Analysis of zz-www.sudokuoftheday.co.uk-20060323-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006
level: medium
position: .5......2.3.1.46..4...5...98.2.39....9..2..3....64.2..1....742..84.....19........ initial
Autosolve
position: .5.....4223.1.46..4...5...9842.39....9..2..34...64.29.16...742..84.6.9.192.41.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 6,7 => CTR => C1: 1,8,9 * DIS # G3: 1,7 => CTR => G3: 3,8 * DIS # C5: 1,7 => CTR => C5: 5,6 * PRF # D5: 8 => SOL * DIS # C9: 3,5 => CTR => C9: 7 * DIS # D7: 3,5 => CTR => D7: 8,9 * DIS # D7: 3,5 => CTR => D7: 8,9 * DIS # H9: 5,7 => CTR => H9: 6,8 * CNT 8 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 6,7 => CTR => C1: 1,8,9 * DIS C1: 1,8,9 # G3: 1,7 => CTR => G3: 3,8 * DIS C1: 1,8,9 + G3: 3,8 # C5: 1,7 => CTR => C5: 5,6 * DIS C1: 1,8,9 + G3: 3,8 + C5: 5,6 # D5: 5,7 => CTR => D5: 8 * PRF C1: 1,8,9 + G3: 3,8 + C5: 5,6 + D5: 8 => SOL * STA C1: 1,8,9 + G3: 3,8 + C5: 5,6 + D5: 8 * CNT 5 HDP CHAINS / 21 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .5......2.3.1.46..4...5...98.2.39....9..2..3....64.2..1....742..84.....19........ | initial |
| .5.....4223.1.46..4...5...9842.39....9..2..34...64.29.16...742..84.6.9.192.41.... | autosolve |
| 659378142238194657471256389842739516596821734713645298165987423384562971927413865 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) A1: 6,7 B3: 1,7 B6: 1,7 D4: 5,7 C7: 3,5 E7: 8,9 H8: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F5,F6: 1.. / F5 = 1 => 8 pairs (_) / F6 = 1 => 0 pairs (X) G4,H4: 1.. / G4 = 1 => 10 pairs (_) / H4 = 1 => 12 pairs (_) C1,G1: 1.. / C1 = 1 => 10 pairs (_) / G1 = 1 => 11 pairs (_) C5,F5: 1.. / C5 = 1 => 0 pairs (X) / F5 = 1 => 8 pairs (_) B3,B6: 1.. / B3 = 1 => 13 pairs (_) / B6 = 1 => 11 pairs (_) H3,H4: 1.. / H3 = 1 => 10 pairs (_) / H4 = 1 => 12 pairs (_) D3,F3: 2.. / D3 = 2 => 8 pairs (_) / F3 = 2 => 0 pairs (X) D8,F8: 2.. / D8 = 2 => 0 pairs (X) / F8 = 2 => 8 pairs (_) D3,D8: 2.. / D3 = 2 => 8 pairs (_) / D8 = 2 => 0 pairs (X) F3,F8: 2.. / F3 = 2 => 0 pairs (X) / F8 = 2 => 8 pairs (_) G1,G3: 3.. / G1 = 3 => 0 pairs (X) / G3 = 3 => 8 pairs (_) A6,C6: 3.. / A6 = 3 => 12 pairs (_) / C6 = 3 => 15 pairs (_) I7,I9: 3.. / I7 = 3 => 10 pairs (_) / I9 = 3 => 13 pairs (_) A6,A8: 3.. / A6 = 3 => 12 pairs (_) / A8 = 3 => 15 pairs (_) H2,I2: 5.. / H2 = 5 => 13 pairs (_) / I2 = 5 => 11 pairs (_) F1,F3: 6.. / F1 = 6 => 0 pairs (X) / F3 = 6 => 9 pairs (_) A5,C5: 6.. / A5 = 6 => 0 pairs (X) / C5 = 6 => 10 pairs (_) H4,I4: 6.. / H4 = 6 => 15 pairs (_) / I4 = 6 => 8 pairs (_) H9,I9: 6.. / H9 = 6 => 8 pairs (_) / I9 = 6 => 15 pairs (_) C3,F3: 6.. / C3 = 6 => 0 pairs (X) / F3 = 6 => 9 pairs (_) A1,A5: 6.. / A1 = 6 => 10 pairs (_) / A5 = 6 => 0 pairs (X) H4,H9: 6.. / H4 = 6 => 15 pairs (_) / H9 = 6 => 8 pairs (_) I4,I9: 6.. / I4 = 6 => 8 pairs (_) / I9 = 6 => 15 pairs (_) E1,E2: 7.. / E1 = 7 => 12 pairs (_) / E2 = 7 => 14 pairs (_) D4,D5: 7.. / D4 = 7 => 11 pairs (_) / D5 = 7 => 18 pairs (_) A8,C9: 7.. / A8 = 7 => 0 pairs (X) / C9 = 7 => 11 pairs (_) A8,H8: 7.. / A8 = 7 => 0 pairs (X) / H8 = 7 => 11 pairs (_) B3,B6: 7.. / B3 = 7 => 11 pairs (_) / B6 = 7 => 13 pairs (_) G5,I6: 8.. / G5 = 8 => 18 pairs (_) / I6 = 8 => 14 pairs (_) F6,I6: 8.. / F6 = 8 => 18 pairs (_) / I6 = 8 => 14 pairs (_) C1,C2: 9.. / C1 = 9 => 16 pairs (_) / C2 = 9 => 8 pairs (_) D7,E7: 9.. / D7 = 9 => 11 pairs (_) / E7 = 9 => 10 pairs (_) C2,E2: 9.. / C2 = 9 => 8 pairs (_) / E2 = 9 => 16 pairs (_) D1,D7: 9.. / D1 = 9 => 10 pairs (_) / D7 = 9 => 11 pairs (_) * DURATION: 0:00:34.013249 START: 21:49:43.927813 END: 21:50:17.941062 2019-04-30 * CP COUNT: (34) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B3,B6,C7,D4,E7,H8) * .5.....4223.1.46..4...5...9842.39....9..2..34...64.29.16...742..84.6.9.192.41.... * PAIR A1: 6,7 BLK 1 C1: 6,7,1,8,9 # reduction candidate for 6,7 C1: 6,7 => CTR * 657...142239174685418256379842.39.16596.21.3437164529816.5.742.784.6295192.41..67 C1: 1,8,9 # 7 pairs C3: 6,7,1,8 # reduction candidate for 6,7 C3: 6,7 # 16 pairs * PAIR A1: 6,7 COL A A5: 6,7,5 # reduction candidate for 6,7 A5: 5 # 14 pairs A5: 6,7 # 13 pairs * PAIR B3: 1,7 BLK 1 C1: 1,7,6,8,9 # reduction candidate for 1,7 C1: 1,7 # 13 pairs C3: 1,7,6,8 # reduction candidate for 1,7 C3: 1,7 # 17 pairs * PAIR B3: 1,7 ROW 3 G3: 1,7,3,8 # reduction candidate for 1,7 G3: 1,7 => CTR * .51...3422391.46..478.561.9842.39....9..2..34...64.29.16...742..84.6.9.192.41.... G3: 3,8 # 8 pairs H3: 1,7,8 # reduction candidate for 1,7 H3: 1,7 # 10 pairs * PAIR B6: 1,7 BLK 4 C5: 1,7,5,6 # reduction candidate for 1,7 C5: 1,7 => CTR * 75.....4223.1746..41..5...9842.39.1669..2..34.7.64.29.16...742..84.6.97192741..6. C5: 5,6 # 9 pairs C6: 1,7,3,5 # reduction candidate for 1,7 C6: 1,7 # 19 pairs * PAIR D4: 5,7 BLK 5 D5: 5,7,8 # reduction candidate for 5,7 D5: 8 => SOLVED * 659378142238194657471256389842739516596821734713645298165987423384562971927413865 D5: 5,7 # 15 pairs * PAIR D4: 5,7 ROW 4 G4: 5,7,1 # reduction candidate for 5,7 G4: 5,7 # 12 pairs H4: 5,7,1,6 # reduction candidate for 5,7 H4: 5,7 # 14 pairs I4: 5,7,6 # reduction candidate for 5,7 I4: 5,7 # 15 pairs * PAIR C7: 3,5 BLK 7 A8: 3,5,7 # reduction candidate for 3,5 A8: 3,5 # 11 pairs C9: 3,5,7 # reduction candidate for 3,5 C9: 3,5 => CTR * 65.....4223.1.46.54...56..9842.39...596.21.343..64529816.5.742.784.6.95192.41.... C9: 7 # 11 pairs * PAIR C7: 3,5 ROW 7 D7: 3,5,8,9 # reduction candidate for 3,5 D7: 3,5 => CTR * .5.9...422391.46..4...5...9842.39....9..2..34...64.29.16..97428.84.6.9.192.418..3 D7: 8,9 # 10 pairs I7: 3,5,8 # reduction candidate for 3,5 I7: 3,5 # 10 pairs * PAIR C7: 3,5 COL C C6: 3,5,1,7 # reduction candidate for 3,5 C6: 1,7 # 19 pairs C6: 3,5 # 13 pairs * PAIR E7: 8,9 BLK 8 D7: 8,9,3,5 # reduction candidate for 8,9 D7: 3,5 => CTR * .5.9...422391.46..4...5...9842.39....9..2..34...64.29.16..97428.84.6.9.192.418..3 D7: 8,9 # 10 pairs * PAIR E7: 8,9 COL E E1: 8,9,7 # reduction candidate for 8,9 E1: 8,9 # 14 pairs E2: 8,9,7 # reduction candidate for 8,9 E2: 8,9 # 12 pairs * PAIR H8: 5,7 BLK 9 G9: 5,7,8 # reduction candidate for 5,7 G9: 5,7 # 10 pairs H9: 5,7,6,8 # reduction candidate for 5,7 H9: 5,7 => CTR * .51....422391.4685478.56319842539167.9672..34.1.64.29.16...7423.84.6.9.192.41.8.6 H9: 6,8 # 8 pairs I9: 5,7,3,6,8 # reduction candidate for 5,7 I9: 5,7 # 17 pairs * PAIR H8: 5,7 ROW 8 A8: 5,7,3 # reduction candidate for 5,7 A8: 3 # 15 pairs A8: 5,7 # 12 pairs * PAIR H8: 5,7 COL H H2: 5,7,8 # reduction candidate for 5,7 H2: 5,7 # 11 pairs H4: 5,7,1,6 # reduction candidate for 5,7 H4: 5,7 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060323-absurd-base-pr-000.dot * REASONING * DIS # C1: 6,7 => CTR => C1: 1,8,9 * DIS # G3: 1,7 => CTR => G3: 3,8 * DIS # C5: 1,7 => CTR => C5: 5,6 * PRF # D5: 8 => SOL * DIS # C9: 3,5 => CTR => C9: 7 * DIS # D7: 3,5 => CTR => D7: 8,9 * DIS # D7: 3,5 => CTR => D7: 8,9 * DIS # H9: 5,7 => CTR => H9: 6,8 * CNT 8 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B3,B6,C7,D4,E7,H8) * .5.....4223.1.46..4...5...9842.39....9..2..34...64.29.16...742..84.6.9.192.41.... * PAIR A1: 6,7 BLK 1 C1: 6,7,1,8,9 # reduction candidate for 6,7 C1: 6,7 => CTR * 657...142239174685418256379842.39.16596.21.3437164529816.5.742.784.6295192.41..67 C3: 6,7,1,8 # reduction candidate for 6,7 C3: 6,7 # 16 pairs * RESTART * PAIR A1: 6,7 BLK 1 C3: 6,7,1,8 # reduction candidate for 6,7 C3: 6,7 # 16 pairs C3: 1,8 # 11 pairs * PAIR A1: 6,7 COL A A5: 6,7,5 # reduction candidate for 6,7 A5: 5 # 14 pairs A5: 6,7 # 13 pairs * PAIR B3: 1,7 BLK 1 C3: 1,7,6,8 # reduction candidate for 1,7 C3: 1,7 # 17 pairs C3: 6,8 # 8 pairs * PAIR B3: 1,7 ROW 3 G3: 1,7,3,8 # reduction candidate for 1,7 G3: 1,7 => CTR * .51...3422391.46..478.561.9842.39....9..2..34...64.29.16...742..84.6.9.192.41.... H3: 1,7,8 # reduction candidate for 1,7 H3: 1,7 # 10 pairs * RESTART * PAIR B3: 1,7 ROW 3 H3: 1,7,8 # reduction candidate for 1,7 H3: 8 # 17 pairs H3: 1,7 # 10 pairs * PAIR RESTART * PAIR B3: 1,7 BLK 1 C3: 1,7,6,8 # reduction candidate for 1,7 C3: 1,7 # 17 pairs C3: 6,8 # 10 pairs * PAIR B3: 1,7 ROW 3 H3: 1,7,8 # reduction candidate for 1,7 H3: 8 # 17 pairs H3: 1,7 # 10 pairs * PAIR B6: 1,7 BLK 4 C5: 1,7,5,6 # reduction candidate for 1,7 C5: 1,7 => CTR * 75...6.4223.1746..416.5..79842.39.1669..2..34.7.64.29.16...742..84.6.951927415863 C6: 1,7,3,5 # reduction candidate for 1,7 C6: 1,7 # 20 pairs * RESTART * PAIR B6: 1,7 BLK 4 C6: 1,7,3,5 # reduction candidate for 1,7 C6: 1,7 # 20 pairs C6: 3,5 # 14 pairs * PAIR D4: 5,7 BLK 5 D5: 5,7,8 # reduction candidate for 5,7 D5: 5,7 => CTR * 65..7314223.1.46.54..2563.9842.39516.96521834...64829.165..7423.843629519234157.. D5: 8 => SOLVED * 659378142238194657471256389842739516596821734713645298165987423384562971927413865 * DURATION: 0:00:14.347973 START: 21:50:39.348164 END: 21:50:53.696137 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060323-absurd-base-pr-001.dot * REASONING * DIS # C1: 6,7 => CTR => C1: 1,8,9 * DIS C1: 1,8,9 # G3: 1,7 => CTR => G3: 3,8 * DIS C1: 1,8,9 + G3: 3,8 # C5: 1,7 => CTR => C5: 5,6 * DIS C1: 1,8,9 + G3: 3,8 + C5: 5,6 # D5: 5,7 => CTR => D5: 8 * PRF C1: 1,8,9 + G3: 3,8 + C5: 5,6 + D5: 8 => SOL * STA C1: 1,8,9 + G3: 3,8 + C5: 5,6 + D5: 8 * CNT 5 HDP CHAINS / 21 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060323, absurd
Solution
position: 659378142238194657471256389842739516596821734713645298165987423384562971927413865 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 # C1: 6,7 => CTR => C1: 1,8,9 * INC # C1: 1,8,9 => UNS * INC # C3: 6,7 => UNS * INC # A5: 6,7 => UNS * INC # A5: 5 => UNS * INC # C1: 1,7 => UNS * INC # C3: 1,7 => UNS * DIS # G3: 1,7 => CTR => G3: 3,8 * INC # G3: 3,8 => UNS * INC # H3: 1,7 => UNS * DIS # C5: 1,7 => CTR => C5: 5,6 * INC # C5: 5,6 => UNS * INC # C6: 1,7 => UNS * INC # D5: 5,7 => UNS * PRF # D5: 8 => SOL * INC # G4: 5,7 => UNS * INC # H4: 5,7 => UNS * INC # I4: 5,7 => UNS * INC # A8: 3,5 => UNS * DIS # C9: 3,5 => CTR => C9: 7 * INC # C9: 7 => UNS * DIS # D7: 3,5 => CTR => D7: 8,9 * INC # D7: 8,9 => UNS * INC # I7: 3,5 => UNS * INC # C6: 3,5 => UNS * INC # C6: 1,7 => UNS * INC # D7: 8,9 => UNS * DIS # D7: 3,5 => CTR => D7: 8,9 * INC # E1: 8,9 => UNS * INC # E2: 8,9 => UNS * INC # G9: 5,7 => UNS * DIS # H9: 5,7 => CTR => H9: 6,8 * INC # H9: 6,8 => UNS * INC # I9: 5,7 => UNS * INC # A8: 5,7 => UNS * INC # A8: 3 => UNS * INC # H2: 5,7 => UNS * INC # H4: 5,7 => UNS * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C1: 6,7 => CTR => C1: 1,8,9 * INC C1: 1,8,9 # C3: 6,7 => UNS * INC C1: 1,8,9 # C3: 6,7 => UNS * INC C1: 1,8,9 # C3: 1,8 => UNS * INC C1: 1,8,9 # A5: 6,7 => UNS * INC C1: 1,8,9 # A5: 5 => UNS * INC C1: 1,8,9 # C3: 1,7 => UNS * INC C1: 1,8,9 # C3: 6,8 => UNS * DIS C1: 1,8,9 # G3: 1,7 => CTR => G3: 3,8 * INC C1: 1,8,9 + G3: 3,8 # H3: 1,7 => UNS * INC C1: 1,8,9 + G3: 3,8 # H3: 1,7 => UNS * INC C1: 1,8,9 + G3: 3,8 # H3: 8 => UNS * INC C1: 1,8,9 + G3: 3,8 # C3: 1,7 => UNS * INC C1: 1,8,9 + G3: 3,8 # C3: 6,8 => UNS * INC C1: 1,8,9 + G3: 3,8 # H3: 1,7 => UNS * INC C1: 1,8,9 + G3: 3,8 # H3: 8 => UNS * DIS C1: 1,8,9 + G3: 3,8 # C5: 1,7 => CTR => C5: 5,6 * INC C1: 1,8,9 + G3: 3,8 + C5: 5,6 # C6: 1,7 => UNS * INC C1: 1,8,9 + G3: 3,8 + C5: 5,6 # C6: 1,7 => UNS * INC C1: 1,8,9 + G3: 3,8 + C5: 5,6 # C6: 3,5 => UNS * DIS C1: 1,8,9 + G3: 3,8 + C5: 5,6 # D5: 5,7 => CTR => D5: 8 * PRF C1: 1,8,9 + G3: 3,8 + C5: 5,6 + D5: 8 => SOL * STA C1: 1,8,9 + G3: 3,8 + C5: 5,6 + D5: 8 * CNT 22 HDP CHAINS / 21 HYP OPENED