5 => UNS * INC # G3: 2,5 => UNS * INC # H7: 2,5 => UNS * INC # H8: 2,5 => UNS * INC # B6: 5,9 => UNS * INC # C6: 5,9 => UNS * INC # A2: 5,9 => UNS * PRF # A7: 5,9 => SOL * INC # A7: 2,4 => UNS * DIS # D4: 4,7 => CTR => D4: 3 * INC # D4: 3 => UNS * INC # D6: 4,7 => UNS * INC # E2: 3,5 => UNS * DIS # E2: 4 => CTR => E2: 3,5 * DIS # H7: 2,7 => CTR => H7: 5,9 * INC # H7: 5,9 => UNS * INC # I7: 2,7 => UNS * DIS # I7: 4 => CTR => I7: 2,7 * DIS # I7: 2,4 => CTR => I7: 7 * INC # I7: 7 => UNS * INC # D8: 2,4 => UNS * INC # F8: 2,4 => UNS * INC # H7: 2,5 => UNS * INC # H8: 2,5 => UNS * INC # B9: 2,5 => UNS * INC # C9: 2,5 => UNS * INC # D9: 2,5 => UNS * INC # G2: 2,5 => UNS * INC # G3: 2,5 => UNS * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A2: 2,5 => CTR => A2: 4,9 * DIS A2: 4,9 # B2: 2,5 => CTR => B2: 8,9 * DIS A2: 4,9 + B2: 8,9 # C2: 2,5 => CTR => C2: 4,8,9 * INC A2: 4,9 + B2: 8,9 + C2: 4,8,9 # B9: 2,5 => UNS * INC A2: 4,9 + B2: 8,9 + C2: 4,8,9 # B9: 9 => UNS * INC A2: 4,9 + B2: 8,9 + C2: 4,8,9 # G2: 2,5 => UNS * INC A2: 4,9 + B2: 8,9 + C2: 4,8,9 # G3: 2,5 => UNS * INC A2: 4,9 + B2: 8,9 + C2: 4,8,9 # H7: 2,5 => UNS * INC A2: 4,9 + B2: 8,9 + C2: 4,8,9 # H8: 2,5 => UNS * INC A2: 4,9 + B2: 8,9 + C2: 4,8,9 # B6: 5,9 => UNS * INC A2: 4,9 + B2: 8,9 + C2: 4,8,9 # C6: 5,9 => UNS * PRF A2: 4,9 + B2: 8,9 + C2: 4,8,9 # A7: 5,9 => SOL * STA A2: 4,9 + B2: 8,9 + C2: 4,8,9 + A7: 5,9 * CNT 12 HDP CHAINS / 12 HYP OPENED