Analysis of zz-www.sudokuoftheday.co.uk-20060421-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006
level: medium
position: .96.7..3.5...9.84..2......6.89.15...1.............4.6......97.....48761........54 initial
Autosolve
position: 496.7..3.5...9.84..2..4...6.89.154..1.............4.6.....597.....48761........54 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # D2: 1,3 => SOL * DIS # F2: 1,3 => CTR => F2: 2,6 * DIS # D3: 1,3 => CTR => D3: 5 * PRF # D3: 5 => SOL * PRF # C3: 1,3 => SOL * DIS # H5: 2,8 => CTR => H5: 7,9 * DIS # D5: 8,9 => CTR => D5: 2,3,6,7 * PRF # D5: 2,3,6,7 => SOL * DIS # I6: 1 => CTR => I6: 8,9 * DIS # D4: 2,3 => CTR => D4: 6,7 * DIS # D5: 2,3 => CTR => D5: 6,7,8,9 * DIS # F5: 2,3 => CTR => F5: 6,8 * DIS # A6: 2,3 => CTR => A6: 7 * DIS # E9: 2,3 => CTR => E9: 6 * PRF # I4: 2,7 => SOL * DIS # I4: 3 => CTR => I4: 2,7 * DIS # H5: 2,7 => CTR => H5: 8,9 * DIS # I5: 2,7 => CTR => I5: 3,5,8,9 * DIS # D4: 2,7 => CTR => D4: 3,6 * PRF # D4: 3,6 => SOL * DIS # I6: 1,9 => CTR => I6: 8 * PRF # G3: 1,9 => SOL * DIS # G3: 5 => CTR => G3: 1,9 * DIS # B6: 7 => CTR => B6: 3,5 * PRF # I7: 3 => SOL * DIS # H5: 2,8 => CTR => H5: 7,9 * CNT 26 HDP CHAINS / 48 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # D2: 1,3 => SOL * STA D2: 1,3 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .96.7..3.5...9.84..2......6.89.15...1.............4.6......97.....48761........54 | initial |
| 496.7..3.5...9.84..2..4...6.89.154..1.............4.6.....597.....48761........54 | autosolve |
| 496872531517396842823541976389615427164728395752934168641259783235487619978163254 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) F3: 1,3 H3: 7,9 D6: 8,9 E6: 2,3 H4: 2,7 G6: 1,9 B8: 3,5 H7: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G6,I6: 1.. / G6 = 1 => 10 pairs (_) / I6 = 1 => 0 pairs (X) G5,G9: 3.. / G5 = 3 => 0 pairs (*) / G9 = 3 => 0 pairs (X) B5,C5: 4.. / B5 = 4 => 0 pairs (X) / C5 = 4 => 9 pairs (_) B7,C7: 4.. / B7 = 4 => 9 pairs (_) / C7 = 4 => 0 pairs (X) B5,B7: 4.. / B5 = 4 => 0 pairs (X) / B7 = 4 => 9 pairs (_) C5,C7: 4.. / C5 = 4 => 9 pairs (_) / C7 = 4 => 0 pairs (X) D1,D3: 5.. / D1 = 5 => 0 pairs (X) / D3 = 5 => 0 pairs (_) B6,C6: 5.. / B6 = 5 => 12 pairs (_) / C6 = 5 => 9 pairs (_) G5,I5: 5.. / G5 = 5 => 0 pairs (X) / I5 = 5 => 9 pairs (_) B8,C8: 5.. / B8 = 5 => 9 pairs (_) / C8 = 5 => 12 pairs (_) D3,G3: 5.. / D3 = 5 => 0 pairs (*) / G3 = 5 => 0 pairs (X) B6,B8: 5.. / B6 = 5 => 12 pairs (_) / B8 = 5 => 9 pairs (_) C6,C8: 5.. / C6 = 5 => 9 pairs (_) / C8 = 5 => 12 pairs (_) I1,I5: 5.. / I1 = 5 => 0 pairs (X) / I5 = 5 => 9 pairs (_) D2,F2: 6.. / D2 = 6 => 0 pairs (X) / F2 = 6 => 8 pairs (_) A4,B5: 6.. / A4 = 6 => 0 pairs (X) / B5 = 6 => 0 pairs (_) A4,D4: 6.. / A4 = 6 => 0 pairs (X) / D4 = 6 => 0 pairs (_) E5,E9: 6.. / E5 = 6 => 0 pairs (X) / E9 = 6 => 13 pairs (_) I2,H3: 7.. / I2 = 7 => 16 pairs (_) / H3 = 7 => 0 pairs (*) D4,D5: 7.. / D4 = 7 => 0 pairs (X) / D5 = 7 => 0 pairs (_) A3,C3: 8.. / A3 = 8 => 8 pairs (_) / C3 = 8 => 0 pairs (X) D1,F1: 8.. / D1 = 8 => 0 pairs (*) / F1 = 8 => 0 pairs (X) A9,C9: 8.. / A9 = 8 => 0 pairs (X) / C9 = 8 => 8 pairs (_) H7,I7: 8.. / H7 = 8 => 9 pairs (_) / I7 = 8 => 0 pairs (X) D6,I6: 8.. / D6 = 8 => 0 pairs (X) / I6 = 8 => 9 pairs (_) A3,A9: 8.. / A3 = 8 => 8 pairs (_) / A9 = 8 => 0 pairs (X) C3,C9: 8.. / C3 = 8 => 0 pairs (X) / C9 = 8 => 8 pairs (_) F1,F5: 8.. / F1 = 8 => 0 pairs (X) / F5 = 8 => 0 pairs (_) H5,H7: 8.. / H5 = 8 => 0 pairs (X) / H7 = 8 => 9 pairs (_) G3,H3: 9.. / G3 = 9 => 0 pairs (*) / H3 = 9 => 0 pairs (X) D5,D6: 9.. / D5 = 9 => 0 pairs (X) / D6 = 9 => 9 pairs (_) A8,A9: 9.. / A8 = 9 => 0 pairs (X) / A9 = 9 => 0 pairs (_) I8,G9: 9.. / I8 = 9 => 0 pairs (*) / G9 = 9 => 0 pairs (X) A8,I8: 9.. / A8 = 9 => 0 pairs (X) / I8 = 9 => 0 pairs (_) A9,G9: 9.. / A9 = 9 => 0 pairs (*) / G9 = 9 => 0 pairs (X) H3,H5: 9.. / H3 = 9 => 16 pairs (_) / H5 = 9 => 0 pairs (*) * DURATION: 0:00:43.796327 START: 22:32:14.203743 END: 22:32:58.000070 2019-04-30 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,D6,E6,F3,G6,H3,H4,H7) * 496.7..3.5...9.84..2..4...6.89.154..1.............4.6.....597.....48761........54 * PAIR F3: 1,3 BLK 2 D2: 1,3,2,6 # reduction candidate for 1,3 D2: 1,3 => SOLVED * 496872531517396842823541976389615427164728395752934168641259783235487619978163254 D2: 2,6 # 9 pairs F2: 1,3,2,6 # reduction candidate for 1,3 F2: 1,3 => CTR * 496.7..3.5..69.842.2..4..76689.1542.1......9....9.4168.64159783...4876199.8...254 F2: 2,6 # 9 pairs D3: 1,3,5 # reduction candidate for 1,3 D3: 1,3 => CTR * 4965782315...9.847827.4.5966897154231..8..9757..9.41683...5978225.4876199.8...354 D3: 5 => SOLVED * 496872531517396842823541976389615427164728395752934168641259783235487619978163254 * PAIR F3: 1,3 ROW 3 C3: 1,3,7,8 # reduction candidate for 1,3 C3: 1,3 => SOLVED * 496872531517396842823541976389615427164728395752934168641259783235487619978163254 C3: 7,8 # 10 pairs * PAIR F3: 1,3 COL F F9: 1,3,2,6 # reduction candidate for 1,3 F9: 1,3 # 11 pairs F9: 2,6 # 10 pairs * PAIR H3: 7,9 COL H H5: 7,9,2,8 # reduction candidate for 7,9 H5: 2,8 => CTR * 49687..3.5...9.847.2.54..96.89.1547.1..7........9.4168....5978....48761........54 H5: 7,9 # 10 pairs * PAIR D6: 8,9 BLK 5 D5: 8,9,2,3,6,7 # reduction candidate for 8,9 D5: 8,9 => CTR * 496.7.23.5...9.84.82..4...66897154231........7....4.6.3...5978225.4876199.8...354 D5: 2,3,6,7 => SOLVED * 496872531517396842823541976389615427164728395752934168641259783235487619978163254 * PAIR D6: 8,9 ROW 6 I6: 8,9,1 # reduction candidate for 8,9 I6: 1 => CTR * 496.782355...9.8478275431966897154231..9..5787..8.496136..597822..487619978...354 I6: 8,9 # 10 pairs * PAIR E6: 2,3 BLK 5 D4: 2,3,6,7 # reduction candidate for 2,3 D4: 2,3 => CTR * 49687.53.5.7.9.84.82.54.9766893154271.27683957..924168.6..5978....487619978.3.254 D4: 6,7 # 9 pairs D5: 2,3,6,7,8,9 # reduction candidate for 2,3 D5: 2,3 => CTR * 49687.2355...9.8418215439766897154231....85977..9.41683.4.5978225.4876199.8...354 D5: 6,7,8,9 # 8 pairs E5: 2,3,6 # reduction candidate for 2,3 E5: 2,3 # 13 pairs F5: 2,3,6,8 # reduction candidate for 2,3 F5: 2,3 => CTR * 496.7823.5...9.84.82..4...66897154231...6....7...34.6.3...5978225.4876199.8...354 F5: 6,8 # 9 pairs * PAIR E6: 2,3 ROW 6 A6: 2,3,7 # reduction candidate for 2,3 A6: 2,3 => CTR * 496.7.2315...9.847.2..4.596.89.154.21..9..3.5.....4169....597.89..487613......954 A6: 7 # 12 pairs C6: 2,3,5,7 # reduction candidate for 2,3 C6: 2,3 # 14 pairs * PAIR E6: 2,3 COL E E9: 2,3,6 # reduction candidate for 2,3 E9: 2,3 => CTR * 496.7..3.5...9.84..2..4...66893154..1..76.3.5...924168....5978....487619.......54 E9: 6 # 13 pairs * PAIR H4: 2,7 BLK 6 I4: 2,7,3 # reduction candidate for 2,7 I4: 2,7 => SOLVED * 496872531517396842823541976389615427164728395752934168641259783235487619978163254 I4: 3 => CTR * 49687.2355...9.84.82..4...62896154731647.....735924168641359782352487619978.6.354 H5: 2,7,8,9 # reduction candidate for 2,7 H5: 2,7 => CTR * 496.7.23.5...9.847827.43.9628961547316473.925735924168641359782352487619978.6.354 H5: 8,9 # 9 pairs I5: 2,7,3,5,8,9 # reduction candidate for 2,7 I5: 2,7 => CTR * 496.7.2355...9.84.82.54...62896154731647..59.7....4.6....3597..352487619978...354 I5: 3,5,8,9 # 8 pairs * PAIR H4: 2,7 ROW 4 D4: 2,7,3,6 # reduction candidate for 2,7 D4: 2,7 => CTR * 496.7..3.5...9.84.82..4...6689.154.31........7....4.6.26.3597.....4876199.8...354 D4: 3,6 => SOLVED * 496872531517396842823541976389615427164728395752934168641259783235487619978163254 * PAIR G6: 1,9 BLK 6 I6: 1,9,8 # reduction candidate for 1,9 I6: 1,9 => CTR * 496.782355...9.8478275431966897154231..9..5787..8.49613...5978225.4876199.8...354 I6: 8 # 9 pairs * PAIR G6: 1,9 COL G G3: 1,9,5 # reduction candidate for 1,9 G3: 1,9 => SOLVED * 496872531517396842823541976389615427164728395752934168641259783235487619978163254 G3: 5 => CTR * 4965782315...9.847827.4.5966897154231..8..9757..9.41683...5978225.4876199.8...354 * PAIR B8: 3,5 BLK 7 C8: 3,5,2 # reduction candidate for 3,5 C8: 3,5 # 12 pairs C8: 2 # 12 pairs * PAIR B8: 3,5 COL B B6: 3,5,7 # reduction candidate for 3,5 B6: 7 => CTR * 496.7.2315...9.847.2..4.596.89.154.21..9..3.5.75..4169....597.895.487613......954 B6: 3,5 # 11 pairs * PAIR H7: 2,8 BLK 9 I7: 2,8,3 # reduction candidate for 2,8 I7: 3 => SOLVED * 496872531517396842823541976389615427164728395752934168641259783235487619978163254 I7: 2,8 # 12 pairs * PAIR H7: 2,8 COL H H5: 2,8,7,9 # reduction candidate for 2,8 H5: 2,8 => CTR * 49687..3.5...9.847.2.54..96.89.1547.1..7........9.4168....5978....48761........54 H5: 7,9 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060421-absurd-base-pr-000.dot * REASONING * PRF # D2: 1,3 => SOL * DIS # F2: 1,3 => CTR => F2: 2,6 * DIS # D3: 1,3 => CTR => D3: 5 * PRF # D3: 5 => SOL * PRF # C3: 1,3 => SOL * DIS # H5: 2,8 => CTR => H5: 7,9 * DIS # D5: 8,9 => CTR => D5: 2,3,6,7 * PRF # D5: 2,3,6,7 => SOL * DIS # I6: 1 => CTR => I6: 8,9 * DIS # D4: 2,3 => CTR => D4: 6,7 * DIS # D5: 2,3 => CTR => D5: 6,7,8,9 * DIS # F5: 2,3 => CTR => F5: 6,8 * DIS # A6: 2,3 => CTR => A6: 7 * DIS # E9: 2,3 => CTR => E9: 6 * PRF # I4: 2,7 => SOL * DIS # I4: 3 => CTR => I4: 2,7 * DIS # H5: 2,7 => CTR => H5: 8,9 * DIS # I5: 2,7 => CTR => I5: 3,5,8,9 * DIS # D4: 2,7 => CTR => D4: 3,6 * PRF # D4: 3,6 => SOL * DIS # I6: 1,9 => CTR => I6: 8 * PRF # G3: 1,9 => SOL * DIS # G3: 5 => CTR => G3: 1,9 * DIS # B6: 7 => CTR => B6: 3,5 * PRF # I7: 3 => SOL * DIS # H5: 2,8 => CTR => H5: 7,9 * CNT 26 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,D6,E6,F3,G6,H3,H4,H7) * 496.7..3.5...9.84..2..4...6.89.154..1.............4.6.....597.....48761........54 * PAIR F3: 1,3 BLK 2 D2: 1,3,2,6 # reduction candidate for 1,3 D2: 1,3 => SOLVED * 496872531517396842823541976389615427164728395752934168641259783235487619978163254 * DURATION: 0:00:01.778676 START: 22:33:30.578556 END: 22:33:32.357232 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060421-absurd-base-pr-001.dot * REASONING * PRF # D2: 1,3 => SOL * STA D2: 1,3 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060421, absurd
Solution
position: 496872531517396842823541976389615427164728395752934168641259783235487619978163254 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 # D2: 1,3 => SOL * INC # D2: 2,6 => UNS * DIS # F2: 1,3 => CTR => F2: 2,6 * INC # F2: 2,6 => UNS * DIS # D3: 1,3 => CTR => D3: 5 * PRF # D3: 5 => SOL * PRF # C3: 1,3 => SOL * INC # C3: 7,8 => UNS * INC # F9: 1,3 => UNS * INC # F9: 2,6 => UNS * INC # H5: 7,9 => UNS * DIS # H5: 2,8 => CTR => H5: 7,9 * DIS # D5: 8,9 => CTR => D5: 2,3,6,7 * PRF # D5: 2,3,6,7 => SOL * INC # I6: 8,9 => UNS * DIS # I6: 1 => CTR => I6: 8,9 * DIS # D4: 2,3 => CTR => D4: 6,7 * INC # D4: 6,7 => UNS * DIS # D5: 2,3 => CTR => D5: 6,7,8,9 * INC # D5: 6,7,8,9 => UNS * INC # E5: 2,3 => UNS * DIS # F5: 2,3 => CTR => F5: 6,8 * INC # F5: 6,8 => UNS * DIS # A6: 2,3 => CTR => A6: 7 * INC # A6: 7 => UNS * INC # C6: 2,3 => UNS * DIS # E9: 2,3 => CTR => E9: 6 * INC # E9: 6 => UNS * PRF # I4: 2,7 => SOL * DIS # I4: 3 => CTR => I4: 2,7 * DIS # H5: 2,7 => CTR => H5: 8,9 * INC # H5: 8,9 => UNS * DIS # I5: 2,7 => CTR => I5: 3,5,8,9 * INC # I5: 3,5,8,9 => UNS * DIS # D4: 2,7 => CTR => D4: 3,6 * PRF # D4: 3,6 => SOL * DIS # I6: 1,9 => CTR => I6: 8 * INC # I6: 8 => UNS * PRF # G3: 1,9 => SOL * DIS # G3: 5 => CTR => G3: 1,9 * INC # C8: 3,5 => UNS * INC # C8: 2 => UNS * INC # B6: 3,5 => UNS * DIS # B6: 7 => CTR => B6: 3,5 * INC # I7: 2,8 => UNS * PRF # I7: 3 => SOL * DIS # H5: 2,8 => CTR => H5: 7,9 * INC # H5: 7,9 => UNS * CNT 48 HDP CHAINS / 48 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # D2: 1,3 => SOL * STA D2: 1,3 * CNT 1 HDP CHAINS / 1 HYP OPENED