Analysis of zz-www.sudokuoftheday.co.uk-20190115-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019
level: medium
position: 7.634..9....87.....8..964..6.....98..3...4..1.95....2.5....8.....7.1.2.8......15. initial
Autosolve
position: 7.634.89....87.....8..964..67....98..3.9.4..1.95.8..2.5....8.....7.1.2.8......15. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # I2: 2,5 => SOL * DIS # I3: 2,5 => CTR => I3: 3,7 * DIS # F1: 2,5 => CTR => F1: 1 * DIS # C2: 1,4 => CTR => C2: 2,3,9 * DIS # F4: 1,2 => CTR => F4: 3 * DIS # D3: 1,2 => CTR => D3: 5 * DIS # G5: 7 => CTR => G5: 5,6 * PRF # G5: 5 => SOL * DIS # H7: 6,7 => CTR => H7: 3,4 * PRF # I6: 3,6 => SOL * PRF # G2: 3,6 => SOL * DIS # G7: 3,6 => CTR => G7: 7 * DIS # H8: 4,6 => CTR => H8: 3 * CNT 13 HDP CHAINS / 37 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # I2: 2,5 => SOL * STA I2: 2,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7.634..9....87.....8..964..6.....98..3...4..1.95....2.5....8.....7.1.2.8......15. | initial |
| 7.634.89....87.....8..964..67....98..3.9.4..1.95.8..2.5....8.....7.1.2.8......15. | autosolve |
| 756341892149872365382596417671253984238964571495187623513628749967415238824739156 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) I1: 2,5 C4: 1,4 A5: 2,8 C5: 2,8 A6: 1,4 D4: 1,2 E5: 5,6 H5: 6,7 G6: 3,6 B8: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H2,H3: 1.. / H2 = 1 => 12 pairs (_) / H3 = 1 => 26 pairs (_) C4,A6: 1.. / C4 = 1 => 0 pairs (*) / A6 = 1 => 0 pairs (X) B7,C7: 1.. / B7 = 1 => 15 pairs (_) / C7 = 1 => 21 pairs (_) B1,F1: 1.. / B1 = 1 => 0 pairs (X) / F1 = 1 => 15 pairs (_) A5,C5: 2.. / A5 = 2 => 9 pairs (_) / C5 = 2 => 9 pairs (_) C4,A6: 4.. / C4 = 4 => 12 pairs (_) / A6 = 4 => 0 pairs (*) I4,I6: 4.. / I4 = 4 => 0 pairs (*) / I6 = 4 => 0 pairs (X) H7,H8: 4.. / H7 = 4 => 11 pairs (_) / H8 = 4 => 0 pairs (X) C4,I4: 4.. / C4 = 4 => 12 pairs (_) / I4 = 4 => 0 pairs (*) A6,I6: 4.. / A6 = 4 => 0 pairs (*) / I6 = 4 => 0 pairs (X) B1,B2: 5.. / B1 = 5 => 13 pairs (_) / B2 = 5 => 0 pairs (X) E4,E5: 5.. / E4 = 5 => 0 pairs (*) / E5 = 5 => 0 pairs (X) I4,G5: 5.. / I4 = 5 => 21 pairs (_) / G5 = 5 => 0 pairs (*) D8,F8: 5.. / D8 = 5 => 0 pairs (X) / F8 = 5 => 20 pairs (_) D3,I3: 5.. / D3 = 5 => 20 pairs (_) / I3 = 5 => 0 pairs (X) E4,I4: 5.. / E4 = 5 => 0 pairs (*) / I4 = 5 => 0 pairs (X) E5,G5: 5.. / E5 = 5 => 21 pairs (_) / G5 = 5 => 0 pairs (*) D3,D8: 5.. / D3 = 5 => 20 pairs (_) / D8 = 5 => 0 pairs (X) G2,G5: 5.. / G2 = 5 => 21 pairs (_) / G5 = 5 => 0 pairs (*) E5,D6: 6.. / E5 = 6 => 0 pairs (*) / D6 = 6 => 0 pairs (X) H3,I3: 7.. / H3 = 7 => 0 pairs (X) / I3 = 7 => 26 pairs (_) D6,F6: 7.. / D6 = 7 => 0 pairs (X) / F6 = 7 => 12 pairs (_) G5,H5: 7.. / G5 = 7 => 0 pairs (X) / H5 = 7 => 26 pairs (_) F6,F9: 7.. / F6 = 7 => 12 pairs (_) / F9 = 7 => 0 pairs (X) G5,G7: 7.. / G5 = 7 => 0 pairs (X) / G7 = 7 => 26 pairs (_) A5,C5: 8.. / A5 = 8 => 9 pairs (_) / C5 = 8 => 9 pairs (_) A9,C9: 8.. / A9 = 8 => 9 pairs (_) / C9 = 8 => 9 pairs (_) A5,A9: 8.. / A5 = 8 => 9 pairs (_) / A9 = 8 => 9 pairs (_) C5,C9: 8.. / C5 = 8 => 9 pairs (_) / C9 = 8 => 9 pairs (_) A2,C2: 9.. / A2 = 9 => 0 pairs (X) / C2 = 9 => 10 pairs (_) F8,F9: 9.. / F8 = 9 => 0 pairs (X) / F9 = 9 => 13 pairs (_) I7,I9: 9.. / I7 = 9 => 10 pairs (_) / I9 = 9 => 0 pairs (X) C7,I7: 9.. / C7 = 9 => 0 pairs (X) / I7 = 9 => 10 pairs (_) A8,F8: 9.. / A8 = 9 => 13 pairs (_) / F8 = 9 => 0 pairs (X) * DURATION: 0:00:36.362018 START: 02:57:48.019197 END: 02:58:24.381215 2019-05-01 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B8,C4,C5,D4,E5,G6,H5,I1) * 7.634.89....87.....8..964..67....98..3.9.4..1.95.8..2.5....8.....7.1.2.8......15. * PAIR I1: 2,5 BLK 3 I2: 2,5,3,6 # reduction candidate for 2,5 I2: 2,5 => SOLVED * 756341892149872365382596417671253984238964571495187623513628749967415238824739156 I2: 3,6 # 11 pairs I3: 2,5,3,7 # reduction candidate for 2,5 I3: 2,5 => CTR * 7.634.89....87.51..8..9647.67....98..3.9.4761.956873245....86...67.1.2.8....6.15. I3: 3,7 # 23 pairs * PAIR I1: 2,5 ROW 1 B1: 2,5,1 # reduction candidate for 2,5 B1: 2,5 # 15 pairs F1: 2,5,1 # reduction candidate for 2,5 F1: 2,5 => CTR * 71634.89545987.362.8.596417674152983.3.9645711957836245.1..87.9..7.1.2.8.....7156 F1: 1 # 15 pairs * PAIR C4: 1,4 COL C C2: 1,4,2,3,9 # reduction candidate for 1,4 C2: 1,4 => CTR * 7.634.89.9..87.....8..964.567..5.98..3.964571.95.8..2.5....87....75192.8......15. C2: 2,3,9 # 10 pairs C7: 1,4,2,3,9 # reduction candidate for 1,4 C7: 1,4 # 14 pairs * PAIR A5: 2,8 COL A A9: 2,8,3,4,9 # reduction candidate for 2,8 A9: 2,8 # 12 pairs A9: 3,4,9 # 10 pairs * PAIR C5: 2,8 COL C C9: 2,8,3,4,9 # reduction candidate for 2,8 C9: 2,8 # 12 pairs C9: 3,4,9 # 9 pairs * PAIR A6: 1,4 COL A A2: 1,4,2,3,9 # reduction candidate for 1,4 A2: 1,4 # 14 pairs A2: 2,3,9 # 10 pairs * PAIR D4: 1,2 BLK 5 F4: 1,2,3 # reduction candidate for 1,2 F4: 1,2 => CTR * 7.634.89....87.....8..964.5674.5.983.3.9645711957836245....87....75192.8.....715. F4: 3 # 14 pairs * PAIR D4: 1,2 COL D D3: 1,2,5 # reduction candidate for 1,2 D3: 1,2 => CTR * 7.634.89....87.....8..964.567..5.98..3.964571.95.8..2.5....87....751.2.8......15. D3: 5 # 20 pairs * PAIR E5: 5,6 ROW 5 G5: 5,6,7 # reduction candidate for 5,6 G5: 7 => CTR * 756341892...872516.8.596473674123985.3.95476119568732451.738649967415238.2..69157 G5: 5,6 # 26 pairs * PAIR H5: 6,7 BLK 6 G5: 6,7,5 # reduction candidate for 6,7 G5: 5 => SOLVED * 756341892149872365382596417671253984238964571495187623513628749967415238824739156 G5: 6,7 # 21 pairs * PAIR H5: 6,7 COL H H7: 6,7,3,4 # reduction candidate for 6,7 H7: 6,7 => CTR * 7.634.89....87.....8..964.567..5.98..3.964571.95.8..2.5....876..6751.248...6.715. H7: 3,4 # 11 pairs * PAIR G6: 3,6 BLK 6 I6: 3,6,4 # reduction candidate for 3,6 I6: 3,6 => SOLVED * 756341892149872365382596417671253984238964571495187623513628749967415238824739156 I6: 4 # 12 pairs * PAIR G6: 3,6 COL G G2: 3,6,5 # reduction candidate for 3,6 G2: 3,6 => SOLVED * 756341892149872365382596417671253984238964571495187623513628749967415238824739156 G2: 5 # 21 pairs G7: 3,6,7 # reduction candidate for 3,6 G7: 3,6 => CTR * 756341892...872516.81596473674123985.3.95476119568732451.738649967415238.2..69157 G7: 7 # 26 pairs * PAIR B8: 4,6 BLK 7 B7: 4,6,1,2 # reduction candidate for 4,6 B7: 4,6 # 24 pairs B9: 4,6,2 # reduction candidate for 4,6 B9: 4,6 # 16 pairs * PAIR B8: 4,6 ROW 8 D8: 4,6,5 # reduction candidate for 4,6 D8: 4,6 # 20 pairs H8: 4,6,3 # reduction candidate for 4,6 H8: 4,6 => CTR * 7.634.89....87.....8..964.567..5.98..3.964571.9578..2.5....87....751.2.8.....715. H8: 3 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190115-absurd-base-pr-000.dot * REASONING * PRF # I2: 2,5 => SOL * DIS # I3: 2,5 => CTR => I3: 3,7 * DIS # F1: 2,5 => CTR => F1: 1 * DIS # C2: 1,4 => CTR => C2: 2,3,9 * DIS # F4: 1,2 => CTR => F4: 3 * DIS # D3: 1,2 => CTR => D3: 5 * DIS # G5: 7 => CTR => G5: 5,6 * PRF # G5: 5 => SOL * DIS # H7: 6,7 => CTR => H7: 3,4 * PRF # I6: 3,6 => SOL * PRF # G2: 3,6 => SOL * DIS # G7: 3,6 => CTR => G7: 7 * DIS # H8: 4,6 => CTR => H8: 3 * CNT 13 HDP CHAINS / 37 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B8,C4,C5,D4,E5,G6,H5,I1) * 7.634.89....87.....8..964..67....98..3.9.4..1.95.8..2.5....8.....7.1.2.8......15. * PAIR I1: 2,5 BLK 3 I2: 2,5,3,6 # reduction candidate for 2,5 I2: 2,5 => SOLVED * 756341892149872365382596417671253984238964571495187623513628749967415238824739156 * DURATION: 0:00:01.852463 START: 02:58:46.684108 END: 02:58:48.536571 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190115-absurd-base-pr-001.dot * REASONING * PRF # I2: 2,5 => SOL * STA I2: 2,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190115, absurd
Solution
position: 756341892149872365382596417671253984238964571495187623513628749967415238824739156 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 # I2: 2,5 => SOL * INC # I2: 3,6 => UNS * DIS # I3: 2,5 => CTR => I3: 3,7 * INC # I3: 3,7 => UNS * INC # B1: 2,5 => UNS * DIS # F1: 2,5 => CTR => F1: 1 * INC # F1: 1 => UNS * DIS # C2: 1,4 => CTR => C2: 2,3,9 * INC # C2: 2,3,9 => UNS * INC # C7: 1,4 => UNS * INC # A9: 2,8 => UNS * INC # A9: 3,4,9 => UNS * INC # C9: 2,8 => UNS * INC # C9: 3,4,9 => UNS * INC # A2: 1,4 => UNS * INC # A2: 2,3,9 => UNS * DIS # F4: 1,2 => CTR => F4: 3 * INC # F4: 3 => UNS * DIS # D3: 1,2 => CTR => D3: 5 * INC # D3: 5 => UNS * INC # G5: 5,6 => UNS * DIS # G5: 7 => CTR => G5: 5,6 * INC # G5: 6,7 => UNS * PRF # G5: 5 => SOL * DIS # H7: 6,7 => CTR => H7: 3,4 * INC # H7: 3,4 => UNS * PRF # I6: 3,6 => SOL * INC # I6: 4 => UNS * PRF # G2: 3,6 => SOL * INC # G2: 5 => UNS * DIS # G7: 3,6 => CTR => G7: 7 * INC # G7: 7 => UNS * INC # B7: 4,6 => UNS * INC # B9: 4,6 => UNS * INC # D8: 4,6 => UNS * DIS # H8: 4,6 => CTR => H8: 3 * INC # H8: 3 => UNS * CNT 37 HDP CHAINS / 37 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # I2: 2,5 => SOL * STA I2: 2,5 * CNT 1 HDP CHAINS / 1 HYP OPENED