Analysis of zz-www.sudokuoftheday.co.uk-20060714-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006
level: medium
position: .7.....3.....7.......6.84...61.538.4.24....7...5...........91..4.......6.5..6.2.8 initial
Autosolve
position: .78....3..4..7..8.5..6.8417.61.53824.24..6.7...5....61.8...91.341....7.6.5..6.2.8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 3,9 => CTR => C2: 2,6 * PRF # C2: 2,6 => SOL * PRF # C3: 3,9 => SOL * DIS # C3: 2 => CTR => C3: 3,9 * DIS # E3: 3,9 => CTR => E3: 2 * PRF # E3: 2 => SOL * DIS # D6: 7,8 => CTR => D6: 2,4 * DIS # A5: 3,9 => CTR => A5: 8 * PRF # A5: 8 => SOL * DIS # G5: 5,9 => CTR => G5: 3 * DIS # G5: 5 => CTR => G5: 3,9 * DIS # C7: 2,6 => CTR => C7: 7 * PRF # C7: 7 => SOL * DIS # C8: 3,9 => CTR => C8: 2 * PRF # C8: 2 => SOL * PRF # C9: 3,9 => SOL * DIS # C9: 7 => CTR => C9: 3,9 * DIS # A5: 3,9 => CTR => A5: 8 * PRF # A5: 8 => SOL * PRF # D7: 2,4 => SOL * DIS # E1: 2,4 => CTR => E1: 1,9 * DIS # E6: 2,4 => CTR => E6: 8 * PRF # E6: 8 => SOL * PRF # D7: 2,5 => SOL * DIS # D8: 2,5 => CTR => D8: 3,8 * DIS # D7: 4,5 => CTR => D7: 2,7 * CNT 26 HDP CHAINS / 40 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 3,9 => CTR => C2: 2,6 * PRF C2: 2,6 => SOL * STA C2: 2,6 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .7.....3.....7.......6.84...61.538.4.24....7...5...........91..4.......6.5..6.2.8 | initial |
| .78....3..4..7..8.5..6.8417.61.53824.24..6.7...5....61.8...91.341....7.6.5..6.2.8 | autosolve |
| 178594632246371589593628417961753824824916375735482961687249153412835796359167248 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) B3: 3,9 A4: 7,9 A6: 7,8 B6: 3,9 D4: 7,9 I5: 5,9 G6: 3,9 A7: 2,6 A9: 3,9 E7: 2,4 F8: 2,5 H7: 4,5 H8: 5,9 H9: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A2: 1.. / A1 = 1 => 17 pairs (_) / A2 = 1 => 18 pairs (_) D5,E5: 1.. / D5 = 1 => 0 pairs (X) / E5 = 1 => 15 pairs (_) D9,F9: 1.. / D9 = 1 => 19 pairs (_) / F9 = 1 => 0 pairs (X) E1,E5: 1.. / E1 = 1 => 0 pairs (X) / E5 = 1 => 15 pairs (_) I1,I2: 2.. / I1 = 2 => 16 pairs (_) / I2 = 2 => 17 pairs (_) C3,E3: 2.. / C3 = 2 => 0 pairs (X) / E3 = 2 => 0 pairs (_) D2,E3: 3.. / D2 = 3 => 17 pairs (_) / E3 = 3 => 0 pairs (X) A5,B6: 3.. / A5 = 3 => 0 pairs (X) / B6 = 3 => 22 pairs (_) G5,G6: 3.. / G5 = 3 => 22 pairs (_) / G6 = 3 => 0 pairs (X) C2,D2: 3.. / C2 = 3 => 0 pairs (X) / D2 = 3 => 17 pairs (_) A5,G5: 3.. / A5 = 3 => 0 pairs (X) / G5 = 3 => 22 pairs (_) B6,G6: 3.. / B6 = 3 => 22 pairs (_) / G6 = 3 => 0 pairs (X) A5,A9: 3.. / A5 = 3 => 0 pairs (X) / A9 = 3 => 22 pairs (_) B3,B6: 3.. / B3 = 3 => 0 pairs (X) / B6 = 3 => 22 pairs (_) E3,E8: 3.. / E3 = 3 => 0 pairs (X) / E8 = 3 => 17 pairs (_) H7,H9: 4.. / H7 = 4 => 0 pairs (X) / H9 = 4 => 13 pairs (_) G5,I5: 5.. / G5 = 5 => 0 pairs (X) / I5 = 5 => 18 pairs (_) H7,H8: 5.. / H7 = 5 => 13 pairs (_) / H8 = 5 => 0 pairs (X) D7,H7: 5.. / D7 = 5 => 0 pairs (X) / H7 = 5 => 13 pairs (_) G1,G2: 6.. / G1 = 6 => 16 pairs (_) / G2 = 6 => 0 pairs (X) A7,C7: 6.. / A7 = 6 => 0 pairs (*) / C7 = 6 => 0 pairs (X) A1,G1: 6.. / A1 = 6 => 0 pairs (X) / G1 = 6 => 16 pairs (_) C2,C7: 6.. / C2 = 6 => 0 pairs (*) / C7 = 6 => 0 pairs (X) A4,A6: 7.. / A4 = 7 => 0 pairs (X) / A6 = 7 => 0 pairs (_) C7,C9: 7.. / C7 = 7 => 0 pairs (*) / C9 = 7 => 0 pairs (X) A4,D4: 7.. / A4 = 7 => 0 pairs (X) / D4 = 7 => 0 pairs (_) C7,D7: 7.. / C7 = 7 => 0 pairs (*) / D7 = 7 => 0 pairs (X) F6,F9: 7.. / F6 = 7 => 0 pairs (X) / F9 = 7 => 0 pairs (_) A5,A6: 8.. / A5 = 8 => 0 pairs (*) / A6 = 8 => 0 pairs (X) D8,E8: 8.. / D8 = 8 => 16 pairs (_) / E8 = 8 => 0 pairs (X) H8,H9: 9.. / H8 = 9 => 13 pairs (_) / H9 = 9 => 0 pairs (X) A4,D4: 9.. / A4 = 9 => 0 pairs (*) / D4 = 9 => 0 pairs (X) B6,G6: 9.. / B6 = 9 => 0 pairs (X) / G6 = 9 => 22 pairs (_) C8,H8: 9.. / C8 = 9 => 0 pairs (X) / H8 = 9 => 13 pairs (_) B3,B6: 9.. / B3 = 9 => 22 pairs (_) / B6 = 9 => 0 pairs (X) * DURATION: 0:00:41.489707 START: 00:40:40.958979 END: 00:41:22.448686 2019-05-01 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,A7,A9,B3,B6,D4,E7,F8,G6,H7,H8,H9,I5) * .78....3..4..7..8.5..6.8417.61.53824.24..6.7...5....61.8...91.341....7.6.5..6.2.8 * PAIR B3: 3,9 BLK 1 C2: 3,9,2,6 # reduction candidate for 3,9 C2: 3,9 => CTR * .78....3..4..7..8.5..6.8417761953824.24..6.7.8.5..7.61286749153413...796957361248 C2: 2,6 => SOLVED * 178594632246371589593628417961753824824916375735482961687249153412835796359167248 C3: 3,9,2 # reduction candidate for 3,9 C3: 3,9 => SOLVED * 178594632246371589593628417961753824824916375735482961687249153412835796359167248 C3: 2 => CTR * .78....3..4937..8.5.26.8417.61.53824.24..6.7...5....6128674915341....796.57.61248 * PAIR B3: 3,9 ROW 3 E3: 3,9,2 # reduction candidate for 3,9 E3: 3,9 => CTR * .78....3..4937..8.5.26.8417.61.53824.24..6.7...5....6128674915341....796.57.61248 E3: 2 => SOLVED * 178594632246371589593628417961753824824916375735482961687249153412835796359167248 * PAIR A6: 7,8 ROW 6 D6: 7,8,2,4 # reduction candidate for 7,8 D6: 7,8 => CTR * .78....3..4..7..8.5.26.8417.61.53824.24..6.7...5....6128674915341....796.57.61248 D6: 2,4 # 15 pairs * PAIR B6: 3,9 BLK 4 A5: 3,9,8 # reduction candidate for 3,9 A5: 3,9 => CTR * .78....3..4937..8.5.26.8417761953824.24..6.7.8.5....6128674915341....796.57.61248 A5: 8 => SOLVED * 178594632246371589593628417961753824824916375735482961687249153412835796359167248 * PAIR I5: 5,9 BLK 6 G5: 5,9,3 # reduction candidate for 5,9 G5: 5,9 => CTR * .78514.3..4.37..8.53.6.8417761953824324.86.7.895...361.87..9153412835796953.6.248 G5: 3 # 22 pairs * PAIR I5: 5,9 COL I I1: 5,9,2 # reduction candidate for 5,9 I1: 5,9 # 17 pairs I2: 5,9,2 # reduction candidate for 5,9 I2: 5,9 # 16 pairs * PAIR G6: 3,9 BLK 6 G5: 3,9,5 # reduction candidate for 3,9 G5: 5 => CTR * .78514.3..4.37..8.53.6.8417761953824324.86579895...361.87..9153412835796953.6.248 G5: 3,9 # 18 pairs * PAIR A7: 2,6 BLK 7 C7: 2,6,7 # reduction candidate for 2,6 C7: 2,6 => CTR * .78..4.3..43.7..8.59.6.8417761953824.24..6.7.8.5..7.61.8.74915341....796957361248 C7: 7 => SOLVED * 178594632246371589593628417961753824824916375735482961687249153412835796359167248 * PAIR A7: 2,6 COL A A1: 2,6,1 # reduction candidate for 2,6 A1: 2,6 # 18 pairs A2: 2,6,1 # reduction candidate for 2,6 A2: 2,6 # 17 pairs * PAIR A9: 3,9 BLK 7 C8: 3,9,2 # reduction candidate for 3,9 C8: 3,9 => CTR * .78....3..4..7..8.5..6.8417.61.53824.24..6.7...5....61.8.749153413...796957361248 C8: 2 => SOLVED * 178594632246371589593628417961753824824916375735482961687249153412835796359167248 C9: 3,9,7 # reduction candidate for 3,9 C9: 3,9 => SOLVED * 178594632246371589593628417961753824824916375735482961687249153412835796359167248 C9: 7 => CTR * .78..4.3..43.7..8.59.6.8417.61.53824.24..6.7...5..7.61.8.7.915341....796957361248 * PAIR A9: 3,9 COL A A5: 3,9,8 # reduction candidate for 3,9 A5: 3,9 => CTR * .78....3..4937..8.5.26.8417761953824.24..6.7.8.5....6128674915341....796.57.61248 A5: 8 => SOLVED * 178594632246371589593628417961753824824916375735482961687249153412835796359167248 * PAIR E7: 2,4 BLK 8 D7: 2,4,5,7 # reduction candidate for 2,4 D7: 2,4 => SOLVED * 178594632246371589593628417961753824824916375735482961687249153412835796359167248 D7: 5,7 # 15 pairs * PAIR E7: 2,4 COL E E1: 2,4,1,9 # reduction candidate for 2,4 E1: 2,4 => CTR * .78....3..4..7..8.5..698417.61.53824.24.16.7..95...361.8...91.341..3.7.6953.6.248 E1: 1,9 # 15 pairs E6: 2,4,8 # reduction candidate for 2,4 E6: 2,4 => CTR * .78....3..4937..8.5.26.8417.61.53824.24..6.7...5....6128674915341....796.57.61248 E6: 8 => SOLVED * 178594632246371589593628417961753824824916375735482961687249153412835796359167248 * PAIR F8: 2,5 BLK 8 D7: 2,5,4,7 # reduction candidate for 2,5 D7: 2,5 => SOLVED * 178594632246371589593628417961753824824916375735482961687249153412835796359167248 D7: 4,7 # 14 pairs D8: 2,5,3,8 # reduction candidate for 2,5 D8: 2,5 => CTR * .78....3..43.7..8.592638417.61.53824324..6.7...5....61.8...91.341..8.7.6.5.361248 D8: 3,8 # 15 pairs * PAIR F8: 2,5 COL F F1: 2,5,1,4 # reduction candidate for 2,5 F1: 2,5 # 23 pairs F2: 2,5,1 # reduction candidate for 2,5 F2: 2,5 # 17 pairs * PAIR H7: 4,5 ROW 7 D7: 4,5,2,7 # reduction candidate for 4,5 D7: 4,5 => CTR * .78....3..4637..8.5..6.8417.61.53824.24..6.7...5....61687.291.3412.35796.5..6.248 D7: 2,7 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060714-absurd-base-pr-000.dot * REASONING * DIS # C2: 3,9 => CTR => C2: 2,6 * PRF # C2: 2,6 => SOL * PRF # C3: 3,9 => SOL * DIS # C3: 2 => CTR => C3: 3,9 * DIS # E3: 3,9 => CTR => E3: 2 * PRF # E3: 2 => SOL * DIS # D6: 7,8 => CTR => D6: 2,4 * DIS # A5: 3,9 => CTR => A5: 8 * PRF # A5: 8 => SOL * DIS # G5: 5,9 => CTR => G5: 3 * DIS # G5: 5 => CTR => G5: 3,9 * DIS # C7: 2,6 => CTR => C7: 7 * PRF # C7: 7 => SOL * DIS # C8: 3,9 => CTR => C8: 2 * PRF # C8: 2 => SOL * PRF # C9: 3,9 => SOL * DIS # C9: 7 => CTR => C9: 3,9 * DIS # A5: 3,9 => CTR => A5: 8 * PRF # A5: 8 => SOL * PRF # D7: 2,4 => SOL * DIS # E1: 2,4 => CTR => E1: 1,9 * DIS # E6: 2,4 => CTR => E6: 8 * PRF # E6: 8 => SOL * PRF # D7: 2,5 => SOL * DIS # D8: 2,5 => CTR => D8: 3,8 * DIS # D7: 4,5 => CTR => D7: 2,7 * CNT 26 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,A7,A9,B3,B6,D4,E7,F8,G6,H7,H8,H9,I5) * .78....3..4..7..8.5..6.8417.61.53824.24..6.7...5....61.8...91.341....7.6.5..6.2.8 * PAIR B3: 3,9 BLK 1 C2: 3,9,2,6 # reduction candidate for 3,9 C2: 3,9 => CTR * .78....3..4..7..8.5..6.8417761953824.24..6.7.8.5..7.61286749153413...796957361248 C2: 2,6 => SOLVED * 178594632246371589593628417961753824824916375735482961687249153412835796359167248 * DURATION: 0:00:01.355737 START: 00:41:52.226841 END: 00:41:53.582578 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060714-absurd-base-pr-001.dot * REASONING * DIS # C2: 3,9 => CTR => C2: 2,6 * PRF C2: 2,6 => SOL * STA C2: 2,6 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060714, absurd
Solution
position: 178594632246371589593628417961753824824916375735482961687249153412835796359167248 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 # C2: 3,9 => CTR => C2: 2,6 * PRF # C2: 2,6 => SOL * PRF # C3: 3,9 => SOL * DIS # C3: 2 => CTR => C3: 3,9 * DIS # E3: 3,9 => CTR => E3: 2 * PRF # E3: 2 => SOL * DIS # D6: 7,8 => CTR => D6: 2,4 * INC # D6: 2,4 => UNS * DIS # A5: 3,9 => CTR => A5: 8 * PRF # A5: 8 => SOL * DIS # G5: 5,9 => CTR => G5: 3 * INC # G5: 3 => UNS * INC # I1: 5,9 => UNS * INC # I2: 5,9 => UNS * INC # G5: 3,9 => UNS * DIS # G5: 5 => CTR => G5: 3,9 * DIS # C7: 2,6 => CTR => C7: 7 * PRF # C7: 7 => SOL * INC # A1: 2,6 => UNS * INC # A2: 2,6 => UNS * DIS # C8: 3,9 => CTR => C8: 2 * PRF # C8: 2 => SOL * PRF # C9: 3,9 => SOL * DIS # C9: 7 => CTR => C9: 3,9 * DIS # A5: 3,9 => CTR => A5: 8 * PRF # A5: 8 => SOL * PRF # D7: 2,4 => SOL * INC # D7: 5,7 => UNS * DIS # E1: 2,4 => CTR => E1: 1,9 * INC # E1: 1,9 => UNS * DIS # E6: 2,4 => CTR => E6: 8 * PRF # E6: 8 => SOL * PRF # D7: 2,5 => SOL * INC # D7: 4,7 => UNS * DIS # D8: 2,5 => CTR => D8: 3,8 * INC # D8: 3,8 => UNS * INC # F1: 2,5 => UNS * INC # F2: 2,5 => UNS * DIS # D7: 4,5 => CTR => D7: 2,7 * INC # D7: 2,7 => UNS * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C2: 3,9 => CTR => C2: 2,6 * PRF C2: 2,6 => SOL * STA C2: 2,6 * CNT 2 HDP CHAINS / 1 HYP OPENED