Analysis of zz-www.sudokuoftheday.co.uk-20060506-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: 6...1934.5.3.....84......1...6........4.27.6.......7.......19...72.9.5......73.2. initial
Autosolve
position: 62..1934.5137...984......1.7.6.....2..4.27.6.2.....7.....2.197..72.9.5......73.2. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 7,8 => CTR => C3: 9 * DIS # C3: 7 => CTR => C3: 8,9 * DIS # B5: 8,9 => CTR => B5: 3,5 * DIS # B6: 8,9 => CTR => B6: 3,5 * DIS # D3: 5,8 => CTR => D3: 3,6 * DIS # E3: 5,8 => CTR => E3: 3,6 * DIS # D4: 5,8 => CTR => D4: 1,3,4,9 * DIS # D5: 5,8 => CTR => D5: 1,3,9 * DIS # D6: 5,8 => CTR => D6: 1,3,4,6,9 * DIS # E7: 4,6 => CTR => E7: 5,8 * PRF # G4: 1,8 => SOL * DIS # D5: 1,8 => CTR => D5: 3,5,9 * PRF # G9: 4 => SOL * DIS # A8: 3,8 => CTR => A8: 1 * DIS # E7: 4,6 => CTR => E7: 5,8 * DIS # C9: 1,9 => CTR => C9: 5,8 * DIS # E7: 4,6 => CTR => E7: 5,8 * DIS # D9: 4,6 => CTR => D9: 5,8 * DIS # A8: 3,8 => CTR => A8: 1 * CNT 19 HDP CHAINS / 53 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 7,8 => CTR => C3: 9 * DIS C3: 9 # E7: 4,6 => CTR => E7: 5,8 * PRF C3: 9 + E7: 5,8 # G4: 1,8 => SOL * STA C3: 9 + E7: 5,8 + G4: 1,8 * CNT 3 HDP CHAINS / 16 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6...1934.5.3.....84......1...6........4.27.6.......7.......19...72.9.5......73.2. | initial |
| 62..1934.5137...984......1.7.6.....2..4.27.6.2.....7.....2.197..72.9.5......73.2. | autosolve |
| 627819345513742698489635217796154832854327169231968754345281976172496583968573421 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) C1: 7,8 B3: 8,9 D1: 5,8 E2: 4,6 I1: 5,7 G2: 2,6 G3: 2,6 I3: 5,7 G5: 1,8 A7: 3,8 B7: 4,6 C7: 5,8 B9: 4,6 H8: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A5,C6: 1.. / A5 = 1 => 0 pairs (X) / C6 = 1 => 15 pairs (_) D4,G4: 1.. / D4 = 1 => 16 pairs (_) / G4 = 1 => 0 pairs (X) A8,I8: 1.. / A8 = 1 => 17 pairs (_) / I8 = 1 => 0 pairs (X) C6,C9: 1.. / C6 = 1 => 15 pairs (_) / C9 = 1 => 0 pairs (X) F2,F3: 2.. / F2 = 2 => 11 pairs (_) / F3 = 2 => 13 pairs (_) G2,G3: 2.. / G2 = 2 => 13 pairs (_) / G3 = 2 => 11 pairs (_) F2,G2: 2.. / F2 = 2 => 11 pairs (_) / G2 = 2 => 13 pairs (_) F3,G3: 2.. / F3 = 2 => 13 pairs (_) / G3 = 2 => 11 pairs (_) D3,E3: 3.. / D3 = 3 => 14 pairs (_) / E3 = 3 => 15 pairs (_) A7,A8: 3.. / A7 = 3 => 16 pairs (_) / A8 = 3 => 0 pairs (X) A7,I7: 3.. / A7 = 3 => 16 pairs (_) / I7 = 3 => 0 pairs (X) E2,F2: 4.. / E2 = 4 => 14 pairs (_) / F2 = 4 => 13 pairs (_) G4,I6: 4.. / G4 = 4 => 17 pairs (_) / I6 = 4 => 0 pairs (*) B7,B9: 4.. / B7 = 4 => 14 pairs (_) / B9 = 4 => 18 pairs (_) G4,G9: 4.. / G4 = 4 => 17 pairs (_) / G9 = 4 => 0 pairs (*) I1,I3: 5.. / I1 = 5 => 12 pairs (_) / I3 = 5 => 0 pairs (X) H4,H6: 5.. / H4 = 5 => 16 pairs (_) / H6 = 5 => 15 pairs (_) C7,C9: 5.. / C7 = 5 => 12 pairs (_) / C9 = 5 => 0 pairs (X) E7,D9: 5.. / E7 = 5 => 0 pairs (X) / D9 = 5 => 12 pairs (_) D1,I1: 5.. / D1 = 5 => 0 pairs (X) / I1 = 5 => 12 pairs (_) B5,D5: 5.. / B5 = 5 => 14 pairs (_) / D5 = 5 => 0 pairs (X) C7,E7: 5.. / C7 = 5 => 12 pairs (_) / E7 = 5 => 0 pairs (X) C9,D9: 5.. / C9 = 5 => 0 pairs (X) / D9 = 5 => 12 pairs (_) G2,G3: 6.. / G2 = 6 => 11 pairs (_) / G3 = 6 => 13 pairs (_) B7,B9: 6.. / B7 = 6 => 18 pairs (_) / B9 = 6 => 14 pairs (_) C1,C3: 7.. / C1 = 7 => 12 pairs (_) / C3 = 7 => 0 pairs (X) I1,I3: 7.. / I1 = 7 => 0 pairs (X) / I3 = 7 => 12 pairs (_) C1,I1: 7.. / C1 = 7 => 12 pairs (_) / I1 = 7 => 0 pairs (X) C3,I3: 7.. / C3 = 7 => 0 pairs (X) / I3 = 7 => 12 pairs (_) H8,G9: 8.. / H8 = 8 => 0 pairs (*) / G9 = 8 => 0 pairs (X) C1,D1: 8.. / C1 = 8 => 0 pairs (X) / D1 = 8 => 12 pairs (_) B3,C3: 9.. / B3 = 9 => 0 pairs (X) / C3 = 9 => 13 pairs (_) I5,I6: 9.. / I5 = 9 => 20 pairs (_) / I6 = 9 => 0 pairs (X) A9,C9: 9.. / A9 = 9 => 16 pairs (_) / C9 = 9 => 0 pairs (X) B4,D4: 9.. / B4 = 9 => 15 pairs (_) / D4 = 9 => 0 pairs (X) A5,A9: 9.. / A5 = 9 => 0 pairs (X) / A9 = 9 => 16 pairs (_) * DURATION: 0:00:40.557231 START: 22:57:07.919532 END: 22:57:48.476763 2019-04-30 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B3,B7,B9,C1,C7,D1,E2,G2,G3,G5,H8,I1,I3) * 62..1934.5137...984......1.7.6.....2..4.27.6.2.....7.....2.197..72.9.5......73.2. * PAIR C1: 7,8 BLK 1 C3: 7,8,9 # reduction candidate for 7,8 C3: 7,8 => CTR * 62..1934.5137...9849.....1.7.69..1.2..4.278692.91..7.4.4.2.197..7249658.961.7342. C3: 9 # 13 pairs * PAIR B3: 8,9 BLK 1 C3: 8,9,7 # reduction candidate for 8,9 C3: 7 => CTR * 6285193475137...98497....157.69..1.2.54.278692.91..7.4.4.2.197..72.9.58.....7342. C3: 8,9 # 12 pairs * PAIR B3: 8,9 COL B B4: 8,9,3,5 # reduction candidate for 8,9 B4: 8,9 # 17 pairs B5: 8,9,3,5 # reduction candidate for 8,9 B5: 8,9 => CTR * 62.8193455137...984.9..52177.69....2..4527.632.....7.93..25197..72.9.53...5.7382. B5: 3,5 # 15 pairs B6: 8,9,3,5 # reduction candidate for 8,9 B6: 8,9 => CTR * 62..1934.5137...984......1.7.69..1.21.4.278692..16.7348452.197..7249658.96..73421 B6: 3,5 # 15 pairs * PAIR D1: 5,8 BLK 2 D3: 5,8,3,6 # reduction candidate for 5,8 D3: 5,8 => CTR * 6278193455137...9848953..177.618.4.2854.2716.2.1...7..3.825197.172.9853.9.5.73821 D3: 3,6 # 15 pairs E3: 5,8,3,6 # reduction candidate for 5,8 E3: 5,8 => CTR * 62.5193475137...984..3...1.7.61..4.2.549271632.1...7.93..2.197..72.9.53.9.5.73821 E3: 3,6 # 15 pairs F3: 5,8,2,6 # reduction candidate for 5,8 F3: 5,8 # 14 pairs * PAIR D1: 5,8 COL D D4: 5,8,1,3,4,9 # reduction candidate for 5,8 D4: 5,8 => CTR * 62..1934.5137...98489....17796...1.21.4.278692.8...7.4...2.197..72.9.58.9...7342. D4: 1,3,4,9 # 14 pairs D5: 5,8,1,3,9 # reduction candidate for 5,8 D5: 5,8 => CTR * 6278193455137...98489365.1.7.6...4.2..4.2716.2.19..7.33.825197.172.9853.9.5.73821 D5: 1,3,9 # 14 pairs D6: 5,8,1,3,4,6,9 # reduction candidate for 5,8 D6: 5,8 => CTR * 62..1934.5137...984.93...1779613.482854927163231...7593.825197.172.9853.9.5.73821 D6: 1,3,4,6,9 # 14 pairs D9: 5,8,4,6 # reduction candidate for 5,8 D9: 5,8 # 17 pairs * PAIR E2: 4,6 BLK 2 F2: 4,6,2 # reduction candidate for 4,6 F2: 4,6 # 13 pairs F2: 2 # 11 pairs * PAIR E2: 4,6 COL E E6: 4,6,3,5,8 # reduction candidate for 4,6 E6: 4,6 # 17 pairs E7: 4,6,5,8 # reduction candidate for 4,6 E7: 4,6 => CTR * 62.8193455137...984......177.6.....2.54.27.6.2.....7..8.52.1973372.985.....573.2. E7: 5,8 # 16 pairs * PAIR G2: 2,6 ROW 2 F2: 2,6,4 # reduction candidate for 2,6 F2: 2,6 # 14 pairs F2: 4 # 13 pairs * PAIR G3: 2,6 ROW 3 F3: 2,6,5,8 # reduction candidate for 2,6 F3: 2,6 # 15 pairs F3: 5,8 # 14 pairs * PAIR G5: 1,8 BLK 6 G4: 1,8,4 # reduction candidate for 1,8 G4: 1,8 => SOLVED * 627819345513742698489635217796154832854327169231968754345281976172496583968573421 G4: 4 # 17 pairs * PAIR G5: 1,8 ROW 5 A5: 1,8,9 # reduction candidate for 1,8 A5: 1,8 # 16 pairs D5: 1,8,3,5,9 # reduction candidate for 1,8 D5: 1,8 => CTR * 62..1934.5137...984......1.7.69....2.54.27.632.....7.93..2.197..72.9.53.....7382. D5: 3,5,9 # 14 pairs * PAIR G5: 1,8 COL G G9: 1,8,4 # reduction candidate for 1,8 G9: 4 => SOLVED * 627819345513742698489635217796154832854327169231968754345281976172496583968573421 G9: 1,8 # 17 pairs * PAIR A7: 3,8 BLK 7 A8: 3,8,1 # reduction candidate for 3,8 A8: 3,8 => CTR * 62..1934.5137...984......1.7.6...4.2.54.27.6.2.....7.....2.197..72.9.5.1....73.2. A8: 1 # 17 pairs * PAIR B7: 4,6 ROW 7 E7: 4,6,5,8 # reduction candidate for 4,6 E7: 4,6 => CTR * 62.8193455137...984......177.6.....2.54.27.6.2.....7..8.52.1973372.985.....573.2. E7: 5,8 # 16 pairs I7: 4,6,3 # reduction candidate for 4,6 I7: 4,6 # 16 pairs * PAIR C7: 5,8 BLK 7 C9: 5,8,1,9 # reduction candidate for 5,8 C9: 1,9 => CTR * 6278193455137...98498....177.69..1.29541278632.....7....52.197..72.9.58.8.9573.2. C9: 5,8 # 16 pairs * PAIR C7: 5,8 ROW 7 E7: 5,8,4,6 # reduction candidate for 5,8 E7: 4,6 => CTR * 62.8193455137...984......177.6.....2.54.27.6.2.....7..8.52.1973372.985.....573.2. E7: 5,8 # 16 pairs * PAIR B9: 4,6 ROW 9 D9: 4,6,5,8 # reduction candidate for 4,6 D9: 4,6 => CTR * 62781934551374..984895...177.61.5482854.2716.2.1.8.75.3.825197.172.9853.9.5.73821 D9: 5,8 # 17 pairs I9: 4,6,1 # reduction candidate for 4,6 I9: 4,6 # 20 pairs * PAIR H8: 3,8 ROW 8 A8: 3,8,1 # reduction candidate for 3,8 A8: 3,8 => CTR * 62..1934.5137...984......1.7.6...4.2.54.27.6.2.....7.....2.197..72.9.5.1....73.2. A8: 1 # 17 pairs * PAIR H8: 3,8 COL H H4: 3,8,5 # reduction candidate for 3,8 H4: 3,8 # 15 pairs H6: 3,8,5 # reduction candidate for 3,8 H6: 3,8 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060506-absurd-base-pr-000.dot * REASONING * DIS # C3: 7,8 => CTR => C3: 9 * DIS # C3: 7 => CTR => C3: 8,9 * DIS # B5: 8,9 => CTR => B5: 3,5 * DIS # B6: 8,9 => CTR => B6: 3,5 * DIS # D3: 5,8 => CTR => D3: 3,6 * DIS # E3: 5,8 => CTR => E3: 3,6 * DIS # D4: 5,8 => CTR => D4: 1,3,4,9 * DIS # D5: 5,8 => CTR => D5: 1,3,9 * DIS # D6: 5,8 => CTR => D6: 1,3,4,6,9 * DIS # E7: 4,6 => CTR => E7: 5,8 * PRF # G4: 1,8 => SOL * DIS # D5: 1,8 => CTR => D5: 3,5,9 * PRF # G9: 4 => SOL * DIS # A8: 3,8 => CTR => A8: 1 * DIS # E7: 4,6 => CTR => E7: 5,8 * DIS # C9: 1,9 => CTR => C9: 5,8 * DIS # E7: 4,6 => CTR => E7: 5,8 * DIS # D9: 4,6 => CTR => D9: 5,8 * DIS # A8: 3,8 => CTR => A8: 1 * CNT 19 HDP CHAINS / 53 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B3,B7,B9,C1,C7,D1,E2,G2,G3,G5,H8,I1,I3) * 62..1934.5137...984......1.7.6.....2..4.27.6.2.....7.....2.197..72.9.5......73.2. * PAIR C1: 7,8 BLK 1 C3: 7,8,9 # reduction candidate for 7,8 C3: 7,8 => CTR * 62..1934.5137...9849.....1.7.69..1.2..4.278692.91..7.4.4.2.197..7249658.961.7342. * PAIR E2: 4,6 BLK 2 F2: 4,6,2 # reduction candidate for 4,6 F2: 4,6 # 17 pairs F2: 2 # 11 pairs * PAIR E2: 4,6 COL E E6: 4,6,3,5,8 # reduction candidate for 4,6 E6: 4,6 # 17 pairs E7: 4,6,5,8 # reduction candidate for 4,6 E7: 4,6 => CTR * 6278193455137...98489....177.6.....2..4.27.6.2.....7....52.197..72.9853.9..57382. * RESTART * PAIR E2: 4,6 COL E E6: 4,6,3,5,8 # reduction candidate for 4,6 E6: 3,5,8 # 18 pairs E6: 4,6 # 17 pairs * PAIR RESTART * PAIR E2: 4,6 BLK 2 F2: 4,6,2 # reduction candidate for 4,6 F2: 4,6 # 19 pairs F2: 2 # 13 pairs * PAIR E2: 4,6 COL E E6: 4,6,3,5,8 # reduction candidate for 4,6 E6: 3,5,8 # 18 pairs E6: 4,6 # 17 pairs * PAIR G2: 2,6 ROW 2 F2: 2,6,4 # reduction candidate for 2,6 F2: 4 # 19 pairs F2: 2,6 # 15 pairs * PAIR G3: 2,6 ROW 3 F3: 2,6,5 # reduction candidate for 2,6 F3: 2,6 # 21 pairs F3: 5 # 15 pairs * PAIR G5: 1,8 BLK 6 G4: 1,8,4 # reduction candidate for 1,8 G4: 1,8 => SOLVED * 627819345513742698489635217796154832854327169231968754345281976172496583968573421 * DURATION: 0:00:12.731741 START: 22:58:20.833971 END: 22:58:33.565712 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060506-absurd-base-pr-001.dot * REASONING * DIS # C3: 7,8 => CTR => C3: 9 * DIS C3: 9 # E7: 4,6 => CTR => E7: 5,8 * PRF C3: 9 + E7: 5,8 # G4: 1,8 => SOL * STA C3: 9 + E7: 5,8 + G4: 1,8 * CNT 3 HDP CHAINS / 16 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060506, absurd
Solution
position: 627819345513742698489635217796154832854327169231968754345281976172496583968573421 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 # C3: 7,8 => CTR => C3: 9 * INC # C3: 9 => UNS * INC # C3: 8,9 => UNS * DIS # C3: 7 => CTR => C3: 8,9 * INC # B4: 8,9 => UNS * DIS # B5: 8,9 => CTR => B5: 3,5 * INC # B5: 3,5 => UNS * DIS # B6: 8,9 => CTR => B6: 3,5 * INC # B6: 3,5 => UNS * DIS # D3: 5,8 => CTR => D3: 3,6 * INC # D3: 3,6 => UNS * DIS # E3: 5,8 => CTR => E3: 3,6 * INC # E3: 3,6 => UNS * INC # F3: 5,8 => UNS * DIS # D4: 5,8 => CTR => D4: 1,3,4,9 * INC # D4: 1,3,4,9 => UNS * DIS # D5: 5,8 => CTR => D5: 1,3,9 * INC # D5: 1,3,9 => UNS * DIS # D6: 5,8 => CTR => D6: 1,3,4,6,9 * INC # D6: 1,3,4,6,9 => UNS * INC # D9: 5,8 => UNS * INC # F2: 4,6 => UNS * INC # F2: 2 => UNS * INC # E6: 4,6 => UNS * DIS # E7: 4,6 => CTR => E7: 5,8 * INC # E7: 5,8 => UNS * INC # F2: 2,6 => UNS * INC # F2: 4 => UNS * INC # F3: 2,6 => UNS * INC # F3: 5,8 => UNS * PRF # G4: 1,8 => SOL * INC # G4: 4 => UNS * INC # A5: 1,8 => UNS * DIS # D5: 1,8 => CTR => D5: 3,5,9 * INC # D5: 3,5,9 => UNS * INC # G9: 1,8 => UNS * PRF # G9: 4 => SOL * DIS # A8: 3,8 => CTR => A8: 1 * INC # A8: 1 => UNS * DIS # E7: 4,6 => CTR => E7: 5,8 * INC # E7: 5,8 => UNS * INC # I7: 4,6 => UNS * INC # C9: 5,8 => UNS * DIS # C9: 1,9 => CTR => C9: 5,8 * INC # E7: 5,8 => UNS * DIS # E7: 4,6 => CTR => E7: 5,8 * DIS # D9: 4,6 => CTR => D9: 5,8 * INC # D9: 5,8 => UNS * INC # I9: 4,6 => UNS * DIS # A8: 3,8 => CTR => A8: 1 * INC # A8: 1 => UNS * INC # H4: 3,8 => UNS * INC # H6: 3,8 => UNS * CNT 53 HDP CHAINS / 53 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C3: 7,8 => CTR => C3: 9 * INC C3: 9 # F2: 4,6 => UNS * INC C3: 9 # F2: 2 => UNS * INC C3: 9 # E6: 4,6 => UNS * DIS C3: 9 # E7: 4,6 => CTR => E7: 5,8 * INC C3: 9 + E7: 5,8 # E6: 4,6 => UNS * INC C3: 9 + E7: 5,8 # E6: 3,5,8 => UNS * INC C3: 9 + E7: 5,8 # F2: 4,6 => UNS * INC C3: 9 + E7: 5,8 # F2: 2 => UNS * INC C3: 9 + E7: 5,8 # E6: 4,6 => UNS * INC C3: 9 + E7: 5,8 # E6: 3,5,8 => UNS * INC C3: 9 + E7: 5,8 # F2: 2,6 => UNS * INC C3: 9 + E7: 5,8 # F2: 4 => UNS * INC C3: 9 + E7: 5,8 # F3: 2,6 => UNS * INC C3: 9 + E7: 5,8 # F3: 5 => UNS * PRF C3: 9 + E7: 5,8 # G4: 1,8 => SOL * STA C3: 9 + E7: 5,8 + G4: 1,8 * CNT 16 HDP CHAINS / 16 HYP OPENED