Analysis of zz-www.sudokuoftheday.co.uk-20060509-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006
level: medium
position: 82.97..5....3...4....5.182...3..9..7.............2.41...8.9.....9.214...1....56.. initial
Autosolve
position: 824976351...38274..3.54182...3..92.7......9.....72.41...869713.3962145781..83569. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 6 => CTR => A3: 7,9 * DIS # A2: 5 => CTR => A2: 6,9 * DIS # A3: 6,9 => CTR => A3: 7 * PRF # A3: 7 => SOL * DIS # B4: 4,5 => CTR => B4: 1,8 * PRF # A7: 4,5 => SOL * DIS # A7: 2 => CTR => A7: 4,5 * DIS # A6: 6 => CTR => A6: 5,9 * DIS # C2: 5,9 => CTR => C2: 1 * PRF # C2: 1 => SOL * DIS # B4: 1,4 => CTR => B4: 5,8 * PRF # B5: 1,4 => SOL * DIS # B5: 7 => CTR => B5: 1,4 * PRF # A7: 4,5 => SOL * DIS # A7: 2 => CTR => A7: 4,5 * DIS # B4: 4,5 => CTR => B4: 1,8 * PRF # B5: 1 => SOL * PRF # C5: 2,7 => SOL * DIS # C5: 1 => CTR => C5: 2,7 * PRF # A7: 5 => SOL * CNT 20 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 6 => CTR => A3: 7,9 * DIS A3: 7,9 # B4: 4,5 => CTR => B4: 1,8 * PRF A3: 7,9 + B4: 1,8 # A7: 4,5 => SOL * STA A3: 7,9 + B4: 1,8 + A7: 4,5 * CNT 3 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 82.97..5....3...4....5.182...3..9..7.............2.41...8.9.....9.214...1....56.. | initial |
| 824976351...38274..3.54182...3..92.7......9.....72.41...869713.3962145781..83569. | autosolve |
| 824976351651382749739541826483159267217463985965728413548697132396214578172835694 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) C3: 7,9 I2: 6,9 I3: 6,9 A4: 4,5 C6: 5,9 D4: 1,4 E4: 5,6 D5: 1,4 E5: 5,6 F5: 3,8 F6: 3,8 H4: 6,8 H5: 6,8 I5: 3,5 I6: 3,5 B7: 4,5 B9: 4,7 C9: 2,7 I7: 2,4 I9: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,C2: 1.. / B2 = 1 => 0 pairs (X) / C2 = 1 => 0 pairs (_) D4,D5: 1.. / D4 = 1 => 20 pairs (_) / D5 = 1 => 0 pairs (X) B4,D4: 1.. / B4 = 1 => 0 pairs (X) / D4 = 1 => 20 pairs (_) C2,C5: 1.. / C2 = 1 => 0 pairs (*) / C5 = 1 => 0 pairs (X) A5,C5: 2.. / A5 = 2 => 0 pairs (*) / C5 = 2 => 0 pairs (X) A7,C9: 2.. / A7 = 2 => 0 pairs (X) / C9 = 2 => 0 pairs (_) I7,I9: 2.. / I7 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) A7,I7: 2.. / A7 = 2 => 0 pairs (X) / I7 = 2 => 0 pairs (_) C9,I9: 2.. / C9 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) A5,A7: 2.. / A5 = 2 => 0 pairs (*) / A7 = 2 => 0 pairs (X) C5,C9: 2.. / C5 = 2 => 0 pairs (X) / C9 = 2 => 0 pairs (_) F5,F6: 3.. / F5 = 3 => 13 pairs (_) / F6 = 3 => 0 pairs (X) I5,I6: 3.. / I5 = 3 => 0 pairs (X) / I6 = 3 => 13 pairs (_) F5,I5: 3.. / F5 = 3 => 13 pairs (_) / I5 = 3 => 0 pairs (X) F6,I6: 3.. / F6 = 3 => 0 pairs (X) / I6 = 3 => 13 pairs (_) D4,D5: 4.. / D4 = 4 => 0 pairs (X) / D5 = 4 => 20 pairs (_) I7,I9: 4.. / I7 = 4 => 0 pairs (X) / I9 = 4 => 0 pairs (_) B9,I9: 4.. / B9 = 4 => 0 pairs (X) / I9 = 4 => 0 pairs (_) E4,E5: 5.. / E4 = 5 => 13 pairs (_) / E5 = 5 => 0 pairs (X) I5,I6: 5.. / I5 = 5 => 13 pairs (_) / I6 = 5 => 0 pairs (X) A7,B7: 5.. / A7 = 5 => 0 pairs (*) / B7 = 5 => 0 pairs (X) E5,I5: 5.. / E5 = 5 => 0 pairs (X) / I5 = 5 => 13 pairs (_) C2,C6: 5.. / C2 = 5 => 0 pairs (X) / C6 = 5 => 15 pairs (_) I2,I3: 6.. / I2 = 6 => 0 pairs (X) / I3 = 6 => 21 pairs (_) A6,B6: 6.. / A6 = 6 => 0 pairs (X) / B6 = 6 => 14 pairs (_) E4,E5: 6.. / E4 = 6 => 0 pairs (X) / E5 = 6 => 13 pairs (_) H4,H5: 6.. / H4 = 6 => 13 pairs (_) / H5 = 6 => 0 pairs (X) A3,I3: 6.. / A3 = 6 => 0 pairs (X) / I3 = 6 => 21 pairs (_) E4,H4: 6.. / E4 = 6 => 0 pairs (X) / H4 = 6 => 13 pairs (_) E5,H5: 6.. / E5 = 6 => 13 pairs (_) / H5 = 6 => 0 pairs (X) B2,B6: 6.. / B2 = 6 => 0 pairs (X) / B6 = 6 => 14 pairs (_) A3,C3: 7.. / A3 = 7 => 0 pairs (*) / C3 = 7 => 0 pairs (X) B9,C9: 7.. / B9 = 7 => 0 pairs (*) / C9 = 7 => 0 pairs (X) A3,A5: 7.. / A3 = 7 => 0 pairs (*) / A5 = 7 => 0 pairs (X) B5,B9: 7.. / B5 = 7 => 0 pairs (X) / B9 = 7 => 0 pairs (_) B4,B6: 8.. / B4 = 8 => 13 pairs (_) / B6 = 8 => 0 pairs (X) F5,F6: 8.. / F5 = 8 => 0 pairs (X) / F6 = 8 => 13 pairs (_) H4,H5: 8.. / H4 = 8 => 0 pairs (X) / H5 = 8 => 13 pairs (_) B4,H4: 8.. / B4 = 8 => 13 pairs (_) / H4 = 8 => 0 pairs (X) F5,H5: 8.. / F5 = 8 => 0 pairs (X) / H5 = 8 => 13 pairs (_) B6,F6: 8.. / B6 = 8 => 0 pairs (X) / F6 = 8 => 13 pairs (_) I2,I3: 9.. / I2 = 9 => 21 pairs (_) / I3 = 9 => 0 pairs (X) A6,C6: 9.. / A6 = 9 => 15 pairs (_) / C6 = 9 => 0 pairs (X) * DURATION: 0:00:56.768386 START: 23:01:28.062765 END: 23:02:24.831151 2019-04-30 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B7,B9,C3,C6,C9,D4,D5,E4,E5,F5,F6,H4,H5,I2,I3,I5,I6,I7,I9) * 824976351...38274..3.54182...3..92.7......9.....72.41...869713.3962145781..83569. * PAIR C3: 7,9 BLK 1 A3: 7,9,6 # reduction candidate for 7,9 A3: 6 => CTR * 824976351...38274.637541829..3..92.77.2...9.....72.41...869713.3962145781..83569. A3: 7,9 # 21 pairs * PAIR I2: 6,9 ROW 2 A2: 6,9,5 # reduction candidate for 6,9 A2: 5 => CTR * 8249763515..38274.73.54182.4.31.92.7...4..9....572.413258697134396214578147835692 A2: 6,9 # 16 pairs * PAIR I3: 6,9 ROW 3 A3: 6,9,7 # reduction candidate for 6,9 A3: 6,9 => CTR * 824976351...38274..3754182...3..92.77.2...9.....72.41...869713.3962145781..83569. A3: 7 => SOLVED * 824976351651382749739541826483159267217463985965728413548697132396214578172835694 * PAIR A4: 4,5 BLK 4 B4: 4,5,1,8 # reduction candidate for 4,5 B4: 4,5 => CTR * 824976351.6.38274..3.54182...31.9287...4.8963.8.723415..869713.3962145781..83569. B4: 1,8 # 21 pairs * PAIR A4: 4,5 COL A A7: 4,5,2 # reduction candidate for 4,5 A7: 4,5 => SOLVED * 824976351651382749739541826483159267217463985965728413548697132396214578172835694 A7: 2 => CTR * 824976351...38274.739541826..3..92.74721..9..96572.41.258697134396214578147835692 * PAIR C6: 5,9 BLK 4 A6: 5,9,6 # reduction candidate for 5,9 A6: 6 => CTR * 824976351.6.38274..3.54182...3..92.7......9..6.972.41...869713.3962145781..83569. A6: 5,9 # 14 pairs * PAIR C6: 5,9 COL C C2: 5,9,1 # reduction candidate for 5,9 C2: 5,9 => CTR * 824976351.1.38274..3.54182...31.92.7..14..9...6.728413..869713.3962145781.2835694 C2: 1 => SOLVED * 824976351651382749739541826483159267217463985965728413548697132396214578172835694 * PAIR D4: 1,4 ROW 4 B4: 1,4,5,8 # reduction candidate for 1,4 B4: 1,4 => CTR * 824976351.6.38274..3.54182...3..9287.....8963.8.723415..869713.3962145781..83569. B4: 5,8 # 21 pairs * PAIR D5: 1,4 ROW 5 B5: 1,4,7 # reduction candidate for 1,4 B5: 1,4 => SOLVED * 824976351651382749739541826483159267217463985965728413548697132396214578172835694 B5: 7 => CTR * 824976351...38274.739541826..3..92.7.721..9..96572.41...869713.396214578147835692 * PAIR B7: 4,5 BLK 7 A7: 4,5,2 # reduction candidate for 4,5 A7: 4,5 => SOLVED * 824976351651382749739541826483159267217463985965728413548697132396214578172835694 A7: 2 => CTR * 824976351...38274.739541826..3..92.74721..9..96572.41.258697134396214578147835692 * PAIR B7: 4,5 COL B B4: 4,5,1,8 # reduction candidate for 4,5 B4: 4,5 => CTR * 824976351.6.38274..3.54182...31.9287...4.8963.8.723415..869713.3962145781..83569. B4: 1,8 # 21 pairs * PAIR B9: 4,7 COL B B5: 4,7,1 # reduction candidate for 4,7 B5: 1 => SOLVED * 824976351651382749739541826483159267217463985965728413548697132396214578172835694 B5: 4,7 # 24 pairs * PAIR C9: 2,7 COL C C5: 2,7,1 # reduction candidate for 2,7 C5: 2,7 => SOLVED * 824976351651382749739541826483159267217463985965728413548697132396214578172835694 C5: 1 => CTR * 824976351...38274..3.54182...3..92.7271...9.....72.41...869713.3962145781..83569. * PAIR I7: 2,4 ROW 7 A7: 2,4,5 # reduction candidate for 2,4 A7: 5 => SOLVED * 824976351651382749739541826483159267217463985965728413548697132396214578172835694 A7: 2,4 # 22 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060509-absurd-base-pr-000.dot * REASONING * DIS # A3: 6 => CTR => A3: 7,9 * DIS # A2: 5 => CTR => A2: 6,9 * DIS # A3: 6,9 => CTR => A3: 7 * PRF # A3: 7 => SOL * DIS # B4: 4,5 => CTR => B4: 1,8 * PRF # A7: 4,5 => SOL * DIS # A7: 2 => CTR => A7: 4,5 * DIS # A6: 6 => CTR => A6: 5,9 * DIS # C2: 5,9 => CTR => C2: 1 * PRF # C2: 1 => SOL * DIS # B4: 1,4 => CTR => B4: 5,8 * PRF # B5: 1,4 => SOL * DIS # B5: 7 => CTR => B5: 1,4 * PRF # A7: 4,5 => SOL * DIS # A7: 2 => CTR => A7: 4,5 * DIS # B4: 4,5 => CTR => B4: 1,8 * PRF # B5: 1 => SOL * PRF # C5: 2,7 => SOL * DIS # C5: 1 => CTR => C5: 2,7 * PRF # A7: 5 => SOL * CNT 20 HDP CHAINS / 28 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B7,B9,C3,C6,C9,D4,D5,E4,E5,F5,F6,H4,H5,I2,I3,I5,I6,I7,I9) * 824976351...38274..3.54182...3..92.7......9.....72.41...869713.3962145781..83569. * PAIR C3: 7,9 BLK 1 A3: 7,9,6 # reduction candidate for 7,9 A3: 6 => CTR * 824976351...38274.637541829..3..92.77.2...9.....72.41...869713.3962145781..83569. * PAIR A4: 4,5 BLK 4 B4: 4,5,1,8 # reduction candidate for 4,5 B4: 4,5 => CTR * 824976351.6.382749.3.541826..31.9287...4.8963.8.723415..869713.3962145781..83569. * PAIR A4: 4,5 COL A A7: 4,5,2 # reduction candidate for 4,5 A7: 4,5 => SOLVED * 824976351651382749739541826483159267217463985965728413548697132396214578172835694 * DURATION: 0:00:04.507416 START: 23:02:47.380577 END: 23:02:51.887993 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060509-absurd-base-pr-001.dot * REASONING * DIS # A3: 6 => CTR => A3: 7,9 * DIS A3: 7,9 # B4: 4,5 => CTR => B4: 1,8 * PRF A3: 7,9 + B4: 1,8 # A7: 4,5 => SOL * STA A3: 7,9 + B4: 1,8 + A7: 4,5 * CNT 3 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060509, absurd
Solution
position: 824976351651382749739541826483159267217463985965728413548697132396214578172835694 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:
* INC # A3: 7,9 => UNS * DIS # A3: 6 => CTR => A3: 7,9 * INC # A2: 6,9 => UNS * DIS # A2: 5 => CTR => A2: 6,9 * DIS # A3: 6,9 => CTR => A3: 7 * PRF # A3: 7 => SOL * DIS # B4: 4,5 => CTR => B4: 1,8 * INC # B4: 1,8 => UNS * PRF # A7: 4,5 => SOL * DIS # A7: 2 => CTR => A7: 4,5 * INC # A6: 5,9 => UNS * DIS # A6: 6 => CTR => A6: 5,9 * DIS # C2: 5,9 => CTR => C2: 1 * PRF # C2: 1 => SOL * DIS # B4: 1,4 => CTR => B4: 5,8 * INC # B4: 5,8 => UNS * PRF # B5: 1,4 => SOL * DIS # B5: 7 => CTR => B5: 1,4 * PRF # A7: 4,5 => SOL * DIS # A7: 2 => CTR => A7: 4,5 * DIS # B4: 4,5 => CTR => B4: 1,8 * INC # B4: 1,8 => UNS * INC # B5: 4,7 => UNS * PRF # B5: 1 => SOL * PRF # C5: 2,7 => SOL * DIS # C5: 1 => CTR => C5: 2,7 * INC # A7: 2,4 => UNS * PRF # A7: 5 => SOL * CNT 28 HDP CHAINS / 28 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 7,9 => UNS * DIS # A3: 6 => CTR => A3: 7,9 * DIS A3: 7,9 # B4: 4,5 => CTR => B4: 1,8 * PRF A3: 7,9 + B4: 1,8 # A7: 4,5 => SOL * STA A3: 7,9 + B4: 1,8 + A7: 4,5 * CNT 4 HDP CHAINS / 4 HYP OPENED