Analysis of zz-www.sudokuoftheday.co.uk-20190225-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: 7.....3....5....84.....8..2.61.49..8.9.....5.82..1...3..6.....94...3..1..7.9.1... initial
Autosolve
position: 782...3...15..3784.43..8..2561349278394....5.827.1.943136....29459.3..172789.143. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E2: 6,9 => CTR => E2: 2 * PRF # E2: 2 => SOL * DIS # E2: 9 => CTR => E2: 2,6 * DIS # D8: 2,6 => CTR => D8: 8 * PRF # D8: 8 => SOL * DIS # D3: 5,7 => CTR => D3: 1 * PRF # D3: 1 => SOL * PRF # E7: 5,7 => SOL * DIS # E7: 8 => CTR => E7: 5,7 * DIS # E1: 5 => CTR => E1: 6,9 * PRF # D1: 4,6 => SOL * DIS # D3: 7 => CTR => D3: 1,5 * PRF # D5: 2,7 => SOL * DIS # D5: 8 => CTR => D5: 2,7 * DIS # E5: 2,7 => CTR => E5: 8 * PRF # E5: 8 => SOL * DIS # D1: 5,6 => CTR => D1: 1,4 * PRF # F1: 5,6 => SOL * DIS # D8: 2,6 => CTR => D8: 8 * PRF # D8: 8 => SOL * DIS # E1: 5,6 => CTR => E1: 9 * DIS # D7: 5,8 => CTR => D7: 4,7 * DIS # D8: 2 => CTR => D8: 6,8 * CNT 23 HDP CHAINS / 33 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E2: 6,9 => CTR => E2: 2 * PRF E2: 2 => SOL * STA E2: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7.....3....5....84.....8..2.61.49..8.9.....5.82..1...3..6.....94...3..1..7.9.1... | initial |
| 782...3...15..3784.43..8..2561349278394....5.827.1.943136....29459.3..172789.143. | autosolve |
| 782495361915623784643178592561349278394287156827516943136754829459832617278961435 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) A2: 6,9 A3: 6,9 D2: 2,6 E3: 5,7 H1: 6,9 I1: 1,5 G3: 1,5 H3: 6,9 F5: 2,7 D6: 5,6 F6: 5,6 G5: 1,6 I5: 1,6 F8: 2,6 E9: 5,6 G7: 5,8 G8: 6,8 I9: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,D3: 1.. / D1 = 1 => 0 pairs (X) / D3 = 1 => 0 pairs (_) I1,G3: 1.. / I1 = 1 => 0 pairs (*) / G3 = 1 => 0 pairs (X) G5,I5: 1.. / G5 = 1 => 0 pairs (*) / I5 = 1 => 0 pairs (X) D1,I1: 1.. / D1 = 1 => 0 pairs (X) / I1 = 1 => 0 pairs (_) D3,G3: 1.. / D3 = 1 => 0 pairs (*) / G3 = 1 => 0 pairs (X) G3,G5: 1.. / G3 = 1 => 0 pairs (X) / G5 = 1 => 0 pairs (_) I1,I5: 1.. / I1 = 1 => 0 pairs (*) / I5 = 1 => 0 pairs (X) D2,E2: 2.. / D2 = 2 => 0 pairs (X) / E2 = 2 => 0 pairs (_) D8,F8: 2.. / D8 = 2 => 0 pairs (X) / F8 = 2 => 23 pairs (_) E2,E5: 2.. / E2 = 2 => 0 pairs (*) / E5 = 2 => 0 pairs (X) F5,F8: 2.. / F5 = 2 => 0 pairs (X) / F8 = 2 => 23 pairs (_) D1,F1: 4.. / D1 = 4 => 0 pairs (*) / F1 = 4 => 0 pairs (X) D7,F7: 4.. / D7 = 4 => 19 pairs (_) / F7 = 4 => 0 pairs (*) D1,D7: 4.. / D1 = 4 => 0 pairs (*) / D7 = 4 => 0 pairs (X) F1,F7: 4.. / F1 = 4 => 19 pairs (_) / F7 = 4 => 0 pairs (*) I1,G3: 5.. / I1 = 5 => 0 pairs (X) / G3 = 5 => 0 pairs (_) D6,F6: 5.. / D6 = 5 => 20 pairs (_) / F6 = 5 => 0 pairs (X) G7,I9: 5.. / G7 = 5 => 0 pairs (X) / I9 = 5 => 0 pairs (_) E9,I9: 5.. / E9 = 5 => 0 pairs (X) / I9 = 5 => 0 pairs (_) G3,G7: 5.. / G3 = 5 => 0 pairs (*) / G7 = 5 => 0 pairs (X) I1,I9: 5.. / I1 = 5 => 0 pairs (X) / I9 = 5 => 0 pairs (_) A2,A3: 6.. / A2 = 6 => 0 pairs (X) / A3 = 6 => 16 pairs (_) H1,H3: 6.. / H1 = 6 => 16 pairs (_) / H3 = 6 => 0 pairs (X) D6,F6: 6.. / D6 = 6 => 0 pairs (X) / F6 = 6 => 20 pairs (_) G5,I5: 6.. / G5 = 6 => 0 pairs (X) / I5 = 6 => 0 pairs (_) G8,I9: 6.. / G8 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) A3,H3: 6.. / A3 = 6 => 16 pairs (_) / H3 = 6 => 0 pairs (X) E9,I9: 6.. / E9 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) G5,G8: 6.. / G5 = 6 => 0 pairs (X) / G8 = 6 => 0 pairs (_) I5,I9: 6.. / I5 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) D3,E3: 7.. / D3 = 7 => 0 pairs (X) / E3 = 7 => 24 pairs (_) F5,F7: 7.. / F5 = 7 => 23 pairs (_) / F7 = 7 => 0 pairs (X) D5,E5: 8.. / D5 = 8 => 0 pairs (X) / E5 = 8 => 0 pairs (_) G7,G8: 8.. / G7 = 8 => 0 pairs (*) / G8 = 8 => 0 pairs (X) D8,G8: 8.. / D8 = 8 => 0 pairs (*) / G8 = 8 => 0 pairs (X) E5,E7: 8.. / E5 = 8 => 0 pairs (*) / E7 = 8 => 0 pairs (X) A2,A3: 9.. / A2 = 9 => 16 pairs (_) / A3 = 9 => 0 pairs (X) E1,E2: 9.. / E1 = 9 => 16 pairs (_) / E2 = 9 => 0 pairs (X) H1,H3: 9.. / H1 = 9 => 0 pairs (X) / H3 = 9 => 16 pairs (_) E1,H1: 9.. / E1 = 9 => 16 pairs (_) / H1 = 9 => 0 pairs (X) A2,E2: 9.. / A2 = 9 => 16 pairs (_) / E2 = 9 => 0 pairs (X) A3,H3: 9.. / A3 = 9 => 0 pairs (X) / H3 = 9 => 16 pairs (_) * DURATION: 0:01:13.003700 START: 04:00:07.909716 END: 04:01:20.913416 2019-05-01 * CP COUNT: (42) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,D2,D6,E3,E9,F5,F6,F8,G3,G5,G7,G8,H1,H3,I1,I5,I9) * 782...3...15..3784.43..8..2561349278394....5.827.1.943136....29459.3..172789.143. * PAIR A2: 6,9 ROW 2 E2: 6,9,2 # reduction candidate for 6,9 E2: 6,9 => CTR * 782...3.5.152.3784.435.8..2561349278394.27.5.827.1.943136.8.529459632817278951436 E2: 2 => SOLVED * 782495361915623784643178592561349278394287156827516943136754829459832617278961435 * PAIR D2: 2,6 BLK 2 E2: 2,6,9 # reduction candidate for 2,6 E2: 9 => CTR * 782.6.3956152937849435.8.62561349278394.27.5.827.1.943136.8.529459632817278951436 E2: 2,6 # 16 pairs * PAIR D2: 2,6 COL D D8: 2,6,8 # reduction candidate for 2,6 D8: 2,6 => CTR * 7821.43.5.15..3784.435781.2561349278394...65182761594313648752945923.817278951436 D8: 8 => SOLVED * 782495361915623784643178592561349278394287156827516943136754829459832617278961435 * PAIR E3: 5,7 BLK 2 D3: 5,7,1 # reduction candidate for 5,7 D3: 5,7 => CTR * 7821.43.5.15..3784.435781.2561349278394...651827.1.9431364..529459.3.817278951436 D3: 1 => SOLVED * 782495361915623784643178592561349278394287156827516943136754829459832617278961435 * PAIR E3: 5,7 COL E E7: 5,7,8 # reduction candidate for 5,7 E7: 5,7 => SOLVED * 782495361915623784643178592561349278394287156827516943136754829459832617278961435 E7: 8 => CTR * 782...3.5.15..3784.435781.2561349278394827651827615943136.8.529459.3.817278951436 * PAIR H1: 6,9 ROW 1 E1: 6,9,5 # reduction candidate for 6,9 E1: 5 => CTR * 782.5.391.15.93784943178562561349278394.27156827.1.94313678..29459.3..172789.143. E1: 6,9 # 20 pairs * PAIR I1: 1,5 ROW 1 D1: 1,5,4,6 # reduction candidate for 1,5 D1: 4,6 => SOLVED * 782495361915623784643178592561349278394287156827516943136754829459832617278961435 D1: 1,5 # 21 pairs * PAIR G3: 1,5 ROW 3 D3: 1,5,7 # reduction candidate for 1,5 D3: 7 => CTR * 7821.43.5.15..3784.437581.2561349278394...651827.1.9431364.5829459.3..172789.143. D3: 1,5 # 24 pairs * PAIR F5: 2,7 BLK 5 D5: 2,7,8 # reduction candidate for 2,7 D5: 2,7 => SOLVED * 782495361915623784643178592561349278394287156827516943136754829459832617278961435 D5: 8 => CTR * 782...3.5.15..3784.435781.2561349278394827651827615943136.8.529459.3.817278951436 E5: 2,7,8 # reduction candidate for 2,7 E5: 2,7 => CTR * 782...3.5.15..3784.435781.2561349278394827651827615943136.8.529459.3.817278951436 E5: 8 => SOLVED * 782495361915623784643178592561349278394287156827516943136754829459832617278961435 * PAIR D6: 5,6 COL D D1: 5,6,1,4 # reduction candidate for 5,6 D1: 5,6 => CTR * 782..43.1.15..3784.431785.2561349278394...156827.1.9431364.7829459832.172789.143. D1: 1,4 # 19 pairs * PAIR F6: 5,6 COL F F1: 5,6,4 # reduction candidate for 5,6 F1: 5,6 => SOLVED * 782495361915623784643178592561349278394287156827516943136754829459832617278961435 F1: 4 # 19 pairs * PAIR F8: 2,6 BLK 8 D8: 2,6,8 # reduction candidate for 2,6 D8: 2,6 => CTR * 7821.43.5.15..3784.435781.2561349278394...65182761594313648752945923.817278951436 D8: 8 => SOLVED * 782495361915623784643178592561349278394287156827516943136754829459832617278961435 * PAIR E9: 5,6 COL E E1: 5,6,9 # reduction candidate for 5,6 E1: 5,6 => CTR * 782.6.395615293784943578162561349278394827.5.827.1.943136.8.529459.32817278951436 E1: 9 # 16 pairs * PAIR G7: 5,8 ROW 7 D7: 5,8,4,7 # reduction candidate for 5,8 D7: 5,8 => CTR * 7824..3.1.15..3784.431785.2561349278394782.5.827.1.943136....29459.3..172789.143. D7: 4,7 # 19 pairs E7: 5,8,7 # reduction candidate for 5,8 E7: 5,8 # 24 pairs * PAIR G8: 6,8 ROW 8 D8: 6,8,2 # reduction candidate for 6,8 D8: 2 => CTR * 782...3.5.156237846435.8..2561349278394....5.827.1.943136....29459236817278951436 D8: 6,8 # 23 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190225-absurd-base-pr-000.dot * REASONING * DIS # E2: 6,9 => CTR => E2: 2 * PRF # E2: 2 => SOL * DIS # E2: 9 => CTR => E2: 2,6 * DIS # D8: 2,6 => CTR => D8: 8 * PRF # D8: 8 => SOL * DIS # D3: 5,7 => CTR => D3: 1 * PRF # D3: 1 => SOL * PRF # E7: 5,7 => SOL * DIS # E7: 8 => CTR => E7: 5,7 * DIS # E1: 5 => CTR => E1: 6,9 * PRF # D1: 4,6 => SOL * DIS # D3: 7 => CTR => D3: 1,5 * PRF # D5: 2,7 => SOL * DIS # D5: 8 => CTR => D5: 2,7 * DIS # E5: 2,7 => CTR => E5: 8 * PRF # E5: 8 => SOL * DIS # D1: 5,6 => CTR => D1: 1,4 * PRF # F1: 5,6 => SOL * DIS # D8: 2,6 => CTR => D8: 8 * PRF # D8: 8 => SOL * DIS # E1: 5,6 => CTR => E1: 9 * DIS # D7: 5,8 => CTR => D7: 4,7 * DIS # D8: 2 => CTR => D8: 6,8 * CNT 23 HDP CHAINS / 33 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,D2,D6,E3,E9,F5,F6,F8,G3,G5,G7,G8,H1,H3,I1,I5,I9) * 782...3...15..3784.43..8..2561349278394....5.827.1.943136....29459.3..172789.143. * PAIR A2: 6,9 ROW 2 E2: 6,9,2 # reduction candidate for 6,9 E2: 6,9 => CTR * 782...3.5.152.3784.435.8..2561349278394.27.5.827.1.943136.8.529459632817278951436 E2: 2 => SOLVED * 782495361915623784643178592561349278394287156827516943136754829459832617278961435 * DURATION: 0:00:02.806993 START: 04:01:55.785756 END: 04:01:58.592749 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190225-absurd-base-pr-001.dot * REASONING * DIS # E2: 6,9 => CTR => E2: 2 * PRF E2: 2 => SOL * STA E2: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190225, absurd
Solution
position: 782495361915623784643178592561349278394287156827516943136754829459832617278961435 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 # E2: 6,9 => CTR => E2: 2 * PRF # E2: 2 => SOL * INC # E2: 2,6 => UNS * DIS # E2: 9 => CTR => E2: 2,6 * DIS # D8: 2,6 => CTR => D8: 8 * PRF # D8: 8 => SOL * DIS # D3: 5,7 => CTR => D3: 1 * PRF # D3: 1 => SOL * PRF # E7: 5,7 => SOL * DIS # E7: 8 => CTR => E7: 5,7 * INC # E1: 6,9 => UNS * DIS # E1: 5 => CTR => E1: 6,9 * INC # D1: 1,5 => UNS * PRF # D1: 4,6 => SOL * INC # D3: 1,5 => UNS * DIS # D3: 7 => CTR => D3: 1,5 * PRF # D5: 2,7 => SOL * DIS # D5: 8 => CTR => D5: 2,7 * DIS # E5: 2,7 => CTR => E5: 8 * PRF # E5: 8 => SOL * DIS # D1: 5,6 => CTR => D1: 1,4 * INC # D1: 1,4 => UNS * PRF # F1: 5,6 => SOL * INC # F1: 4 => UNS * DIS # D8: 2,6 => CTR => D8: 8 * PRF # D8: 8 => SOL * DIS # E1: 5,6 => CTR => E1: 9 * INC # E1: 9 => UNS * DIS # D7: 5,8 => CTR => D7: 4,7 * INC # D7: 4,7 => UNS * INC # E7: 5,8 => UNS * INC # D8: 6,8 => UNS * DIS # D8: 2 => CTR => D8: 6,8 * CNT 33 HDP CHAINS / 33 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # E2: 6,9 => CTR => E2: 2 * PRF E2: 2 => SOL * STA E2: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED