Analysis of zz-www.sudokuoftheday.co.uk-20060730-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: ..2..679..61....3...........74..832.8..2...4.....7..1.9..3.......8.4....6..1.9574 initial
Autosolve
position: ..2..679..61....3........56.746.832.8..2..6472.6.7.81.94.36..8...8.42963623189574 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G3: 1 => CTR => G3: 2,4 * PRF # B5: 1,5 => SOL * DIS # A8: 1,5 => CTR => A8: 7 * PRF # A8: 7 => SOL * DIS # E4: 1 => CTR => E4: 5,9 * DIS # A8: 1 => CTR => A8: 5,7 * DIS # A8: 1,5 => CTR => A8: 7 * PRF # A8: 7 => SOL * PRF # B5: 1,5 => SOL * DIS # F2: 4 => CTR => F2: 5,7 * DIS # A8: 1 => CTR => A8: 5,7 * PRF # D2: 5,7 => SOL * CNT 12 HDP CHAINS / 32 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G3: 1 => CTR => G3: 2,4 * PRF G3: 2,4 # B5: 1,5 => SOL * STA G3: 2,4 + B5: 1,5 * CNT 2 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..2..679..61....3...........74..832.8..2...4.....7..1.9..3.......8.4....6..1.9574 | initial |
| ..2..679..61....3........56.746.832.8..2..6472.6.7.81.94.36..8...8.42963623189574 | autosolve |
| 582436791461795238397821456174658329859213647236974815945367182718542963623189574 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) B1: 5,8 B3: 8,9 C3: 7,9 I1: 1,8 G2: 2,4 I2: 2,8 A4: 1,5 C5: 5,9 I4: 5,9 I6: 5,9 C7: 5,7 B8: 1,5 F7: 5,7 D8: 5,7 G7: 1,2 I7: 1,2 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I1,G3: 1.. / I1 = 1 => 14 pairs (_) / G3 = 1 => 0 pairs (X) A4,B5: 1.. / A4 = 1 => 16 pairs (_) / B5 = 1 => 0 pairs (X) A8,B8: 1.. / A8 = 1 => 0 pairs (X) / B8 = 1 => 16 pairs (_) G7,I7: 1.. / G7 = 1 => 14 pairs (_) / I7 = 1 => 0 pairs (X) E1,I1: 1.. / E1 = 1 => 0 pairs (X) / I1 = 1 => 14 pairs (_) A4,E4: 1.. / A4 = 1 => 16 pairs (_) / E4 = 1 => 0 pairs (X) A4,A8: 1.. / A4 = 1 => 16 pairs (_) / A8 = 1 => 0 pairs (X) B5,B8: 1.. / B5 = 1 => 0 pairs (X) / B8 = 1 => 16 pairs (_) F3,F5: 1.. / F3 = 1 => 16 pairs (_) / F5 = 1 => 26 pairs (_) G3,G7: 1.. / G3 = 1 => 0 pairs (X) / G7 = 1 => 14 pairs (_) I1,I7: 1.. / I1 = 1 => 14 pairs (_) / I7 = 1 => 0 pairs (X) E2,E3: 2.. / E2 = 2 => 20 pairs (_) / E3 = 2 => 20 pairs (_) G7,I7: 2.. / G7 = 2 => 0 pairs (X) / I7 = 2 => 14 pairs (_) E3,G3: 2.. / E3 = 2 => 20 pairs (_) / G3 = 2 => 20 pairs (_) I2,I7: 2.. / I2 = 2 => 0 pairs (X) / I7 = 2 => 14 pairs (_) A1,A3: 3.. / A1 = 3 => 25 pairs (_) / A3 = 3 => 15 pairs (_) B5,B6: 3.. / B5 = 3 => 20 pairs (_) / B6 = 3 => 19 pairs (_) A1,E1: 3.. / A1 = 3 => 25 pairs (_) / E1 = 3 => 15 pairs (_) B6,F6: 3.. / B6 = 3 => 19 pairs (_) / F6 = 3 => 20 pairs (_) G2,G3: 4.. / G2 = 4 => 24 pairs (_) / G3 = 4 => 15 pairs (_) D6,F6: 4.. / D6 = 4 => 19 pairs (_) / F6 = 4 => 20 pairs (_) A1,D1: 4.. / A1 = 4 => 16 pairs (_) / D1 = 4 => 22 pairs (_) I4,I6: 5.. / I4 = 5 => 14 pairs (_) / I6 = 5 => 18 pairs (_) F7,D8: 5.. / F7 = 5 => 0 pairs (X) / D8 = 5 => 0 pairs (_) C7,F7: 5.. / C7 = 5 => 0 pairs (*) / F7 = 5 => 0 pairs (X) C5,C7: 5.. / C5 = 5 => 0 pairs (X) / C7 = 5 => 0 pairs (_) C7,A8: 7.. / C7 = 7 => 0 pairs (X) / A8 = 7 => 0 pairs (_) F7,D8: 7.. / F7 = 7 => 0 pairs (*) / D8 = 7 => 0 pairs (X) C7,F7: 7.. / C7 = 7 => 0 pairs (X) / F7 = 7 => 0 pairs (_) A8,D8: 7.. / A8 = 7 => 0 pairs (*) / D8 = 7 => 0 pairs (X) C3,C7: 7.. / C3 = 7 => 0 pairs (*) / C7 = 7 => 0 pairs (X) B1,B3: 8.. / B1 = 8 => 0 pairs (*) / B3 = 8 => 0 pairs (X) I1,I2: 8.. / I1 = 8 => 0 pairs (X) / I2 = 8 => 14 pairs (_) D2,I2: 8.. / D2 = 8 => 0 pairs (X) / I2 = 8 => 14 pairs (_) B3,D3: 8.. / B3 = 8 => 0 pairs (X) / D3 = 8 => 0 pairs (_) B3,C3: 9.. / B3 = 9 => 0 pairs (*) / C3 = 9 => 0 pairs (X) D2,E2: 9.. / D2 = 9 => 16 pairs (_) / E2 = 9 => 20 pairs (_) I4,I6: 9.. / I4 = 9 => 18 pairs (_) / I6 = 9 => 14 pairs (_) E4,I4: 9.. / E4 = 9 => 14 pairs (_) / I4 = 9 => 18 pairs (_) C3,C5: 9.. / C3 = 9 => 0 pairs (X) / C5 = 9 => 0 pairs (_) D2,D6: 9.. / D2 = 9 => 16 pairs (_) / D6 = 9 => 20 pairs (_) * DURATION: 0:00:48.424934 START: 01:25:05.397190 END: 01:25:53.822124 2019-05-01 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B1,B3,B8,C3,C5,C7,D8,F7,G2,G7,I1,I2,I4,I6,I7) * ..2..679..61....3........56.746.832.8..2..6472.6.7.81.94.36..8...8.42963623189574 * PAIR B1: 5,8 ROW 1 D1: 5,8,4 # reduction candidate for 5,8 D1: 4 # 22 pairs D1: 5,8 # 16 pairs * PAIR G2: 2,4 BLK 3 G3: 2,4,1 # reduction candidate for 2,4 G3: 1 => CTR * ..2.16798.6189.432.89.23156174658329895231647236974815947365281518742963623189574 G3: 2,4 # 14 pairs * PAIR A4: 1,5 BLK 4 B5: 1,5,3,9 # reduction candidate for 1,5 B5: 1,5 => SOLVED * 582436791461795238397821456174658329859213647236974815945367182718542963623189574 B5: 3,9 # 17 pairs * PAIR A4: 1,5 ROW 4 E4: 1,5,9 # reduction candidate for 1,5 E4: 1,5 # 18 pairs E4: 9 # 14 pairs * PAIR A4: 1,5 COL A A8: 1,5,7 # reduction candidate for 1,5 A8: 1,5 => CTR * 452836791761....3..894...561746.832.8.52..6472.6.7481.947365.8.518742963623189574 A8: 7 => SOLVED * 582436791461795238397821456174658329859213647236974815945367182718542963623189574 * PAIR C5: 5,9 BLK 4 B5: 5,9,1,3 # reduction candidate for 5,9 B5: 5,9 # 21 pairs B6: 5,9,3 # reduction candidate for 5,9 B6: 5,9 # 20 pairs * PAIR C5: 5,9 ROW 5 E5: 5,9,1,3 # reduction candidate for 5,9 E5: 5,9 # 19 pairs E5: 1,3 # 18 pairs * PAIR I4: 5,9 ROW 4 E4: 5,9,1 # reduction candidate for 5,9 E4: 1 => CTR * ..2..679..61....3........56.7461832981.2..64723697481594.36..8.158742963623189574 E4: 5,9 # 16 pairs * PAIR I6: 5,9 ROW 6 B6: 5,9,3 # reduction candidate for 5,9 B6: 5,9 # 20 pairs D6: 5,9,4 # reduction candidate for 5,9 D6: 5,9 # 20 pairs * PAIR C7: 5,7 BLK 7 A8: 5,7,1 # reduction candidate for 5,7 A8: 1 => CTR * .82..6791.61....38.9.....56.746.832.8..2..6472.6.7.81.947365.8.158742963623189574 A8: 5,7 # 16 pairs * PAIR B8: 1,5 BLK 7 A8: 1,5,7 # reduction candidate for 1,5 A8: 1,5 => CTR * 452836791761....3..894...561746.832.8.52..6472.6.7481.947365.8.518742963623189574 A8: 7 => SOLVED * 582436791461795238397821456174658329859213647236974815945367182718542963623189574 * PAIR B8: 1,5 COL B B5: 1,5,3,9 # reduction candidate for 1,5 B5: 1,5 => SOLVED * 582436791461795238397821456174658329859213647236974815945367182718542963623189574 B5: 3,9 # 17 pairs * PAIR F7: 5,7 COL F F2: 5,7,4 # reduction candidate for 5,7 F2: 4 => CTR * 4.2.36791.619542383...21456.746.832.8..2..6472.647.81.94.3671827.8.42963623189574 F2: 5,7 # 19 pairs * PAIR D8: 5,7 ROW 8 A8: 5,7,1 # reduction candidate for 5,7 A8: 1 => CTR * .82..6791.61....38.9.....56.746.832.8..2..6472.6.7.81.947365.8.158742963623189574 A8: 5,7 # 16 pairs * PAIR D8: 5,7 COL D D2: 5,7,4,8,9 # reduction candidate for 5,7 D2: 5,7 => SOLVED * 582436791461795238397821456174658329859213647236974815945367182718542963623189574 D2: 4,8,9 # 16 pairs * PAIR G7: 1,2 COL G G3: 1,2,4 # reduction candidate for 1,2 G3: 1,2 # 24 pairs G3: 4 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060730-absurd-base-pr-000.dot * REASONING * DIS # G3: 1 => CTR => G3: 2,4 * PRF # B5: 1,5 => SOL * DIS # A8: 1,5 => CTR => A8: 7 * PRF # A8: 7 => SOL * DIS # E4: 1 => CTR => E4: 5,9 * DIS # A8: 1 => CTR => A8: 5,7 * DIS # A8: 1,5 => CTR => A8: 7 * PRF # A8: 7 => SOL * PRF # B5: 1,5 => SOL * DIS # F2: 4 => CTR => F2: 5,7 * DIS # A8: 1 => CTR => A8: 5,7 * PRF # D2: 5,7 => SOL * CNT 12 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B1,B3,B8,C3,C5,C7,D8,F7,G2,G7,I1,I2,I4,I6,I7) * ..2..679..61....3........56.746.832.8..2..6472.6.7.81.94.36..8...8.42963623189574 * PAIR B1: 5,8 ROW 1 D1: 5,8,4 # reduction candidate for 5,8 D1: 4 # 22 pairs D1: 5,8 # 16 pairs * PAIR G2: 2,4 BLK 3 G3: 2,4,1 # reduction candidate for 2,4 G3: 1 => CTR * ..2.16798.6189.432.89.23156174658329895231647236974815947365281518742963623189574 * PAIR A4: 1,5 BLK 4 B5: 1,5,3,9 # reduction candidate for 1,5 B5: 1,5 => SOLVED * 582436791461795238397821456174658329859213647236974815945367182718542963623189574 * DURATION: 0:00:04.555152 START: 01:26:15.734409 END: 01:26:20.289561 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060730-absurd-base-pr-001.dot * REASONING * DIS # G3: 1 => CTR => G3: 2,4 * PRF G3: 2,4 # B5: 1,5 => SOL * STA G3: 2,4 + B5: 1,5 * CNT 2 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060730, absurd
Solution
position: 582436791461795238397821456174658329859213647236974815945367182718542963623189574 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 # D1: 5,8 => UNS * INC # D1: 4 => UNS * INC # G3: 2,4 => UNS * DIS # G3: 1 => CTR => G3: 2,4 * PRF # B5: 1,5 => SOL * INC # B5: 3,9 => UNS * INC # E4: 1,5 => UNS * INC # E4: 9 => UNS * DIS # A8: 1,5 => CTR => A8: 7 * PRF # A8: 7 => SOL * INC # B5: 5,9 => UNS * INC # B6: 5,9 => UNS * INC # E5: 5,9 => UNS * INC # E5: 1,3 => UNS * INC # E4: 5,9 => UNS * DIS # E4: 1 => CTR => E4: 5,9 * INC # B6: 5,9 => UNS * INC # D6: 5,9 => UNS * INC # A8: 5,7 => UNS * DIS # A8: 1 => CTR => A8: 5,7 * DIS # A8: 1,5 => CTR => A8: 7 * PRF # A8: 7 => SOL * PRF # B5: 1,5 => SOL * INC # B5: 3,9 => UNS * INC # F2: 5,7 => UNS * DIS # F2: 4 => CTR => F2: 5,7 * INC # A8: 5,7 => UNS * DIS # A8: 1 => CTR => A8: 5,7 * PRF # D2: 5,7 => SOL * INC # D2: 4,8,9 => UNS * INC # G3: 1,2 => UNS * INC # G3: 4 => UNS * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D1: 5,8 => UNS * INC # D1: 4 => UNS * INC # G3: 2,4 => UNS * DIS # G3: 1 => CTR => G3: 2,4 * PRF G3: 2,4 # B5: 1,5 => SOL * STA G3: 2,4 + B5: 1,5 * CNT 5 HDP CHAINS / 5 HYP OPENED