Analysis of zz-www.sudokuoftheday.co.uk-20060527-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: ..4.1..7.8....7...37..9...1.6.1....5.4...62...2...39.....7....6..1.6..53....81... initial
Autosolve
position: ..4.1..7.81...7...37..9...1.6.1....5.43..621.12...396....7..1.6..1.6..53....81... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B9: 5,9 => CTR => B9: 3 * PRF # A5: 7,9 => SOL * DIS # A9: 7,9 => CTR => A9: 2,4,5,6 * DIS # A5: 9 => CTR => A5: 5,7 * DIS # G4: 7,8 => CTR => G4: 3,4 * DIS # I9: 4,7 => CTR => I9: 2,9 * DIS # G4: 4,7 => CTR => G4: 3,8 * CNT 7 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B9: 5,9 => CTR => B9: 3 * DIS B9: 3 # B7: 8 => CTR => B7: 5,9 * DIS B9: 3 + B7: 5,9 # C4: 7,9 => CTR => C4: 8 * PRF B9: 3 + B7: 5,9 + C4: 8 => SOL * STA B9: 3 + B7: 5,9 + C4: 8 * CNT 4 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..4.1..7.8....7...37..9...1.6.1....5.4...62...2...39.....7....6..1.6..53....81... | initial |
| ..4.1..7.81...7...37..9...1.6.1....5.43..621.12...396....7..1.6..1.6..53....81... | autosolve |
| 254318679819627534376495821968172345743956218125843967592734186481269753637581492 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) B1: 5,9 A4: 7,9 E5: 5,7 I5: 7,8 B8: 8,9 G9: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E4,F4: 2.. / E4 = 2 => 6 pairs (_) / F4 = 2 => 15 pairs (_) G4,H4: 3.. / G4 = 3 => 8 pairs (_) / H4 = 3 => 7 pairs (_) B7,B9: 3.. / B7 = 3 => 0 pairs (X) / B9 = 3 => 6 pairs (_) E7,D9: 3.. / E7 = 3 => 6 pairs (_) / D9 = 3 => 0 pairs (X) D1,G1: 3.. / D1 = 3 => 6 pairs (_) / G1 = 3 => 8 pairs (_) B7,E7: 3.. / B7 = 3 => 0 pairs (X) / E7 = 3 => 6 pairs (_) B9,D9: 3.. / B9 = 3 => 6 pairs (_) / D9 = 3 => 0 pairs (X) E2,E7: 3.. / E2 = 3 => 0 pairs (X) / E7 = 3 => 6 pairs (_) H2,H4: 3.. / H2 = 3 => 8 pairs (_) / H4 = 3 => 7 pairs (_) A5,C6: 5.. / A5 = 5 => 11 pairs (_) / C6 = 5 => 0 pairs (*) A9,C9: 6.. / A9 = 6 => 8 pairs (_) / C9 = 6 => 16 pairs (_) A1,A9: 6.. / A1 = 6 => 16 pairs (_) / A9 = 6 => 8 pairs (_) A8,G8: 7.. / A8 = 7 => 14 pairs (_) / G8 = 7 => 13 pairs (_) C4,C6: 8.. / C4 = 8 => 9 pairs (_) / C6 = 8 => 19 pairs (_) B7,B8: 8.. / B7 = 8 => 0 pairs (X) / B8 = 8 => 12 pairs (_) H7,G8: 8.. / H7 = 8 => 12 pairs (_) / G8 = 8 => 0 pairs (X) D5,I5: 8.. / D5 = 8 => 0 pairs (X) / I5 = 8 => 9 pairs (_) B7,H7: 8.. / B7 = 8 => 0 pairs (X) / H7 = 8 => 12 pairs (_) B8,G8: 8.. / B8 = 8 => 12 pairs (_) / G8 = 8 => 0 pairs (X) F4,D5: 9.. / F4 = 9 => 0 pairs (X) / D5 = 9 => 10 pairs (_) A5,D5: 9.. / A5 = 9 => 0 pairs (X) / D5 = 9 => 10 pairs (_) * DURATION: 0:00:19.666576 START: 23:26:44.412505 END: 23:27:04.079081 2019-04-30 * CP COUNT: (21) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B1,B8,E5,G9,I5) * ..4.1..7.81...7...37..9...1.6.1....5.43..621.12...396....7..1.6..1.6..53....81... * PAIR B1: 5,9 BLK 1 A1: 5,9,2,6 # reduction candidate for 5,9 A1: 5,9 # 23 pairs C2: 5,9,2,6 # reduction candidate for 5,9 C2: 5,9 # 9 pairs * PAIR B1: 5,9 COL B B7: 5,9,3,8 # reduction candidate for 5,9 B7: 5,9 # 13 pairs B9: 5,9,3 # reduction candidate for 5,9 B9: 5,9 => CTR * .94.1.37881..37...37..9...1.6.1..835.438.6217128.73964.3.7..186.8196..53.5.381... B9: 3 # 6 pairs * PAIR A4: 7,9 BLK 4 C4: 7,9,8 # reduction candidate for 7,9 C4: 7,9 # 19 pairs A5: 7,9,5 # reduction candidate for 7,9 A5: 7,9 => SOLVED * 254318679819627534376495821968172345743956218125843967592734186481269753637581492 A5: 5 # 11 pairs * PAIR A4: 7,9 COL A A8: 7,9,2,4 # reduction candidate for 7,9 A8: 7,9 # 14 pairs A9: 7,9,2,4,5,6 # reduction candidate for 7,9 A9: 7,9 => CTR * 6.431.87.81...7.3437.894621967128345543976218128..3967...73.186.814697537365814.. A9: 2,4,5,6 # 6 pairs * PAIR E5: 5,7 BLK 5 E6: 5,7,4 # reduction candidate for 5,7 E6: 4 # 12 pairs E6: 5,7 # 10 pairs * PAIR E5: 5,7 ROW 5 A5: 5,7,9 # reduction candidate for 5,7 A5: 9 => CTR * ..431.67.81...753437..9...1768129345943..621.125..396....7..186.8196.7536.7.814.. A5: 5,7 # 10 pairs * PAIR I5: 7,8 BLK 6 G4: 7,8,3,4 # reduction candidate for 7,8 G4: 7,8 => CTR * .54.18.7.819..7.4237..9..81.681..735.439.6218127853964.8.73.1.6791.6.853.3..81497 G4: 3,4 # 7 pairs I6: 7,8,4 # reduction candidate for 7,8 I6: 7,8 # 11 pairs * PAIR B8: 8,9 BLK 7 B7: 8,9,3,5 # reduction candidate for 8,9 B7: 3,5 # 16 pairs B7: 8,9 # 9 pairs * PAIR G9: 4,7 BLK 9 G8: 4,7,8 # reduction candidate for 4,7 G8: 4,7 # 12 pairs I9: 4,7,2,9 # reduction candidate for 4,7 I9: 4,7 => CTR * .54.1..79819.4753237..9548196.12.34554397621812.45396748573912679126.853.3.581.9. I9: 2,9 # 7 pairs * PAIR G9: 4,7 ROW 9 A9: 4,7,2,5,6,9 # reduction candidate for 4,7 A9: 4,7 # 25 pairs A9: 2,5,6,9 # 6 pairs * PAIR G9: 4,7 COL G G4: 4,7,3,8 # reduction candidate for 4,7 G4: 4,7 => CTR * 654.1.379819..7...37..9568196.1...3554397621812..5396..857391.6791.6.853.36581.9. G4: 3,8 # 7 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060527-absurd-base-pr-000.dot * REASONING * DIS # B9: 5,9 => CTR => B9: 3 * PRF # A5: 7,9 => SOL * DIS # A9: 7,9 => CTR => A9: 2,4,5,6 * DIS # A5: 9 => CTR => A5: 5,7 * DIS # G4: 7,8 => CTR => G4: 3,4 * DIS # I9: 4,7 => CTR => I9: 2,9 * DIS # G4: 4,7 => CTR => G4: 3,8 * CNT 7 HDP CHAINS / 27 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B1,B8,E5,G9,I5) * ..4.1..7.81...7...37..9...1.6.1....5.43..621.12...396....7..1.6..1.6..53....81... * PAIR B1: 5,9 BLK 1 A1: 5,9,2,6 # reduction candidate for 5,9 A1: 5,9 # 23 pairs C2: 5,9,2,6 # reduction candidate for 5,9 C2: 5,9 # 9 pairs * PAIR B1: 5,9 COL B B7: 5,9,3,8 # reduction candidate for 5,9 B7: 5,9 # 13 pairs B9: 5,9,3 # reduction candidate for 5,9 B9: 5,9 => CTR * .94.1.37881..37...37..9...1.6.1..835.438.6217128.73964.3.7..186.8196..53.5.381... * RESTART * PAIR B1: 5,9 COL B B7: 5,9,8 # reduction candidate for 5,9 B7: 8 => CTR * .54.1..798196.753237..9548196.12.34554397621812.45396748573912679126.853.3.581.9. * PAIR RESTART * PAIR B1: 5,9 BLK 1 A1: 5,9,2,6 # reduction candidate for 5,9 A1: 5,9 # 27 pairs C2: 5,9,2,6 # reduction candidate for 5,9 C2: 5,9 # 16 pairs * PAIR A4: 7,9 BLK 4 C4: 7,9,8 # reduction candidate for 7,9 C4: 7,9 => CTR * ..431.879819.5763437..9..21.6.1.8345543976218128.43967...73.186.81.6..53.3..81.92 C4: 8 => SOLVED * 254318679819627534376495821968172345743956218125843967592734186481269753637581492 * DURATION: 0:00:06.005563 START: 23:27:18.355416 END: 23:27:24.360979 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060527-absurd-base-pr-001.dot * REASONING * DIS # B9: 5,9 => CTR => B9: 3 * DIS B9: 3 # B7: 8 => CTR => B7: 5,9 * DIS B9: 3 + B7: 5,9 # C4: 7,9 => CTR => C4: 8 * PRF B9: 3 + B7: 5,9 + C4: 8 => SOL * STA B9: 3 + B7: 5,9 + C4: 8 * CNT 4 HDP CHAINS / 9 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060527, absurd
Solution
position: 254318679819627534376495821968172345743956218125843967592734186481269753637581492 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 # A1: 5,9 => UNS * INC # C2: 5,9 => UNS * INC # B7: 5,9 => UNS * DIS # B9: 5,9 => CTR => B9: 3 * INC # B9: 3 => UNS * INC # C4: 7,9 => UNS * PRF # A5: 7,9 => SOL * INC # A5: 5 => UNS * INC # A8: 7,9 => UNS * DIS # A9: 7,9 => CTR => A9: 2,4,5,6 * INC # A9: 2,4,5,6 => UNS * INC # E6: 5,7 => UNS * INC # E6: 4 => UNS * INC # A5: 5,7 => UNS * DIS # A5: 9 => CTR => A5: 5,7 * DIS # G4: 7,8 => CTR => G4: 3,4 * INC # G4: 3,4 => UNS * INC # I6: 7,8 => UNS * INC # B7: 8,9 => UNS * INC # B7: 3,5 => UNS * INC # G8: 4,7 => UNS * DIS # I9: 4,7 => CTR => I9: 2,9 * INC # I9: 2,9 => UNS * INC # A9: 4,7 => UNS * INC # A9: 2,5,6,9 => UNS * DIS # G4: 4,7 => CTR => G4: 3,8 * INC # G4: 3,8 => UNS * CNT 27 HDP CHAINS / 27 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 5,9 => UNS * INC # C2: 5,9 => UNS * INC # B7: 5,9 => UNS * DIS # B9: 5,9 => CTR => B9: 3 * INC B9: 3 # B7: 5,9 => UNS * DIS B9: 3 # B7: 8 => CTR => B7: 5,9 * INC B9: 3 + B7: 5,9 # A1: 5,9 => UNS * INC B9: 3 + B7: 5,9 # C2: 5,9 => UNS * DIS B9: 3 + B7: 5,9 # C4: 7,9 => CTR => C4: 8 * PRF B9: 3 + B7: 5,9 + C4: 8 => SOL * STA B9: 3 + B7: 5,9 + C4: 8 * CNT 10 HDP CHAINS / 9 HYP OPENED