Analysis of zz-www.sudokuoftheday.co.uk-20190203-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: 6...9...37..5...28.8.4..........8.......3.4....37.1....6..7.3..2.5....6...92...8. initial
Autosolve
position: 65.89..437.451..28.8.4..........823.8...3.4....37.18.646817.3.22.538..6...92...8. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # F3: 2,7 => SOL * DIS # F3: 3,6 => CTR => F3: 2,7 * DIS # F3: 3,6 => CTR => F3: 2,7 * PRF # F3: 2,7 => SOL * PRF # F3: 2,6 => SOL * DIS # G8: 1,7 => CTR => G8: 9 * PRF # G8: 9 => SOL * PRF # G9: 1,7 => SOL * DIS # G9: 5 => CTR => G9: 1,7 * DIS # G3: 6,9 => CTR => G3: 5 * PRF # G3: 5 => SOL * DIS # G3: 6 => CTR => G3: 5,9 * PRF # I4: 5,9 => SOL * DIS # A4: 1 => CTR => A4: 5,9 * PRF # I5: 1,7 => SOL * PRF # I4: 5,9 => SOL * DIS # B9: 1,7 => CTR => B9: 3 * DIS # G8: 1,7 => CTR => G8: 9 * PRF # G8: 9 => SOL * PRF # I8: 1,7 => SOL * DIS # I8: 4,9 => CTR => I8: 1,7 * DIS # B9: 7 => CTR => B9: 1,3 * DIS # I8: 4,9 => CTR => I8: 1,7 * PRF # I8: 1,7 => SOL * PRF # F9: 5,6 => SOL * DIS # F9: 4 => CTR => F9: 5,6 * CNT 26 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 # F3: 2,7 => SOL * STA F3: 2,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6...9...37..5...28.8.4..........8.......3.4....37.1....6..7.3..2.5....6...92...8. | initial |
| 65.89..437.451..28.8.4..........823.8...3.4....37.18.646817.3.22.538..6...92...8. | autosolve |
| 652897143794513628381462579917648235826935417543721896468179352275384961139256784 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (28) C1: 1,2 B2: 3,9 A3: 3,9 C3: 1,2 F1: 2,7 F2: 3,6 E3: 2,6 G1: 1,7 G2: 6,9 H3: 1,7 I3: 5,9 C4: 6,7 C5: 6,7 A6: 5,9 B6: 2,4 D4: 6,9 E4: 4,5 D5: 6,9 F5: 2,5 E6: 2,4 H5: 1,7 H6: 5,9 B8: 1,7 A9: 1,3 F7: 5,9 F8: 4,9 E9: 5,6 H7: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,C3: 1.. / C1 = 1 => 0 pairs (X) / C3 = 1 => 27 pairs (_) G1,H3: 1.. / G1 = 1 => 27 pairs (_) / H3 = 1 => 0 pairs (X) C1,G1: 1.. / C1 = 1 => 0 pairs (X) / G1 = 1 => 27 pairs (_) C3,H3: 1.. / C3 = 1 => 27 pairs (_) / H3 = 1 => 0 pairs (X) A4,A9: 1.. / A4 = 1 => 0 pairs (X) / A9 = 1 => 28 pairs (_) H3,H5: 1.. / H3 = 1 => 0 pairs (X) / H5 = 1 => 27 pairs (_) C1,C3: 2.. / C1 = 2 => 27 pairs (_) / C3 = 2 => 0 pairs (X) B5,B6: 2.. / B5 = 2 => 0 pairs (*) / B6 = 2 => 0 pairs (X) F5,E6: 2.. / F5 = 2 => 0 pairs (X) / E6 = 2 => 0 pairs (_) C1,F1: 2.. / C1 = 2 => 27 pairs (_) / F1 = 2 => 0 pairs (X) B5,F5: 2.. / B5 = 2 => 0 pairs (*) / F5 = 2 => 0 pairs (X) B6,E6: 2.. / B6 = 2 => 0 pairs (X) / E6 = 2 => 0 pairs (_) E3,E6: 2.. / E3 = 2 => 0 pairs (X) / E6 = 2 => 0 pairs (_) B2,A3: 3.. / B2 = 3 => 0 pairs (X) / A3 = 3 => 28 pairs (_) F2,F3: 3.. / F2 = 3 => 28 pairs (_) / F3 = 3 => 0 pairs (X) A9,B9: 3.. / A9 = 3 => 0 pairs (X) / B9 = 3 => 28 pairs (_) B2,F2: 3.. / B2 = 3 => 0 pairs (X) / F2 = 3 => 28 pairs (_) A3,F3: 3.. / A3 = 3 => 28 pairs (_) / F3 = 3 => 0 pairs (X) A3,A9: 3.. / A3 = 3 => 28 pairs (_) / A9 = 3 => 0 pairs (X) B2,B9: 3.. / B2 = 3 => 0 pairs (X) / B9 = 3 => 28 pairs (_) B4,B6: 4.. / B4 = 4 => 0 pairs (X) / B6 = 4 => 0 pairs (_) E4,E6: 4.. / E4 = 4 => 0 pairs (*) / E6 = 4 => 0 pairs (X) F8,F9: 4.. / F8 = 4 => 0 pairs (*) / F9 = 4 => 0 pairs (X) I8,I9: 4.. / I8 = 4 => 0 pairs (X) / I9 = 4 => 0 pairs (_) B4,E4: 4.. / B4 = 4 => 0 pairs (X) / E4 = 4 => 0 pairs (_) B6,E6: 4.. / B6 = 4 => 0 pairs (*) / E6 = 4 => 0 pairs (X) F8,I8: 4.. / F8 = 4 => 0 pairs (*) / I8 = 4 => 0 pairs (X) F9,I9: 4.. / F9 = 4 => 0 pairs (X) / I9 = 4 => 0 pairs (_) G3,I3: 5.. / G3 = 5 => 0 pairs (*) / I3 = 5 => 0 pairs (X) A4,A6: 5.. / A4 = 5 => 0 pairs (X) / A6 = 5 => 0 pairs (_) E4,F5: 5.. / E4 = 5 => 0 pairs (X) / F5 = 5 => 0 pairs (_) F5,I5: 5.. / F5 = 5 => 0 pairs (*) / I5 = 5 => 0 pairs (X) A6,H6: 5.. / A6 = 5 => 0 pairs (*) / H6 = 5 => 0 pairs (X) F7,H7: 5.. / F7 = 5 => 0 pairs (X) / H7 = 5 => 0 pairs (_) E4,E9: 5.. / E4 = 5 => 0 pairs (X) / E9 = 5 => 0 pairs (_) G3,G9: 5.. / G3 = 5 => 0 pairs (*) / G9 = 5 => 0 pairs (X) H6,H7: 5.. / H6 = 5 => 0 pairs (X) / H7 = 5 => 0 pairs (_) G2,G3: 6.. / G2 = 6 => 28 pairs (_) / G3 = 6 => 0 pairs (X) C4,C5: 6.. / C4 = 6 => 26 pairs (_) / C5 = 6 => 25 pairs (_) D4,D5: 6.. / D4 = 6 => 25 pairs (_) / D5 = 6 => 26 pairs (_) E9,F9: 6.. / E9 = 6 => 0 pairs (X) / F9 = 6 => 0 pairs (_) F2,G2: 6.. / F2 = 6 => 0 pairs (X) / G2 = 6 => 28 pairs (_) C4,D4: 6.. / C4 = 6 => 26 pairs (_) / D4 = 6 => 25 pairs (_) C5,D5: 6.. / C5 = 6 => 25 pairs (_) / D5 = 6 => 26 pairs (_) E3,E9: 6.. / E3 = 6 => 0 pairs (*) / E9 = 6 => 0 pairs (X) F1,F3: 7.. / F1 = 7 => 27 pairs (_) / F3 = 7 => 0 pairs (X) G1,H3: 7.. / G1 = 7 => 0 pairs (X) / H3 = 7 => 27 pairs (_) C4,C5: 7.. / C4 = 7 => 25 pairs (_) / C5 = 7 => 26 pairs (_) B8,B9: 7.. / B8 = 7 => 30 pairs (_) / B9 = 7 => 0 pairs (X) F1,G1: 7.. / F1 = 7 => 27 pairs (_) / G1 = 7 => 0 pairs (X) F3,H3: 7.. / F3 = 7 => 0 pairs (X) / H3 = 7 => 27 pairs (_) C4,I4: 7.. / C4 = 7 => 25 pairs (_) / I4 = 7 => 26 pairs (_) H3,H5: 7.. / H3 = 7 => 27 pairs (_) / H5 = 7 => 0 pairs (X) B2,A3: 9.. / B2 = 9 => 28 pairs (_) / A3 = 9 => 0 pairs (X) D4,D5: 9.. / D4 = 9 => 26 pairs (_) / D5 = 9 => 25 pairs (_) F7,F8: 9.. / F7 = 9 => 0 pairs (*) / F8 = 9 => 0 pairs (X) B2,G2: 9.. / B2 = 9 => 28 pairs (_) / G2 = 9 => 0 pairs (X) A6,H6: 9.. / A6 = 9 => 0 pairs (X) / H6 = 9 => 0 pairs (_) F7,H7: 9.. / F7 = 9 => 0 pairs (*) / H7 = 9 => 0 pairs (X) H6,H7: 9.. / H6 = 9 => 0 pairs (*) / H7 = 9 => 0 pairs (X) * DURATION: 0:01:33.788096 START: 03:25:42.490613 END: 03:27:16.278709 2019-05-01 * CP COUNT: (60) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A6,A9,B2,B6,B8,C1,C3,C4,C5,D4,D5,E3,E4,E6,E9,F1,F2,F5,F7,F8,G1,G2,H3,H5,H6,H7,I3) * 65.89..437.451..28.8.4..........823.8...3.4....37.18.646817.3.22.538..6...92...8. * PAIR F1: 2,7 BLK 2 F3: 2,7,3,6 # reduction candidate for 2,7 F3: 2,7 => SOLVED * 652897143794513628381462579917648235826935417543721896468179352275384961139256784 F3: 3,6 => CTR * 6528971437.451..28.8142.5799....823.8...324155237418964681793522.5384.6...9265784 * PAIR F2: 3,6 BLK 2 F3: 3,6,2,7 # reduction candidate for 3,6 F3: 3,6 => CTR * 6528971437.451..28.8142.5799....823.8...324155237418964681793522.5384.6...9265784 F3: 2,7 => SOLVED * 652897143794513628381462579917648235826935417543721896468179352275384961139256784 * PAIR E3: 2,6 BLK 2 F3: 2,6,3,7 # reduction candidate for 2,6 F3: 2,6 => SOLVED * 652897143794513628381462579917648235826935417543721896468179352275384961139256784 F3: 3,7 # 29 pairs * PAIR G1: 1,7 COL G G8: 1,7,9 # reduction candidate for 1,7 G8: 1,7 => CTR * 65.89..437.451..28.8.4....5.....823.8...354....37218564681793.22.538..6...92...8. G8: 9 => SOLVED * 652897143794513628381462579917648235826935417543721896468179352275384961139256784 G9: 1,7,5 # reduction candidate for 1,7 G9: 1,7 => SOLVED * 652897143794513628381462579917648235826935417543721896468179352275384961139256784 G9: 5 => CTR * 65.89..437.451..28.8.4....5....5823.8...324..52374189646817.3.22.538..6...92..58. * PAIR G2: 6,9 BLK 3 G3: 6,9,5 # reduction candidate for 6,9 G3: 6,9 => CTR * 65.89..437.451..28.8.4....5.....823.8...354....37218564681793.22.538..6...92...8. G3: 5 => SOLVED * 652897143794513628381462579917648235826935417543721896468179352275384961139256784 * PAIR I3: 5,9 BLK 3 G3: 5,9,6 # reduction candidate for 5,9 G3: 6 => CTR * 65.89..437.451..28.8.4..6.5.....823.8...354....37218.646817.3.22.538..6...92...8. G3: 5,9 # 28 pairs * PAIR I3: 5,9 COL I I4: 5,9,1,7 # reduction candidate for 5,9 I4: 5,9 => SOLVED * 652897143794513628381462579917648235826935417543721896468179352275384961139256784 I4: 1,7 # 30 pairs I5: 5,9,1,7 # reduction candidate for 5,9 I5: 5,9 # 30 pairs * PAIR A6: 5,9 BLK 4 A4: 5,9,1 # reduction candidate for 5,9 A4: 1 => CTR * 65.89..43734516928.8.4.....1....823.8...3.4..5.37.18964681793522.5384.6.3.92...84 A4: 5,9 # 28 pairs * PAIR H5: 1,7 BLK 6 I4: 1,7,5,9 # reduction candidate for 1,7 I4: 1,7 # 30 pairs I5: 1,7,5,9 # reduction candidate for 1,7 I5: 1,7 => SOLVED * 652897143794513628381462579917648235826935417543721896468179352275384961139256784 I5: 5,9 # 30 pairs * PAIR H6: 5,9 BLK 6 I4: 5,9,1,7 # reduction candidate for 5,9 I4: 5,9 => SOLVED * 652897143794513628381462579917648235826935417543721896468179352275384961139256784 I4: 1,7 # 30 pairs I5: 5,9,1,7 # reduction candidate for 5,9 I5: 5,9 # 30 pairs * PAIR B8: 1,7 BLK 7 B9: 1,7,3 # reduction candidate for 1,7 B9: 1,7 => CTR * 65.89..4373451692898.423675.....823.8...3.4....37.18.646817.3.22.538..6...92...8. B9: 3 # 28 pairs * PAIR B8: 1,7 ROW 8 G8: 1,7,9 # reduction candidate for 1,7 G8: 1,7 => CTR * 65.89..437.451..28.8.4....5.....823.8...354....37218564681793.22.538..6...92...8. G8: 9 => SOLVED * 652897143794513628381462579917648235826935417543721896468179352275384961139256784 I8: 1,7,4,9 # reduction candidate for 1,7 I8: 1,7 => SOLVED * 652897143794513628381462579917648235826935417543721896468179352275384961139256784 I8: 4,9 => CTR * 65.89..437.451..28.8.4....5.....823.8...354....37218564681793.22.538..6...92...8. * PAIR A9: 1,3 BLK 7 B9: 1,3,7 # reduction candidate for 1,3 B9: 7 => CTR * 65.89..4373451692898.423675.....823.8...3.4....37.18.646817.3.22.538..6...92...8. B9: 1,3 # 30 pairs * PAIR F8: 4,9 ROW 8 I8: 4,9,1,7 # reduction candidate for 4,9 I8: 4,9 => CTR * 65.89..437.451..28.8.4....5.....823.8...354....37218564681793.22.538..6...92...8. I8: 1,7 => SOLVED * 652897143794513628381462579917648235826935417543721896468179352275384961139256784 * PAIR E9: 5,6 BLK 8 F9: 5,6,4 # reduction candidate for 5,6 F9: 5,6 => SOLVED * 652897143794513628381462579917648235826935417543721896468179352275384961139256784 F9: 4 => CTR * 65.89..437.451..28.8.42........5823.8...324.552374189646817.3.22.538..6...9264.8. * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190203-absurd-base-pr-000.dot * REASONING * PRF # F3: 2,7 => SOL * DIS # F3: 3,6 => CTR => F3: 2,7 * DIS # F3: 3,6 => CTR => F3: 2,7 * PRF # F3: 2,7 => SOL * PRF # F3: 2,6 => SOL * DIS # G8: 1,7 => CTR => G8: 9 * PRF # G8: 9 => SOL * PRF # G9: 1,7 => SOL * DIS # G9: 5 => CTR => G9: 1,7 * DIS # G3: 6,9 => CTR => G3: 5 * PRF # G3: 5 => SOL * DIS # G3: 6 => CTR => G3: 5,9 * PRF # I4: 5,9 => SOL * DIS # A4: 1 => CTR => A4: 5,9 * PRF # I5: 1,7 => SOL * PRF # I4: 5,9 => SOL * DIS # B9: 1,7 => CTR => B9: 3 * DIS # G8: 1,7 => CTR => G8: 9 * PRF # G8: 9 => SOL * PRF # I8: 1,7 => SOL * DIS # I8: 4,9 => CTR => I8: 1,7 * DIS # B9: 7 => CTR => B9: 1,3 * DIS # I8: 4,9 => CTR => I8: 1,7 * PRF # I8: 1,7 => SOL * PRF # F9: 5,6 => SOL * DIS # F9: 4 => CTR => F9: 5,6 * CNT 26 HDP CHAINS / 37 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A6,A9,B2,B6,B8,C1,C3,C4,C5,D4,D5,E3,E4,E6,E9,F1,F2,F5,F7,F8,G1,G2,H3,H5,H6,H7,I3) * 65.89..437.451..28.8.4..........823.8...3.4....37.18.646817.3.22.538..6...92...8. * PAIR F1: 2,7 BLK 2 F3: 2,7,3,6 # reduction candidate for 2,7 F3: 2,7 => SOLVED * 652897143794513628381462579917648235826935417543721896468179352275384961139256784 * DURATION: 0:00:02.011539 START: 03:27:51.992296 END: 03:27:54.003835 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190203-absurd-base-pr-001.dot * REASONING * PRF # F3: 2,7 => SOL * STA F3: 2,7 * 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, 20190203, absurd
Solution
position: 652897143794513628381462579917648235826935417543721896468179352275384961139256784 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 # F3: 2,7 => SOL * DIS # F3: 3,6 => CTR => F3: 2,7 * DIS # F3: 3,6 => CTR => F3: 2,7 * PRF # F3: 2,7 => SOL * PRF # F3: 2,6 => SOL * INC # F3: 3,7 => UNS * DIS # G8: 1,7 => CTR => G8: 9 * PRF # G8: 9 => SOL * PRF # G9: 1,7 => SOL * DIS # G9: 5 => CTR => G9: 1,7 * DIS # G3: 6,9 => CTR => G3: 5 * PRF # G3: 5 => SOL * INC # G3: 5,9 => UNS * DIS # G3: 6 => CTR => G3: 5,9 * PRF # I4: 5,9 => SOL * INC # I4: 1,7 => UNS * INC # I5: 5,9 => UNS * INC # A4: 5,9 => UNS * DIS # A4: 1 => CTR => A4: 5,9 * INC # I4: 1,7 => UNS * PRF # I5: 1,7 => SOL * INC # I5: 5,9 => UNS * PRF # I4: 5,9 => SOL * INC # I4: 1,7 => UNS * INC # I5: 5,9 => UNS * DIS # B9: 1,7 => CTR => B9: 3 * INC # B9: 3 => UNS * DIS # G8: 1,7 => CTR => G8: 9 * PRF # G8: 9 => SOL * PRF # I8: 1,7 => SOL * DIS # I8: 4,9 => CTR => I8: 1,7 * INC # B9: 1,3 => UNS * DIS # B9: 7 => CTR => B9: 1,3 * DIS # I8: 4,9 => CTR => I8: 1,7 * PRF # I8: 1,7 => SOL * PRF # F9: 5,6 => SOL * DIS # F9: 4 => CTR => F9: 5,6 * CNT 37 HDP CHAINS / 37 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # F3: 2,7 => SOL * STA F3: 2,7 * CNT 1 HDP CHAINS / 1 HYP OPENED