Analysis of zz-www.sudokuoftheday.co.uk-20060601-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006
level: medium
position: .5...2......74..6.71...3.....5..8..4...26...1.2.51.8...4.9.67.........1..3.....82 initial
Autosolve
position: .5.1.2......74.16.71.6.3...1.53.8..4...26...1.2.51.8..8419267.....83.41..3.4.1.82 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 8,9 => CTR => C2: 2,3 * DIS # I2: 8,9 => CTR => I2: 3,5 * DIS # I1: 8,9 => CTR => I1: 3,7 * DIS # E3: 8 => CTR => E3: 5,9 * DIS # I2: 3,8 => CTR => I2: 5,9 * DIS # I1: 3,9 => CTR => I1: 7,8 * DIS # G5: 3,9 => CTR => G5: 5 * DIS # B4: 7,9 => CTR => B4: 6 * PRF # B4: 6 => SOL * PRF # H4: 7,9 => SOL * DIS # I2: 8,9 => CTR => I2: 3,5 * PRF # A8: 6,9 => SOL * DIS # C8: 6,9 => CTR => C8: 2,7 * DIS # I6: 3,7 => CTR => I6: 6,9 * PRF # G4: 2 => SOL * CNT 15 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 8,9 => CTR => C2: 2,3 * DIS C2: 2,3 # I2: 8,9 => CTR => I2: 3,5 * DIS C2: 2,3 + I2: 3,5 # E3: 8,9 => CTR => E3: 5 * PRF C2: 2,3 + I2: 3,5 + E3: 5 # A8: 6,9 => SOL * STA C2: 2,3 + I2: 3,5 + E3: 5 + A8: 6,9 * CNT 4 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .5...2......74..6.71...3.....5..8..4...26...1.2.51.8...4.9.67.........1..3.....82 | initial |
| .5.1.2......74.16.71.6.3...1.53.8..4...26...1.2.51.8..8419267.....83.41..3.4.1.82 | autosolve |
| 956182347283749165714653928165398274498267531327514896841926753672835419539471682 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) B2: 8,9 E1: 8,9 F2: 5,9 G1: 3,9 E4: 7,9 F8: 5,7 E9: 5,7 H7: 3,5 I7: 3,5 I8: 6,9 G9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,C2: 2.. / A2 = 2 => 11 pairs (_) / C2 = 2 => 17 pairs (_) G3,H3: 2.. / G3 = 2 => 13 pairs (_) / H3 = 2 => 0 pairs (*) G4,H4: 2.. / G4 = 2 => 0 pairs (*) / H4 = 2 => 0 pairs (X) A8,C8: 2.. / A8 = 2 => 17 pairs (_) / C8 = 2 => 11 pairs (_) A2,A8: 2.. / A2 = 2 => 11 pairs (_) / A8 = 2 => 17 pairs (_) C2,C8: 2.. / C2 = 2 => 17 pairs (_) / C8 = 2 => 11 pairs (_) G3,G4: 2.. / G3 = 2 => 13 pairs (_) / G4 = 2 => 0 pairs (*) H3,H4: 2.. / H3 = 2 => 0 pairs (*) / H4 = 2 => 0 pairs (X) H7,I7: 3.. / H7 = 3 => 17 pairs (_) / I7 = 3 => 11 pairs (_) G1,G5: 3.. / G1 = 3 => 13 pairs (_) / G5 = 3 => 0 pairs (X) H1,H3: 4.. / H1 = 4 => 11 pairs (_) / H3 = 4 => 15 pairs (_) F5,F6: 4.. / F5 = 4 => 13 pairs (_) / F6 = 4 => 12 pairs (_) C3,H3: 4.. / C3 = 4 => 11 pairs (_) / H3 = 4 => 15 pairs (_) F2,E3: 5.. / F2 = 5 => 22 pairs (_) / E3 = 5 => 17 pairs (_) G5,H5: 5.. / G5 = 5 => 13 pairs (_) / H5 = 5 => 0 pairs (X) A8,A9: 5.. / A8 = 5 => 22 pairs (_) / A9 = 5 => 17 pairs (_) F8,E9: 5.. / F8 = 5 => 17 pairs (_) / E9 = 5 => 22 pairs (_) H7,I7: 5.. / H7 = 5 => 11 pairs (_) / I7 = 5 => 17 pairs (_) F2,I2: 5.. / F2 = 5 => 22 pairs (_) / I2 = 5 => 17 pairs (_) A8,F8: 5.. / A8 = 5 => 22 pairs (_) / F8 = 5 => 17 pairs (_) A9,E9: 5.. / A9 = 5 => 17 pairs (_) / E9 = 5 => 22 pairs (_) E3,E9: 5.. / E3 = 5 => 17 pairs (_) / E9 = 5 => 22 pairs (_) F2,F8: 5.. / F2 = 5 => 22 pairs (_) / F8 = 5 => 17 pairs (_) G3,G5: 5.. / G3 = 5 => 0 pairs (X) / G5 = 5 => 13 pairs (_) A1,C1: 6.. / A1 = 6 => 12 pairs (_) / C1 = 6 => 12 pairs (_) G4,I6: 6.. / G4 = 6 => 0 pairs (X) / I6 = 6 => 0 pairs (_) I8,G9: 6.. / I8 = 6 => 0 pairs (X) / G9 = 6 => 0 pairs (_) B4,G4: 6.. / B4 = 6 => 0 pairs (*) / G4 = 6 => 0 pairs (X) B4,B8: 6.. / B4 = 6 => 0 pairs (*) / B8 = 6 => 0 pairs (X) G4,G9: 6.. / G4 = 6 => 0 pairs (X) / G9 = 6 => 0 pairs (_) I6,I8: 6.. / I6 = 6 => 0 pairs (*) / I8 = 6 => 0 pairs (X) H1,I1: 7.. / H1 = 7 => 0 pairs (X) / I1 = 7 => 11 pairs (_) F8,E9: 7.. / F8 = 7 => 22 pairs (_) / E9 = 7 => 17 pairs (_) C9,E9: 7.. / C9 = 7 => 22 pairs (_) / E9 = 7 => 17 pairs (_) E4,E9: 7.. / E4 = 7 => 22 pairs (_) / E9 = 7 => 17 pairs (_) I1,I6: 7.. / I1 = 7 => 11 pairs (_) / I6 = 7 => 0 pairs (X) E1,E3: 8.. / E1 = 8 => 11 pairs (_) / E3 = 8 => 0 pairs (X) B5,C5: 8.. / B5 = 8 => 0 pairs (X) / C5 = 8 => 12 pairs (_) B2,B5: 8.. / B2 = 8 => 12 pairs (_) / B5 = 8 => 0 pairs (X) I8,G9: 9.. / I8 = 9 => 0 pairs (*) / G9 = 9 => 0 pairs (X) * DURATION: 0:00:54.043876 START: 23:32:43.256716 END: 23:33:37.300592 2019-04-30 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,E1,E4,E9,F2,F8,G1,G9,H7,I7,I8) * .5.1.2......74.16.71.6.3...1.53.8..4...26...1.2.51.8..8419267.....83.41..3.4.1.82 * PAIR B2: 8,9 BLK 1 C1: 8,9,3,4,6 # reduction candidate for 8,9 C1: 8,9 # 15 pairs C2: 8,9,2,3 # reduction candidate for 8,9 C2: 8,9 => CTR * .5.1.29..2..74516371.6935281.5378294...26.351.2.51.87684192673556283.41..3.4.1.82 C2: 2,3 # 12 pairs C3: 8,9,4 # reduction candidate for 8,9 C3: 8,9 # 15 pairs * PAIR B2: 8,9 ROW 2 I2: 8,9,3,5 # reduction candidate for 8,9 I2: 8,9 => CTR * .561.23..28374516971.6.3...165378294.7826.5.1.2.51.8..8419267..592837416637451982 I2: 3,5 # 14 pairs * PAIR B2: 8,9 COL B B5: 8,9,7 # reduction candidate for 8,9 B5: 7 # 16 pairs B5: 8,9 # 14 pairs * PAIR E1: 8,9 BLK 2 E3: 8,9,5 # reduction candidate for 8,9 E3: 8,9 # 22 pairs E3: 5 # 17 pairs * PAIR E1: 8,9 ROW 1 C1: 8,9,3,4,6 # reduction candidate for 8,9 C1: 8,9 # 15 pairs I1: 8,9,3,7 # reduction candidate for 8,9 I1: 8,9 => CTR * .5.1.237....74.16.71.6.324.1653.8.24...26...1.2.51.8.78419267.....83.416.3.4.1982 I1: 3,7 # 12 pairs * PAIR F2: 5,9 BLK 2 E3: 5,9,8 # reduction candidate for 5,9 E3: 8 => CTR * .5.1923.8283745169719683.451.5378.24.7826.5.1.2.51.8.7841926753592837416637451982 E3: 5,9 # 11 pairs * PAIR F2: 5,9 ROW 2 I2: 5,9,3,8 # reduction candidate for 5,9 I2: 3,8 => CTR * .5.1.29472897451637146935281.5378294.7826.351.2.51.8768419267355.283741..37451.82 I2: 5,9 # 15 pairs * PAIR G1: 3,9 BLK 3 H1: 3,9,4,7 # reduction candidate for 3,9 H1: 3,9 # 19 pairs I1: 3,9,7,8 # reduction candidate for 3,9 I1: 3,9 => CTR * .5.1.2379...74.16.71.6.324.1653.8.24...26...1.2.51.8.78419267.....83.416.3.4.1982 I1: 7,8 # 12 pairs I2: 3,9,5,8 # reduction candidate for 3,9 I2: 3,9 # 22 pairs * PAIR G1: 3,9 ROW 1 A1: 3,9,4,6 # reduction candidate for 3,9 A1: 3,9 # 13 pairs C1: 3,9,4,6,8 # reduction candidate for 3,9 C1: 3,9 # 13 pairs * PAIR G1: 3,9 COL G G5: 3,9,5 # reduction candidate for 3,9 G5: 3,9 => CTR * .5.1.2.47...745163714693528165378294...26.351.2.51.87684192673557.83.419.3.451682 G5: 5 # 13 pairs * PAIR E4: 7,9 BLK 5 F5: 7,9,4 # reduction candidate for 7,9 F5: 7,9 # 12 pairs F6: 7,9,4 # reduction candidate for 7,9 F6: 7,9 # 13 pairs * PAIR E4: 7,9 ROW 4 B4: 7,9,6 # reduction candidate for 7,9 B4: 7,9 => CTR * .5.1.2......74.16.71.6.3...1.53.8624...26...1.2.51.8..8419267...6.83.419.3.4.1.82 B4: 6 => SOLVED * 956182347283749165714653928165398274498267531327514896841926753672835419539471682 H4: 7,9,2 # reduction candidate for 7,9 H4: 7,9 => SOLVED * 956182347283749165714653928165398274498267531327514896841926753672835419539471682 H4: 2 # 13 pairs * PAIR H7: 3,5 COL H H5: 3,5,7,9 # reduction candidate for 3,5 H5: 7,9 # 14 pairs H5: 3,5 # 13 pairs * PAIR I7: 3,5 COL I I2: 3,5,8,9 # reduction candidate for 3,5 I2: 8,9 => CTR * .561.23..28374516971.6.3...165378294.7826.5.1.2.51.8..8419267..592837416637451982 I2: 3,5 # 14 pairs * PAIR I8: 6,9 ROW 8 A8: 6,9,2,5 # reduction candidate for 6,9 A8: 6,9 => SOLVED * 956182347283749165714653928165398274498267531327514896841926753672835419539471682 A8: 2,5 # 12 pairs B8: 6,9,7 # reduction candidate for 6,9 B8: 6,9 # 14 pairs C8: 6,9,2,7 # reduction candidate for 6,9 C8: 6,9 => CTR * .5.1823..38274916571.653..8165398274.9826753142.51.8..84192675327.83541.53.471.82 C8: 2,7 # 12 pairs * PAIR I8: 6,9 COL I I6: 6,9,3,7 # reduction candidate for 6,9 I6: 3,7 => CTR * .5.1.2......74.16.71.6.3...1.53.8624...26...1.2.51.8..8419267...6.83.419.3.4.1.82 I6: 6,9 # 13 pairs * PAIR G9: 6,9 ROW 9 A9: 6,9,5 # reduction candidate for 6,9 A9: 6,9 # 22 pairs C9: 6,9,7 # reduction candidate for 6,9 C9: 6,9 # 17 pairs * PAIR G9: 6,9 COL G G4: 6,9,2 # reduction candidate for 6,9 G4: 2 => SOLVED * 956182347283749165714653928165398274498267531327514896841926753672835419539471682 G4: 6,9 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060601-absurd-base-pr-000.dot * REASONING * DIS # C2: 8,9 => CTR => C2: 2,3 * DIS # I2: 8,9 => CTR => I2: 3,5 * DIS # I1: 8,9 => CTR => I1: 3,7 * DIS # E3: 8 => CTR => E3: 5,9 * DIS # I2: 3,8 => CTR => I2: 5,9 * DIS # I1: 3,9 => CTR => I1: 7,8 * DIS # G5: 3,9 => CTR => G5: 5 * DIS # B4: 7,9 => CTR => B4: 6 * PRF # B4: 6 => SOL * PRF # H4: 7,9 => SOL * DIS # I2: 8,9 => CTR => I2: 3,5 * PRF # A8: 6,9 => SOL * DIS # C8: 6,9 => CTR => C8: 2,7 * DIS # I6: 3,7 => CTR => I6: 6,9 * PRF # G4: 2 => SOL * CNT 15 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,E1,E4,E9,F2,F8,G1,G9,H7,I7,I8) * .5.1.2......74.16.71.6.3...1.53.8..4...26...1.2.51.8..8419267.....83.41..3.4.1.82 * PAIR B2: 8,9 BLK 1 C1: 8,9,3,4,6 # reduction candidate for 8,9 C1: 8,9 # 15 pairs C2: 8,9,2,3 # reduction candidate for 8,9 C2: 8,9 => CTR * .5.1.29..2..74516371.6935281.5378294...26.351.2.51.87684192673556283.41..3.4.1.82 C3: 8,9,4 # reduction candidate for 8,9 C3: 8,9 # 15 pairs * PAIR B2: 8,9 ROW 2 I2: 8,9,3,5 # reduction candidate for 8,9 I2: 8,9 => CTR * .561.23..28374516971.6.3...165378294.7826.5.1.2.51.8..8419267..592837416637451982 * PAIR RESTART * PAIR E1: 8,9 BLK 2 E3: 8,9,5 # reduction candidate for 8,9 E3: 8,9 => CTR * .5.1.2....8.74516371.6.3...1.53.8..4..826.351.2.51.8..8419267355.283.41..3.4.1.82 * PAIR I8: 6,9 ROW 8 A8: 6,9,2 # reduction candidate for 6,9 A8: 6,9 => SOLVED * 956182347283749165714653928165398274498267531327514896841926753672835419539471682 * DURATION: 0:00:07.436697 START: 23:34:10.783023 END: 23:34:18.219720 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060601-absurd-base-pr-001.dot * REASONING * DIS # C2: 8,9 => CTR => C2: 2,3 * DIS C2: 2,3 # I2: 8,9 => CTR => I2: 3,5 * DIS C2: 2,3 + I2: 3,5 # E3: 8,9 => CTR => E3: 5 * PRF C2: 2,3 + I2: 3,5 + E3: 5 # A8: 6,9 => SOL * STA C2: 2,3 + I2: 3,5 + E3: 5 + A8: 6,9 * CNT 4 HDP CHAINS / 6 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060601, absurd
Solution
position: 956182347283749165714653928165398274498267531327514896841926753672835419539471682 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 # C1: 8,9 => UNS * DIS # C2: 8,9 => CTR => C2: 2,3 * INC # C2: 2,3 => UNS * INC # C3: 8,9 => UNS * DIS # I2: 8,9 => CTR => I2: 3,5 * INC # I2: 3,5 => UNS * INC # B5: 8,9 => UNS * INC # B5: 7 => UNS * INC # E3: 8,9 => UNS * INC # E3: 5 => UNS * INC # C1: 8,9 => UNS * DIS # I1: 8,9 => CTR => I1: 3,7 * INC # I1: 3,7 => UNS * INC # E3: 5,9 => UNS * DIS # E3: 8 => CTR => E3: 5,9 * INC # I2: 5,9 => UNS * DIS # I2: 3,8 => CTR => I2: 5,9 * INC # H1: 3,9 => UNS * DIS # I1: 3,9 => CTR => I1: 7,8 * INC # I1: 7,8 => UNS * INC # I2: 3,9 => UNS * INC # A1: 3,9 => UNS * INC # C1: 3,9 => UNS * DIS # G5: 3,9 => CTR => G5: 5 * INC # G5: 5 => UNS * INC # F5: 7,9 => UNS * INC # F6: 7,9 => UNS * DIS # B4: 7,9 => CTR => B4: 6 * PRF # B4: 6 => SOL * PRF # H4: 7,9 => SOL * INC # H4: 2 => UNS * INC # H5: 3,5 => UNS * INC # H5: 7,9 => UNS * INC # I2: 3,5 => UNS * DIS # I2: 8,9 => CTR => I2: 3,5 * PRF # A8: 6,9 => SOL * INC # A8: 2,5 => UNS * INC # B8: 6,9 => UNS * DIS # C8: 6,9 => CTR => C8: 2,7 * INC # C8: 2,7 => UNS * INC # I6: 6,9 => UNS * DIS # I6: 3,7 => CTR => I6: 6,9 * INC # A9: 6,9 => UNS * INC # C9: 6,9 => UNS * INC # G4: 6,9 => UNS * PRF # G4: 2 => SOL * CNT 46 HDP CHAINS / 46 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 8,9 => UNS * DIS # C2: 8,9 => CTR => C2: 2,3 * INC C2: 2,3 # C3: 8,9 => UNS * DIS C2: 2,3 # I2: 8,9 => CTR => I2: 3,5 * DIS C2: 2,3 + I2: 3,5 # E3: 8,9 => CTR => E3: 5 * PRF C2: 2,3 + I2: 3,5 + E3: 5 # A8: 6,9 => SOL * STA C2: 2,3 + I2: 3,5 + E3: 5 + A8: 6,9 * CNT 6 HDP CHAINS / 6 HYP OPENED