Analysis of zz-www.sudokuoftheday.co.uk-20190310-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019
level: medium
position: ..31.....8...9.4.1.4....69.39.5.1.6........2...5.7.....5.9....8.2.....3...9...54. initial
Autosolve
position: 9631...8.872.9.451541.8.69339.52186..1.....25285.7..1..5.9...78.28....3..39...54. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E8: 4,5 => CTR => E8: 1,6 * DIS # F8: 7 => CTR => F8: 4,5 * DIS # D6: 4 => CTR => D6: 3,6 * DIS # F6: 3,6 => CTR => F6: 4,9 * PRF # D9: 8 => SOL * PRF # F9: 2,7 => SOL * DIS # C5: 6 => CTR => C5: 4,7 * DIS # C5: 4,6 => CTR => C5: 7 * PRF # C5: 7 => SOL * PRF # A8: 4,6 => SOL * PRF # D5: 3,4 => SOL * DIS # F5: 3,4 => CTR => F5: 8,9 * DIS # D6: 3,4 => CTR => D6: 6 * DIS # E7: 1,6 => CTR => E7: 3,4 * PRF # G5: 3,9 => SOL * DIS # G5: 7 => CTR => G5: 3,9 * PRF # F6: 3,9 => SOL * DIS # F6: 3,6 => CTR => F6: 4,9 * PRF # A8: 4,6 => SOL * PRF # E7: 4,6 => SOL * DIS # C5: 4,6 => CTR => C5: 7 * PRF # C5: 7 => SOL * DIS # F8: 4,7 => CTR => F8: 5 * DIS # A8: 1,6 => CTR => A8: 4,7 * DIS # E7: 1,6 => CTR => E7: 3,4 * DIS # A9: 1,6 => CTR => A9: 7 * PRF # A9: 7 => SOL * CNT 27 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E8: 4,5 => CTR => E8: 1,6 * PRF E8: 1,6 # D6: 3,6 => SOL * STA E8: 1,6 + D6: 3,6 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..31.....8...9.4.1.4....69.39.5.1.6........2...5.7.....5.9....8.2.....3...9...54. | initial |
| 9631...8.872.9.451541.8.69339.52186..1.....25285.7..1..5.9...78.28....3..39...54. | autosolve |
| 963154782872396451541287693394521867617438925285679314156943278428765139739812546 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (21) E1: 4,5 F1: 4,5 D2: 3,6 F2: 3,6 D3: 2,7 F3: 2,7 G1: 2,7 I1: 2,7 C4: 4,7 A5: 4,6 E5: 3,4 I4: 4,7 G6: 3,9 I6: 4,9 C7: 4,6 D8: 4,7 E9: 1,6 G7: 1,2 G8: 1,9 I8: 6,9 I9: 2,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G7,G8: 1.. / G7 = 1 => 0 pairs (X) / G8 = 1 => 0 pairs (_) A9,E9: 1.. / A9 = 1 => 0 pairs (X) / E9 = 1 => 21 pairs (_) D3,F3: 2.. / D3 = 2 => 23 pairs (_) / F3 = 2 => 0 pairs (X) G1,I1: 2.. / G1 = 2 => 0 pairs (X) / I1 = 2 => 0 pairs (_) G7,I9: 2.. / G7 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) F7,G7: 2.. / F7 = 2 => 0 pairs (X) / G7 = 2 => 0 pairs (_) D3,D9: 2.. / D3 = 2 => 23 pairs (_) / D9 = 2 => 0 pairs (X) G1,G7: 2.. / G1 = 2 => 0 pairs (X) / G7 = 2 => 0 pairs (_) I1,I9: 2.. / I1 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) D2,F2: 3.. / D2 = 3 => 20 pairs (_) / F2 = 3 => 0 pairs (X) G5,G6: 3.. / G5 = 3 => 0 pairs (X) / G6 = 3 => 22 pairs (_) E7,F7: 3.. / E7 = 3 => 0 pairs (X) / F7 = 3 => 0 pairs (_) E5,E7: 3.. / E5 = 3 => 0 pairs (*) / E7 = 3 => 0 pairs (X) E1,F1: 4.. / E1 = 4 => 0 pairs (X) / F1 = 4 => 20 pairs (_) I4,I6: 4.. / I4 = 4 => 0 pairs (X) / I6 = 4 => 0 pairs (_) C4,I4: 4.. / C4 = 4 => 0 pairs (*) / I4 = 4 => 0 pairs (X) E1,F1: 5.. / E1 = 5 => 20 pairs (_) / F1 = 5 => 0 pairs (X) E8,F8: 5.. / E8 = 5 => 0 pairs (X) / F8 = 5 => 20 pairs (_) E1,E8: 5.. / E1 = 5 => 20 pairs (_) / E8 = 5 => 0 pairs (X) F1,F8: 5.. / F1 = 5 => 0 pairs (X) / F8 = 5 => 20 pairs (_) D2,F2: 6.. / D2 = 6 => 0 pairs (X) / F2 = 6 => 20 pairs (_) A5,C5: 6.. / A5 = 6 => 22 pairs (_) / C5 = 6 => 0 pairs (X) D6,F6: 6.. / D6 = 6 => 20 pairs (_) / F6 = 6 => 0 pairs (X) I8,I9: 6.. / I8 = 6 => 0 pairs (X) / I9 = 6 => 0 pairs (_) C5,C7: 6.. / C5 = 6 => 0 pairs (X) / C7 = 6 => 22 pairs (_) D2,D6: 6.. / D2 = 6 => 0 pairs (X) / D6 = 6 => 20 pairs (_) F2,F6: 6.. / F2 = 6 => 20 pairs (_) / F6 = 6 => 0 pairs (X) D3,F3: 7.. / D3 = 7 => 0 pairs (X) / F3 = 7 => 23 pairs (_) G1,I1: 7.. / G1 = 7 => 0 pairs (*) / I1 = 7 => 0 pairs (X) C4,C5: 7.. / C4 = 7 => 0 pairs (X) / C5 = 7 => 0 pairs (_) I4,G5: 7.. / I4 = 7 => 0 pairs (*) / G5 = 7 => 0 pairs (X) A8,A9: 7.. / A8 = 7 => 0 pairs (X) / A9 = 7 => 0 pairs (_) C4,I4: 7.. / C4 = 7 => 0 pairs (X) / I4 = 7 => 0 pairs (_) C5,G5: 7.. / C5 = 7 => 0 pairs (*) / G5 = 7 => 0 pairs (X) G1,G5: 7.. / G1 = 7 => 0 pairs (*) / G5 = 7 => 0 pairs (X) I1,I4: 7.. / I1 = 7 => 0 pairs (X) / I4 = 7 => 0 pairs (_) D5,F5: 8.. / D5 = 8 => 24 pairs (_) / F5 = 8 => 0 pairs (*) D9,F9: 8.. / D9 = 8 => 0 pairs (*) / F9 = 8 => 0 pairs (X) D5,D9: 8.. / D5 = 8 => 24 pairs (_) / D9 = 8 => 0 pairs (*) F5,F9: 8.. / F5 = 8 => 0 pairs (*) / F9 = 8 => 0 pairs (X) F5,F6: 9.. / F5 = 9 => 25 pairs (_) / F6 = 9 => 0 pairs (*) G8,I8: 9.. / G8 = 9 => 0 pairs (X) / I8 = 9 => 0 pairs (_) F5,G5: 9.. / F5 = 9 => 25 pairs (_) / G5 = 9 => 0 pairs (*) I6,I8: 9.. / I6 = 9 => 0 pairs (X) / I8 = 9 => 0 pairs (_) * DURATION: 0:01:13.105658 START: 04:23:19.762829 END: 04:24:32.868487 2019-05-01 * CP COUNT: (44) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,C4,C7,D2,D3,D8,E1,E5,E9,F1,F2,F3,G1,G6,G7,G8,I1,I4,I6,I8,I9) * 9631...8.872.9.451541.8.69339.52186..1.....25285.7..1..5.9...78.28....3..39...54. * PAIR E1: 4,5 COL E E8: 4,5,1,6 # reduction candidate for 4,5 E8: 4,5 => CTR * 9631..782872396451541.8.69339.521867.17.3.92528567931415.9.3278.28...139739.1.546 E8: 1,6 # 24 pairs * PAIR F1: 4,5 COL F F8: 4,5,7 # reduction candidate for 4,5 F8: 7 => CTR * 963145.82872.9.45154178269339.521867.17.3.925285.79314.569...78.28.57.3.739.1.546 F8: 4,5 # 23 pairs * PAIR D2: 3,6 COL D D6: 3,6,4 # reduction candidate for 3,6 D6: 4 => CTR * 9631...8.872693451541.8.69339.52186..1.34..25285.7..1..5.9...78.28....3..39...54. D6: 3,6 # 23 pairs * PAIR F2: 3,6 COL F F6: 3,6,4,9 # reduction candidate for 3,6 F6: 3,6 => CTR * 9631...8.872.9.451541.8.69339.52186..1.849325285.7.914.5.93..78.284..139.39.18546 F6: 4,9 # 21 pairs * PAIR D3: 2,7 COL D D9: 2,7,8 # reduction candidate for 2,7 D9: 8 => SOLVED * 963154782872396451541287693394521867617438925285679314156943278428765139739812546 D9: 2,7 # 24 pairs * PAIR F3: 2,7 COL F F9: 2,7,8 # reduction candidate for 2,7 F9: 2,7 => SOLVED * 963154782872396451541287693394521867617438925285679314156943278428765139739812546 F9: 8 # 24 pairs * PAIR C4: 4,7 BLK 4 C5: 4,7,6 # reduction candidate for 4,7 C5: 6 => CTR * 9631...8.872.9.451541.8.693397521864416.3.725285.7.319.549.3278.28....3..39...54. C5: 4,7 # 22 pairs * PAIR A5: 4,6 BLK 4 C5: 4,6,7 # reduction candidate for 4,6 C5: 4,6 => CTR * 9631..287872.93451541287693397521864.1...9725285.7.319.5.9.2178.28...936.39..8542 C5: 7 => SOLVED * 963154782872396451541287693394521867617438925285679314156943278428765139739812546 * PAIR A5: 4,6 COL A A7: 4,6,1 # reduction candidate for 4,6 A7: 4,6 # 26 pairs A8: 4,6,1,7 # reduction candidate for 4,6 A8: 4,6 => SOLVED * 963154782872396451541287693394521867617438925285679314156943278428765139739812546 A8: 1,7 # 23 pairs * PAIR E5: 3,4 BLK 5 D5: 3,4,8 # reduction candidate for 3,4 D5: 3,4 => SOLVED * 963154782872396451541287693394521867617438925285679314156943278428765139739812546 D5: 8 # 24 pairs F5: 3,4,8,9 # reduction candidate for 3,4 F5: 3,4 => CTR * 9631..782872396451541.8.6933945218676178..92528567931445691..78.284..139.39..8546 F5: 8,9 # 22 pairs D6: 3,4,6 # reduction candidate for 3,4 D6: 3,4 => CTR * 9631...8.872693451541.8.69339.52186..1..49.25285376914.5.93..78.284..139.39.18546 D6: 6 # 20 pairs F6: 3,4,6,9 # reduction candidate for 3,4 F6: 3,4 # 23 pairs * PAIR E5: 3,4 COL E E7: 3,4,1,6 # reduction candidate for 3,4 E7: 1,6 => CTR * 9631..782872396451541.8.69339.521867.17.3.925285679314.56913278.28...139.39...546 E7: 3,4 # 24 pairs * PAIR G6: 3,9 BLK 6 G5: 3,9,7 # reduction candidate for 3,9 G5: 3,9 => SOLVED * 963154782872396451541287693394521867617438925285679314156943278428765139739812546 G5: 7 => CTR * 9631..287872.9.451541287693397521864.1.839725285.7.319.5.9...78.28...936.39..8542 * PAIR G6: 3,9 ROW 6 F6: 3,9,4,6 # reduction candidate for 3,9 F6: 3,9 => SOLVED * 963154782872396451541287693394521867617438925285679314156943278428765139739812546 F6: 4,6 # 26 pairs * PAIR I6: 4,9 ROW 6 F6: 4,9,3,6 # reduction candidate for 4,9 F6: 3,6 => CTR * 9631...8.872.9.451541.8.69339.52186..1.849325285.7.914.5.93..78.284..139.39.18546 F6: 4,9 # 21 pairs * PAIR C7: 4,6 BLK 7 A7: 4,6,1 # reduction candidate for 4,6 A7: 4,6 # 26 pairs A8: 4,6,1,7 # reduction candidate for 4,6 A8: 4,6 => SOLVED * 963154782872396451541287693394521867617438925285679314156943278428765139739812546 A8: 1,7 # 23 pairs * PAIR C7: 4,6 ROW 7 E7: 4,6,1,3 # reduction candidate for 4,6 E7: 4,6 => SOLVED * 963154782872396451541287693394521867617438925285679314156943278428765139739812546 E7: 1,3 # 23 pairs * PAIR C7: 4,6 COL C C5: 4,6,7 # reduction candidate for 4,6 C5: 4,6 => CTR * 9631..287872.93451541287693397521864.1...9725285.7.319.5.9.2178.28...936.39..8542 C5: 7 => SOLVED * 963154782872396451541287693394521867617438925285679314156943278428765139739812546 * PAIR D8: 4,7 BLK 8 F8: 4,7,5 # reduction candidate for 4,7 F8: 4,7 => CTR * 963145782872396451541.8.69339.521867.17.3.925285679314.56913278.28.5.139.39...546 F8: 5 # 20 pairs * PAIR D8: 4,7 ROW 8 A8: 4,7,1,6 # reduction candidate for 4,7 A8: 1,6 => CTR * 9631...82872.9.451541.8.69339.521867.17....25285.7..14.569..278128....3.739.1.546 A8: 4,7 # 24 pairs * PAIR E9: 1,6 BLK 8 E7: 1,6,3,4 # reduction candidate for 1,6 E7: 1,6 => CTR * 9631..782872396451541.8.69339.521867.17.3.925285679314.56913278.28...139.39...546 E7: 3,4 # 24 pairs E8: 1,6,4,5 # reduction candidate for 1,6 E8: 1,6 # 24 pairs * PAIR E9: 1,6 ROW 9 A9: 1,6,7 # reduction candidate for 1,6 A9: 1,6 => CTR * 963154.8.872.9.451541.8.69339.52186..1..4..25285.7..1445693217872841593..39...54. A9: 7 => SOLVED * 963154782872396451541287693394521867617438925285679314156943278428765139739812546 * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190310-absurd-base-pr-000.dot * REASONING * DIS # E8: 4,5 => CTR => E8: 1,6 * DIS # F8: 7 => CTR => F8: 4,5 * DIS # D6: 4 => CTR => D6: 3,6 * DIS # F6: 3,6 => CTR => F6: 4,9 * PRF # D9: 8 => SOL * PRF # F9: 2,7 => SOL * DIS # C5: 6 => CTR => C5: 4,7 * DIS # C5: 4,6 => CTR => C5: 7 * PRF # C5: 7 => SOL * PRF # A8: 4,6 => SOL * PRF # D5: 3,4 => SOL * DIS # F5: 3,4 => CTR => F5: 8,9 * DIS # D6: 3,4 => CTR => D6: 6 * DIS # E7: 1,6 => CTR => E7: 3,4 * PRF # G5: 3,9 => SOL * DIS # G5: 7 => CTR => G5: 3,9 * PRF # F6: 3,9 => SOL * DIS # F6: 3,6 => CTR => F6: 4,9 * PRF # A8: 4,6 => SOL * PRF # E7: 4,6 => SOL * DIS # C5: 4,6 => CTR => C5: 7 * PRF # C5: 7 => SOL * DIS # F8: 4,7 => CTR => F8: 5 * DIS # A8: 1,6 => CTR => A8: 4,7 * DIS # E7: 1,6 => CTR => E7: 3,4 * DIS # A9: 1,6 => CTR => A9: 7 * PRF # A9: 7 => SOL * CNT 27 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,C4,C7,D2,D3,D8,E1,E5,E9,F1,F2,F3,G1,G6,G7,G8,I1,I4,I6,I8,I9) * 9631...8.872.9.451541.8.69339.52186..1.....25285.7..1..5.9...78.28....3..39...54. * PAIR E1: 4,5 COL E E8: 4,5,1,6 # reduction candidate for 4,5 E8: 4,5 => CTR * 9631..782872396451541.8.69339.521867.17.3.92528567931415.9.3278.28...139739.1.546 * PAIR RESTART * PAIR D2: 3,6 COL D D6: 3,6,4 # reduction candidate for 3,6 D6: 3,6 => SOLVED * 963154782872396451541287693394521867617438925285679314156943278428765139739812546 * DURATION: 0:00:03.946592 START: 04:25:19.276425 END: 04:25:23.223017 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190310-absurd-base-pr-001.dot * REASONING * DIS # E8: 4,5 => CTR => E8: 1,6 * PRF E8: 1,6 # D6: 3,6 => SOL * STA E8: 1,6 + D6: 3,6 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190310, absurd
Solution
position: 963154782872396451541287693394521867617438925285679314156943278428765139739812546 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 # E8: 4,5 => CTR => E8: 1,6 * INC # E8: 1,6 => UNS * INC # F8: 4,5 => UNS * DIS # F8: 7 => CTR => F8: 4,5 * INC # D6: 3,6 => UNS * DIS # D6: 4 => CTR => D6: 3,6 * DIS # F6: 3,6 => CTR => F6: 4,9 * INC # F6: 4,9 => UNS * INC # D9: 2,7 => UNS * PRF # D9: 8 => SOL * PRF # F9: 2,7 => SOL * INC # F9: 8 => UNS * INC # C5: 4,7 => UNS * DIS # C5: 6 => CTR => C5: 4,7 * DIS # C5: 4,6 => CTR => C5: 7 * PRF # C5: 7 => SOL * INC # A7: 4,6 => UNS * PRF # A8: 4,6 => SOL * INC # A8: 1,7 => UNS * PRF # D5: 3,4 => SOL * INC # D5: 8 => UNS * DIS # F5: 3,4 => CTR => F5: 8,9 * INC # F5: 8,9 => UNS * DIS # D6: 3,4 => CTR => D6: 6 * INC # D6: 6 => UNS * INC # F6: 3,4 => UNS * INC # E7: 3,4 => UNS * DIS # E7: 1,6 => CTR => E7: 3,4 * PRF # G5: 3,9 => SOL * DIS # G5: 7 => CTR => G5: 3,9 * PRF # F6: 3,9 => SOL * INC # F6: 4,6 => UNS * INC # F6: 4,9 => UNS * DIS # F6: 3,6 => CTR => F6: 4,9 * INC # A7: 4,6 => UNS * PRF # A8: 4,6 => SOL * INC # A8: 1,7 => UNS * PRF # E7: 4,6 => SOL * INC # E7: 1,3 => UNS * DIS # C5: 4,6 => CTR => C5: 7 * PRF # C5: 7 => SOL * DIS # F8: 4,7 => CTR => F8: 5 * INC # F8: 5 => UNS * INC # A8: 4,7 => UNS * DIS # A8: 1,6 => CTR => A8: 4,7 * DIS # E7: 1,6 => CTR => E7: 3,4 * INC # E7: 3,4 => UNS * INC # E8: 1,6 => UNS * DIS # A9: 1,6 => CTR => A9: 7 * PRF # A9: 7 => SOL * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # E8: 4,5 => CTR => E8: 1,6 * PRF E8: 1,6 # D6: 3,6 => SOL * STA E8: 1,6 + D6: 3,6 * CNT 2 HDP CHAINS / 2 HYP OPENED