Analysis of zz-www.sudokuoftheday.co.uk-20060410-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006
level: medium
position: .1..8...3.98....243..2.....1.5.......74..39.........42....9...6...85..7.8..6.24.. initial
Autosolve
position: .1..8...3.98....243..2.....1.5.....7.74..39.........42....9...6...85..7.8..6.24.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 6,7 => CTR => A1: 2,4,5 * PRF # C1: 6,7 => SOL * DIS # G3: 6,7 => CTR => G3: 1,5,8 * PRF # A1: 2,6 => SOL * DIS # C6: 6,9 => CTR => C6: 3 * DIS # D1: 5,7 => CTR => D1: 4,9 * DIS # I5: 1,5 => CTR => I5: 8 * DIS # I5: 1,5 => CTR => I5: 8 * DIS # G3: 1,5 => CTR => G3: 6,7,8 * DIS # G7: 1,5 => CTR => G7: 2,3,8 * DIS # D7: 1,4 => CTR => D7: 3,7 * DIS # F3: 1,4 => CTR => F3: 5,6,7,9 * CNT 12 HDP CHAINS / 52 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 6,7 => CTR => A1: 2,4,5 * PRF A1: 2,4,5 # C1: 6,7 => SOL * STA A1: 2,4,5 + C1: 6,7 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .1..8...3.98....243..2.....1.5.......74..39.........42....9...6...85..7.8..6.24.. | initial |
| .1..8...3.98....243..2.....1.5.....7.74..39.........42....9...6...85..7.8..6.24.. | autosolve |
| 216485793598736124347219865125948637674523918983167542751394286462851379839672451 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) C3: 6,7 B4: 2,8 A5: 2,6 A6: 6,9 D4: 4,9 E4: 2,4 D5: 1,5 E5: 2,6 G4: 3,6 H4: 3,6 G6: 1,5 B9: 3,5 F8: 1,4 I8: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,C1: 2.. / A1 = 2 => 0 pairs (*) / C1 = 2 => 0 pairs (X) B4,A5: 2.. / B4 = 2 => 10 pairs (_) / A5 = 2 => 20 pairs (_) E4,E5: 2.. / E4 = 2 => 20 pairs (_) / E5 = 2 => 10 pairs (_) G7,G8: 2.. / G7 = 2 => 18 pairs (_) / G8 = 2 => 22 pairs (_) B4,E4: 2.. / B4 = 2 => 10 pairs (_) / E4 = 2 => 20 pairs (_) A5,E5: 2.. / A5 = 2 => 20 pairs (_) / E5 = 2 => 10 pairs (_) D2,E2: 3.. / D2 = 3 => 0 pairs (X) / E2 = 3 => 17 pairs (_) B6,C6: 3.. / B6 = 3 => 0 pairs (X) / C6 = 3 => 14 pairs (_) G4,H4: 3.. / G4 = 3 => 22 pairs (_) / H4 = 3 => 18 pairs (_) D7,E9: 3.. / D7 = 3 => 17 pairs (_) / E9 = 3 => 0 pairs (X) D2,D7: 3.. / D2 = 3 => 0 pairs (X) / D7 = 3 => 17 pairs (_) E2,E9: 3.. / E2 = 3 => 17 pairs (_) / E9 = 3 => 0 pairs (X) A1,B3: 4.. / A1 = 4 => 17 pairs (_) / B3 = 4 => 13 pairs (_) E3,E4: 4.. / E3 = 4 => 20 pairs (_) / E4 = 4 => 10 pairs (_) G4,H4: 6.. / G4 = 6 => 18 pairs (_) / H4 = 6 => 22 pairs (_) A5,E5: 6.. / A5 = 6 => 10 pairs (_) / E5 = 6 => 20 pairs (_) C9,E9: 7.. / C9 = 7 => 23 pairs (_) / E9 = 7 => 18 pairs (_) B4,B6: 8.. / B4 = 8 => 20 pairs (_) / B6 = 8 => 10 pairs (_) F4,F6: 8.. / F4 = 8 => 10 pairs (_) / F6 = 8 => 20 pairs (_) H5,I5: 8.. / H5 = 8 => 0 pairs (X) / I5 = 8 => 15 pairs (_) G7,H7: 8.. / G7 = 8 => 0 pairs (X) / H7 = 8 => 15 pairs (_) B4,F4: 8.. / B4 = 8 => 20 pairs (_) / F4 = 8 => 10 pairs (_) B6,F6: 8.. / B6 = 8 => 10 pairs (_) / F6 = 8 => 20 pairs (_) G3,G7: 8.. / G3 = 8 => 15 pairs (_) / G7 = 8 => 0 pairs (X) I3,I5: 8.. / I3 = 8 => 0 pairs (X) / I5 = 8 => 15 pairs (_) A6,C6: 9.. / A6 = 9 => 14 pairs (_) / C6 = 9 => 0 pairs (X) D4,F4: 9.. / D4 = 9 => 14 pairs (_) / F4 = 9 => 18 pairs (_) A6,A8: 9.. / A6 = 9 => 14 pairs (_) / A8 = 9 => 0 pairs (X) D1,D4: 9.. / D1 = 9 => 18 pairs (_) / D4 = 9 => 14 pairs (_) * DURATION: 0:00:30.137588 START: 22:16:55.483051 END: 22:17:25.620639 2019-04-30 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B4,B9,C3,D4,D5,E4,E5,F8,G4,G6,H4,I8) * .1..8...3.98....243..2.....1.5.....7.74..39.........42....9...6...85..7.8..6.24.. * PAIR C3: 6,7 BLK 1 A1: 6,7,2,4,5 # reduction candidate for 6,7 A1: 6,7 => CTR * 7124895635987...243462.58..125948637674.239.89835..14245.39.28626.85437.83.6.24.5 A1: 2,4,5 # 14 pairs C1: 6,7,2 # reduction candidate for 6,7 C1: 6,7 => SOLVED * 216485793598736124347219865125948637674523918983167542751394286462851379839672451 C1: 2 # 14 pairs A2: 6,7,5 # reduction candidate for 6,7 A2: 6,7 # 17 pairs * PAIR C3: 6,7 ROW 3 E3: 6,7,1,4 # reduction candidate for 6,7 E3: 6,7 # 12 pairs F3: 6,7,1,4,5,9 # reduction candidate for 6,7 F3: 6,7 # 18 pairs G3: 6,7,1,5,8 # reduction candidate for 6,7 G3: 6,7 => CTR * .1.48..93.98.3.12434.219.851.5948367.74523918.83167542.2.39.856...85.27.85.6.243. G3: 1,5,8 # 14 pairs * PAIR A5: 2,6 COL A A1: 2,6,4,5,7 # reduction candidate for 2,6 A1: 2,6 => SOLVED * 216485793598736124347219865125948637674523918983167542751394286462851379839672451 A1: 4,5,7 # 14 pairs A8: 2,6,4,9 # reduction candidate for 2,6 A8: 2,6 # 16 pairs * PAIR A6: 6,9 BLK 4 C6: 6,9,3 # reduction candidate for 6,9 C6: 6,9 => CTR * 412.8...359813..2436724...5185429..7274.639...3.7185427..39..56...85..7.85.6724.. C6: 3 # 14 pairs * PAIR A6: 6,9 COL A A8: 6,9,2,4 # reduction candidate for 6,9 A8: 6,9 # 20 pairs A8: 2,4 # 15 pairs * PAIR D4: 4,9 BLK 5 F4: 4,9,8 # reduction candidate for 4,9 F4: 4,9 # 20 pairs F4: 8 # 10 pairs * PAIR D4: 4,9 COL D D1: 4,9,5,7 # reduction candidate for 4,9 D1: 5,7 => CTR * .1..8...3.98....243..2.....1.59....7.74..39.........42...49...6...851.798.96.24.. D1: 4,9 # 16 pairs * PAIR D5: 1,5 BLK 5 D6: 1,5,7 # reduction candidate for 1,5 D6: 1,5 # 17 pairs F6: 1,5,6,7,8 # reduction candidate for 1,5 F6: 1,5 # 13 pairs * PAIR D5: 1,5 ROW 5 H5: 1,5,8 # reduction candidate for 1,5 H5: 1,5 # 15 pairs I5: 1,5,8 # reduction candidate for 1,5 I5: 1,5 => CTR * .1.48..93.98.31.2434.2.95181.5948367.74123985.83...142.2.39.856...85.27.85.612439 I5: 8 # 15 pairs * PAIR D5: 1,5 COL D D2: 1,5,3,7 # reduction candidate for 1,5 D2: 1,5 # 19 pairs D2: 3,7 # 15 pairs * PAIR G6: 1,5 BLK 6 H5: 1,5,8 # reduction candidate for 1,5 H5: 1,5 # 15 pairs I5: 1,5,8 # reduction candidate for 1,5 I5: 1,5 => CTR * .1.48..93.98.31.2434.2.95181.5948367.74123985.83...142.2.39.856...85.27.85.612439 I5: 8 # 15 pairs * PAIR G6: 1,5 ROW 6 D6: 1,5,7 # reduction candidate for 1,5 D6: 1,5 # 17 pairs F6: 1,5,6,7,8 # reduction candidate for 1,5 F6: 1,5 # 13 pairs * PAIR G6: 1,5 COL G G2: 1,5,6,7 # reduction candidate for 1,5 G2: 1,5 # 17 pairs G3: 1,5,6,7,8 # reduction candidate for 1,5 G3: 1,5 => CTR * .1.48..93.98.3..2434.2.9...1.5948367.74.239...83....42.2.39.856...85.27.85.6.243. G3: 6,7,8 # 14 pairs G7: 1,5,2,3,8 # reduction candidate for 1,5 G7: 1,5 => CTR * .1.48..93.98.31.2434.2.98151.5948367.74123958.83...142.2.39.586...85.27.85.612439 G7: 2,3,8 # 14 pairs * PAIR B9: 3,5 BLK 7 B7: 3,5,2,4 # reduction candidate for 3,5 B7: 3,5 # 19 pairs B7: 2,4 # 15 pairs * PAIR B9: 3,5 ROW 9 H9: 3,5,1,9 # reduction candidate for 3,5 H9: 3,5 # 23 pairs H9: 1,9 # 20 pairs * PAIR F8: 1,4 BLK 8 D7: 1,4,3,7 # reduction candidate for 1,4 D7: 1,4 => CTR * .12.8...3.983...243462.....125948..7674.239..983....42.31497..646.85..7.8576324.. D7: 3,7 # 17 pairs F7: 1,4,7 # reduction candidate for 1,4 F7: 1,4 # 19 pairs * PAIR F8: 1,4 COL F F3: 1,4,5,6,7,9 # reduction candidate for 1,4 F3: 1,4 => CTR * .12.8...3.98.3.1243.62417891.5429..7274563918...178542.41397..6...854.718.76124.. F3: 5,6,7,9 # 14 pairs * PAIR I8: 1,9 BLK 9 H9: 1,9,3,5 # reduction candidate for 1,9 H9: 1,9 # 20 pairs I9: 1,9,5 # reduction candidate for 1,9 I9: 1,9 # 23 pairs * PAIR I8: 1,9 ROW 8 C8: 1,9,2,3,6 # reduction candidate for 1,9 C8: 1,9 # 24 pairs C8: 2,3,6 # 14 pairs * PAIR I8: 1,9 COL I I3: 1,9,5,8 # reduction candidate for 1,9 I3: 1,9 # 20 pairs I3: 5,8 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060410-absurd-base-pr-000.dot * REASONING * DIS # A1: 6,7 => CTR => A1: 2,4,5 * PRF # C1: 6,7 => SOL * DIS # G3: 6,7 => CTR => G3: 1,5,8 * PRF # A1: 2,6 => SOL * DIS # C6: 6,9 => CTR => C6: 3 * DIS # D1: 5,7 => CTR => D1: 4,9 * DIS # I5: 1,5 => CTR => I5: 8 * DIS # I5: 1,5 => CTR => I5: 8 * DIS # G3: 1,5 => CTR => G3: 6,7,8 * DIS # G7: 1,5 => CTR => G7: 2,3,8 * DIS # D7: 1,4 => CTR => D7: 3,7 * DIS # F3: 1,4 => CTR => F3: 5,6,7,9 * CNT 12 HDP CHAINS / 52 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B4,B9,C3,D4,D5,E4,E5,F8,G4,G6,H4,I8) * .1..8...3.98....243..2.....1.5.....7.74..39.........42....9...6...85..7.8..6.24.. * PAIR C3: 6,7 BLK 1 A1: 6,7,2,4,5 # reduction candidate for 6,7 A1: 6,7 => CTR * 7124895635987...243462.58..125948637674.239.89835..14245.39.28626.85437.83.6.24.5 C1: 6,7,2 # reduction candidate for 6,7 C1: 6,7 => SOLVED * 216485793598736124347219865125948637674523918983167542751394286462851379839672451 * DURATION: 0:00:02.594268 START: 22:17:54.729995 END: 22:17:57.324263 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060410-absurd-base-pr-001.dot * REASONING * DIS # A1: 6,7 => CTR => A1: 2,4,5 * PRF A1: 2,4,5 # C1: 6,7 => SOL * STA A1: 2,4,5 + C1: 6,7 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060410, absurd
Solution
position: 216485793598736124347219865125948637674523918983167542751394286462851379839672451 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 # A1: 6,7 => CTR => A1: 2,4,5 * INC # A1: 2,4,5 => UNS * PRF # C1: 6,7 => SOL * INC # C1: 2 => UNS * INC # A2: 6,7 => UNS * INC # E3: 6,7 => UNS * INC # F3: 6,7 => UNS * DIS # G3: 6,7 => CTR => G3: 1,5,8 * INC # G3: 1,5,8 => UNS * PRF # A1: 2,6 => SOL * INC # A1: 4,5,7 => UNS * INC # A8: 2,6 => UNS * DIS # C6: 6,9 => CTR => C6: 3 * INC # C6: 3 => UNS * INC # A8: 6,9 => UNS * INC # A8: 2,4 => UNS * INC # F4: 4,9 => UNS * INC # F4: 8 => UNS * INC # D1: 4,9 => UNS * DIS # D1: 5,7 => CTR => D1: 4,9 * INC # D6: 1,5 => UNS * INC # F6: 1,5 => UNS * INC # H5: 1,5 => UNS * DIS # I5: 1,5 => CTR => I5: 8 * INC # I5: 8 => UNS * INC # D2: 1,5 => UNS * INC # D2: 3,7 => UNS * INC # H5: 1,5 => UNS * DIS # I5: 1,5 => CTR => I5: 8 * INC # I5: 8 => UNS * INC # D6: 1,5 => UNS * INC # F6: 1,5 => UNS * INC # G2: 1,5 => UNS * DIS # G3: 1,5 => CTR => G3: 6,7,8 * INC # G3: 6,7,8 => UNS * DIS # G7: 1,5 => CTR => G7: 2,3,8 * INC # G7: 2,3,8 => UNS * INC # B7: 3,5 => UNS * INC # B7: 2,4 => UNS * INC # H9: 3,5 => UNS * INC # H9: 1,9 => UNS * DIS # D7: 1,4 => CTR => D7: 3,7 * INC # D7: 3,7 => UNS * INC # F7: 1,4 => UNS * DIS # F3: 1,4 => CTR => F3: 5,6,7,9 * INC # F3: 5,6,7,9 => UNS * INC # H9: 1,9 => UNS * INC # I9: 1,9 => UNS * INC # C8: 1,9 => UNS * INC # C8: 2,3,6 => UNS * INC # I3: 1,9 => UNS * INC # I3: 5,8 => UNS * CNT 52 HDP CHAINS / 52 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 6,7 => CTR => A1: 2,4,5 * PRF A1: 2,4,5 # C1: 6,7 => SOL * STA A1: 2,4,5 + C1: 6,7 * CNT 2 HDP CHAINS / 2 HYP OPENED