Analysis of zz-www.sudokuoftheday.co.uk-20190223-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019
level: medium
position: ..3.....6..6...95.57.19.8.................568.1.3.9..7.6...1.9.8.......59..7..4.. initial
Autosolve
position: .93.....6.86...95.57.1968.....6....9..9.1.56861.3.9247.6...1.9.8..9..6.59..76.48. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A1: 2,4 => SOL * DIS # A1: 1 => CTR => A1: 2,4 * DIS # A2: 2,4 => CTR => A2: 1 * PRF # A2: 1 => SOL * DIS # A2: 2,4 => CTR => A2: 1 * PRF # A2: 1 => SOL * PRF # H1: 1,7 => SOL * DIS # H1: 2 => CTR => H1: 1,7 * DIS # A2: 2 => CTR => A2: 1,4 * DIS # F5: 2,4 => CTR => F5: 7 * DIS # A5: 2,4 => CTR => A5: 3,7 * DIS # I9: 2,3 => CTR => I9: 1 * PRF # I9: 1 => SOL * DIS # A7: 2,3 => CTR => A7: 4,7 * DIS # E7: 2,3 => CTR => E7: 4,5,8 * PRF # H1: 1,7 => SOL * DIS # H1: 2 => CTR => H1: 1,7 * CNT 17 HDP CHAINS / 41 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A1: 2,4 => SOL * STA A1: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..3.....6..6...95.57.19.8.................568.1.3.9..7.6...1.9.8.......59..7..4.. | initial |
| .93.....6.86...95.57.1968.....6....9..9.1.56861.3.9247.6...1.9.8..9..6.59..76.48. | autosolve |
| 293584716186273954574196823457628139329417568618359247765841392841932675932765481 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) C3: 2,4 D1: 5,8 D2: 2,4 E2: 3,7 F2: 3,7 G1: 1,7 I2: 1,4 H3: 2,3 I3: 3,4 C6: 5,8 D5: 2,4 E6: 5,8 G4: 1,3 H4: 1,3 C8: 1,7 D7: 5,8 G7: 3,7 I7: 2,3 H8: 1,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A2: 1.. / A1 = 1 => 0 pairs (X) / A2 = 1 => 0 pairs (_) G4,H4: 1.. / G4 = 1 => 0 pairs (*) / H4 = 1 => 0 pairs (X) C8,C9: 1.. / C8 = 1 => 0 pairs (*) / C9 = 1 => 0 pairs (X) H8,I9: 1.. / H8 = 1 => 0 pairs (X) / I9 = 1 => 0 pairs (_) A2,I2: 1.. / A2 = 1 => 0 pairs (*) / I2 = 1 => 0 pairs (X) C8,H8: 1.. / C8 = 1 => 0 pairs (*) / H8 = 1 => 0 pairs (X) C9,I9: 1.. / C9 = 1 => 0 pairs (X) / I9 = 1 => 0 pairs (_) G1,G4: 1.. / G1 = 1 => 0 pairs (X) / G4 = 1 => 0 pairs (_) I2,I9: 1.. / I2 = 1 => 0 pairs (X) / I9 = 1 => 0 pairs (_) H1,H3: 2.. / H1 = 2 => 0 pairs (X) / H3 = 2 => 0 pairs (_) I7,I9: 2.. / I7 = 2 => 19 pairs (_) / I9 = 2 => 0 pairs (X) A2,D2: 2.. / A2 = 2 => 0 pairs (X) / D2 = 2 => 21 pairs (_) C3,H3: 2.. / C3 = 2 => 0 pairs (X) / H3 = 2 => 0 pairs (_) D2,D5: 2.. / D2 = 2 => 21 pairs (_) / D5 = 2 => 0 pairs (X) E2,F2: 3.. / E2 = 3 => 0 pairs (X) / F2 = 3 => 19 pairs (_) H3,I3: 3.. / H3 = 3 => 0 pairs (X) / I3 = 3 => 0 pairs (_) A5,B5: 3.. / A5 = 3 => 20 pairs (_) / B5 = 3 => 0 pairs (X) G4,H4: 3.. / G4 = 3 => 0 pairs (X) / H4 = 3 => 0 pairs (_) A5,A7: 3.. / A5 = 3 => 20 pairs (_) / A7 = 3 => 0 pairs (X) G4,G7: 3.. / G4 = 3 => 0 pairs (X) / G7 = 3 => 0 pairs (_) H3,H4: 3.. / H3 = 3 => 0 pairs (X) / H4 = 3 => 0 pairs (_) I2,I3: 4.. / I2 = 4 => 0 pairs (*) / I3 = 4 => 0 pairs (X) C3,I3: 4.. / C3 = 4 => 0 pairs (*) / I3 = 4 => 0 pairs (X) D2,D5: 4.. / D2 = 4 => 0 pairs (X) / D5 = 4 => 21 pairs (_) C6,E6: 5.. / C6 = 5 => 21 pairs (_) / E6 = 5 => 17 pairs (_) B4,B9: 5.. / B4 = 5 => 18 pairs (_) / B9 = 5 => 29 pairs (_) D1,D7: 5.. / D1 = 5 => 17 pairs (_) / D7 = 5 => 19 pairs (_) E2,F2: 7.. / E2 = 7 => 19 pairs (_) / F2 = 7 => 0 pairs (X) G1,H1: 7.. / G1 = 7 => 0 pairs (*) / H1 = 7 => 0 pairs (X) G7,H8: 7.. / G7 = 7 => 0 pairs (X) / H8 = 7 => 0 pairs (_) A5,F5: 7.. / A5 = 7 => 0 pairs (X) / F5 = 7 => 19 pairs (_) C8,H8: 7.. / C8 = 7 => 0 pairs (X) / H8 = 7 => 0 pairs (_) E2,E4: 7.. / E2 = 7 => 19 pairs (_) / E4 = 7 => 0 pairs (X) G1,G7: 7.. / G1 = 7 => 0 pairs (*) / G7 = 7 => 0 pairs (X) H1,H8: 7.. / H1 = 7 => 0 pairs (X) / H8 = 7 => 0 pairs (_) C4,C6: 8.. / C4 = 8 => 21 pairs (_) / C6 = 8 => 17 pairs (_) D7,E7: 8.. / D7 = 8 => 17 pairs (_) / E7 = 8 => 19 pairs (_) C6,E6: 8.. / C6 = 8 => 17 pairs (_) / E6 = 8 => 21 pairs (_) D1,D7: 8.. / D1 = 8 => 19 pairs (_) / D7 = 8 => 17 pairs (_) F1,F4: 8.. / F1 = 8 => 18 pairs (_) / F4 = 8 => 17 pairs (_) * DURATION: 0:01:04.460033 START: 03:56:55.624612 END: 03:58:00.084645 2019-05-01 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C3,C6,C8,D1,D2,D5,D7,E2,E6,F2,G1,G4,G7,H3,H4,H8,I2,I3,I7) * .93.....6.86...95.57.1968.....6....9..9.1.56861.3.9247.6...1.9.8..9..6.59..76.48. * PAIR C3: 2,4 BLK 1 A1: 2,4,1 # reduction candidate for 2,4 A1: 2,4 => SOLVED * 293584716186273954574196823457628139329417568618359247765841392841932675932765481 A1: 1 => CTR * 193...726.862..95157219683....6....9..9.1.56861.3.9247.6...1.9.8..9..6.59..76.48. A2: 2,4,1 # reduction candidate for 2,4 A2: 2,4 => CTR * 193...726.862..95157219683....6....9..9.1.56861.3.9247.6...1.9.8..9..6.59..76.48. A2: 1 => SOLVED * 293584716186273954574196823457628139329417568618359247765841392841932675932765481 * PAIR C3: 2,4 COL C C4: 2,4,5,7,8 # reduction candidate for 2,4 C4: 2,4 # 21 pairs C7: 2,4,5,7 # reduction candidate for 2,4 C7: 2,4 # 28 pairs * PAIR D1: 5,8 BLK 2 E1: 5,8,2,4 # reduction candidate for 5,8 E1: 5,8 # 18 pairs F1: 5,8,2,4 # reduction candidate for 5,8 F1: 5,8 # 21 pairs * PAIR D2: 2,4 BLK 2 E1: 2,4,5,8 # reduction candidate for 2,4 E1: 2,4 # 21 pairs F1: 2,4,5,8 # reduction candidate for 2,4 F1: 2,4 # 18 pairs * PAIR D2: 2,4 ROW 2 A2: 2,4,1 # reduction candidate for 2,4 A2: 2,4 => CTR * 193...726.862..95157219683....6....9..9.1.56861.3.9247.6...1.9.8..9..6.59..76.48. A2: 1 => SOLVED * 293584716186273954574196823457628139329417568618359247765841392841932675932765481 * PAIR G1: 1,7 BLK 3 H1: 1,7,2 # reduction candidate for 1,7 H1: 1,7 => SOLVED * 293584716186273954574196823457628139329417568618359247765841392841932675932765481 H1: 2 => CTR * .93...726.862..95157219683....6....9..9.1.56861.3.9247.6...1.9.8..9..6.59..76.48. * PAIR I2: 1,4 ROW 2 A2: 1,4,2 # reduction candidate for 1,4 A2: 2 => CTR * 193...726286...95.57.1968.....6....9..9.1.56861.3.9247.6...1.9.8..9..6.59..76.48. A2: 1,4 # 21 pairs * PAIR C6: 5,8 BLK 4 C4: 5,8,2,4,7 # reduction candidate for 5,8 C4: 5,8 # 29 pairs C4: 2,4,7 # 18 pairs * PAIR D5: 2,4 BLK 5 E4: 2,4,5,7,8 # reduction candidate for 2,4 E4: 2,4 # 21 pairs F4: 2,4,5,7,8 # reduction candidate for 2,4 F4: 2,4 # 18 pairs F5: 2,4,7 # reduction candidate for 2,4 F5: 2,4 => CTR * .93.....6.86...95.57.1968.....6....9739.1.56861.3.924736...17928.79..6159.176.483 F5: 7 # 19 pairs * PAIR D5: 2,4 ROW 5 A5: 2,4,3,7 # reduction candidate for 2,4 A5: 2,4 => CTR * .93.....6.86...95.57.1968.....6....9.39.1756861.3.924736...17928.79..6159.176.483 A5: 3,7 # 20 pairs B5: 2,4,3 # reduction candidate for 2,4 B5: 2,4 # 20 pairs * PAIR E6: 5,8 BLK 5 E4: 5,8,2,4,7 # reduction candidate for 5,8 E4: 5,8 # 17 pairs F4: 5,8,2,4,7 # reduction candidate for 5,8 F4: 5,8 # 20 pairs * PAIR E6: 5,8 COL E E1: 5,8,2,4 # reduction candidate for 5,8 E1: 5,8 # 18 pairs E7: 5,8,2,3,4 # reduction candidate for 5,8 E7: 5,8 # 26 pairs * PAIR D7: 5,8 BLK 8 E7: 5,8,2,3,4 # reduction candidate for 5,8 E7: 5,8 # 26 pairs E7: 2,3,4 # 17 pairs * PAIR G7: 3,7 ROW 7 A7: 3,7,2,4 # reduction candidate for 3,7 A7: 3,7 # 21 pairs A7: 2,4 # 21 pairs * PAIR I7: 2,3 BLK 9 I9: 2,3,1 # reduction candidate for 2,3 I9: 2,3 => CTR * .93.....6.86...95157.1968.4...6..139..9.1.56861.3.9247.6...13928..9..6.59..76.48. I9: 1 => SOLVED * 293584716186273954574196823457628139329417568618359247765841392841932675932765481 * PAIR I7: 2,3 ROW 7 A7: 2,3,4,7 # reduction candidate for 2,3 A7: 2,3 => CTR * .93.....6.86...95.57.1968.....6..319..9.1.56861.3.9247.6...179.8..9..6.59..76.48. A7: 4,7 # 21 pairs E7: 2,3,4,5,8 # reduction candidate for 2,3 E7: 2,3 => CTR * .935....6.86...95.57.1968...5.6....9..9.1.5686183592474658.179.8.79..6159.176548. E7: 4,5,8 # 19 pairs * PAIR H8: 1,7 COL H H1: 1,7,2 # reduction candidate for 1,7 H1: 1,7 => SOLVED * 293584716186273954574196823457628139329417568618359247765841392841932675932765481 H1: 2 => CTR * .93...726.862..95157219683....6....9..9.1.56861.3.9247.6...1.9.8..9..6.59..76.48. * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190223-absurd-base-pr-000.dot * REASONING * PRF # A1: 2,4 => SOL * DIS # A1: 1 => CTR => A1: 2,4 * DIS # A2: 2,4 => CTR => A2: 1 * PRF # A2: 1 => SOL * DIS # A2: 2,4 => CTR => A2: 1 * PRF # A2: 1 => SOL * PRF # H1: 1,7 => SOL * DIS # H1: 2 => CTR => H1: 1,7 * DIS # A2: 2 => CTR => A2: 1,4 * DIS # F5: 2,4 => CTR => F5: 7 * DIS # A5: 2,4 => CTR => A5: 3,7 * DIS # I9: 2,3 => CTR => I9: 1 * PRF # I9: 1 => SOL * DIS # A7: 2,3 => CTR => A7: 4,7 * DIS # E7: 2,3 => CTR => E7: 4,5,8 * PRF # H1: 1,7 => SOL * DIS # H1: 2 => CTR => H1: 1,7 * CNT 17 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C3,C6,C8,D1,D2,D5,D7,E2,E6,F2,G1,G4,G7,H3,H4,H8,I2,I3,I7) * .93.....6.86...95.57.1968.....6....9..9.1.56861.3.9247.6...1.9.8..9..6.59..76.48. * PAIR C3: 2,4 BLK 1 A1: 2,4,1 # reduction candidate for 2,4 A1: 2,4 => SOLVED * 293584716186273954574196823457628139329417568618359247765841392841932675932765481 * DURATION: 0:00:02.096228 START: 03:58:36.575768 END: 03:58:38.671996 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190223-absurd-base-pr-001.dot * REASONING * PRF # A1: 2,4 => SOL * STA A1: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190223, absurd
Solution
position: 293584716186273954574196823457628139329417568618359247765841392841932675932765481 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:
* PRF # A1: 2,4 => SOL * DIS # A1: 1 => CTR => A1: 2,4 * DIS # A2: 2,4 => CTR => A2: 1 * PRF # A2: 1 => SOL * INC # C4: 2,4 => UNS * INC # C7: 2,4 => UNS * INC # E1: 5,8 => UNS * INC # F1: 5,8 => UNS * INC # E1: 2,4 => UNS * INC # F1: 2,4 => UNS * DIS # A2: 2,4 => CTR => A2: 1 * PRF # A2: 1 => SOL * PRF # H1: 1,7 => SOL * DIS # H1: 2 => CTR => H1: 1,7 * INC # A2: 1,4 => UNS * DIS # A2: 2 => CTR => A2: 1,4 * INC # C4: 5,8 => UNS * INC # C4: 2,4,7 => UNS * INC # E4: 2,4 => UNS * INC # F4: 2,4 => UNS * DIS # F5: 2,4 => CTR => F5: 7 * INC # F5: 7 => UNS * DIS # A5: 2,4 => CTR => A5: 3,7 * INC # A5: 3,7 => UNS * INC # B5: 2,4 => UNS * INC # E4: 5,8 => UNS * INC # F4: 5,8 => UNS * INC # E1: 5,8 => UNS * INC # E7: 5,8 => UNS * INC # E7: 5,8 => UNS * INC # E7: 2,3,4 => UNS * INC # A7: 3,7 => UNS * INC # A7: 2,4 => UNS * DIS # I9: 2,3 => CTR => I9: 1 * PRF # I9: 1 => SOL * DIS # A7: 2,3 => CTR => A7: 4,7 * INC # A7: 4,7 => UNS * DIS # E7: 2,3 => CTR => E7: 4,5,8 * INC # E7: 4,5,8 => UNS * PRF # H1: 1,7 => SOL * DIS # H1: 2 => CTR => H1: 1,7 * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A1: 2,4 => SOL * STA A1: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED