Analysis of zz-www.sudokuoftheday.co.uk-20060324-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: ......1...58.7.....1..4....87..5...9.92..8..7.6.....18......6...236.7...6...1..25 initial
Autosolve
position: .3....1...58.7.....1..4....87..5...9.92..8..7.657...18......6.35236.7..16...1..25 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I2: 2,4 => CTR => I2: 6 * DIS # F2: 6 => CTR => F2: 1,2 * DIS # D4: 4 => CTR => D4: 1,2 * DIS # I1: 2,6 => CTR => I1: 4 * DIS # F3: 2,6 => CTR => F3: 3,5,9 * DIS # A5: 3 => CTR => A5: 1,4 * DIS # D4: 2 => CTR => D4: 1,4 * DIS # A5: 3,4 => CTR => A5: 1 * DIS # D4: 2 => CTR => D4: 1,4 * DIS # A5: 3 => CTR => A5: 1,4 * DIS # E6: 3 => CTR => E6: 2,9 * DIS # F3: 2,9 => CTR => F3: 3,5,6 * DIS # H5: 4,5 => CTR => H5: 6 * DIS # G4: 3 => CTR => G4: 2,4 * DIS # C7: 7,9 => CTR => C7: 1 * DIS # C3: 7,9 => CTR => C3: 6 * DIS # H8: 8,9 => CTR => H8: 4 * DIS # E1: 8,9 => CTR => E1: 2,6 * CNT 18 HDP CHAINS / 49 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I2: 2,4 => CTR => I2: 6 * DIS I2: 6 # G9: 8 => CTR => G9: 7,9 * PRF I2: 6 + G9: 7,9 # E7: 2 => SOL * STA I2: 6 + G9: 7,9 + E7: 2 * CNT 3 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ......1...58.7.....1..4....87..5...9.92..8..7.6.....18......6...236.7...6...1..25 | initial |
| .3....1...58.7.....1..4....87..5...9.92..8..7.657...18......6.35236.7..16...1..25 | autosolve |
| 237869154458271396916543872874156239192438567365792418741925683523687941689314725 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) A2: 2,4 D2: 1,2 G2: 3,9 H2: 3,9 I3: 2,6 C4: 1,4 A6: 3,4 D5: 1,4 E5: 3,6 F6: 2,9 G5: 4,5 G6: 2,4 B7: 4,8 B9: 4,8 C9: 7,9 E8: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,F2: 1.. / D2 = 1 => 0 pairs (X) / F2 = 1 => 15 pairs (_) C4,A5: 1.. / C4 = 1 => 0 pairs (X) / A5 = 1 => 15 pairs (_) A7,C7: 1.. / A7 = 1 => 0 pairs (X) / C7 = 1 => 15 pairs (_) A5,D5: 1.. / A5 = 1 => 15 pairs (_) / D5 = 1 => 0 pairs (X) A5,A7: 1.. / A5 = 1 => 15 pairs (_) / A7 = 1 => 0 pairs (X) C4,C7: 1.. / C4 = 1 => 0 pairs (X) / C7 = 1 => 15 pairs (_) F2,F4: 1.. / F2 = 1 => 15 pairs (_) / F4 = 1 => 0 pairs (X) G4,G6: 2.. / G4 = 2 => 15 pairs (_) / G6 = 2 => 0 pairs (X) E7,F7: 2.. / E7 = 2 => 17 pairs (_) / F7 = 2 => 22 pairs (_) D2,D4: 2.. / D2 = 2 => 15 pairs (_) / D4 = 2 => 0 pairs (X) D3,F3: 3.. / D3 = 3 => 19 pairs (_) / F3 = 3 => 17 pairs (_) G2,H2: 3.. / G2 = 3 => 15 pairs (_) / H2 = 3 => 0 pairs (X) A5,A6: 3.. / A5 = 3 => 0 pairs (X) / A6 = 3 => 15 pairs (_) E5,E6: 3.. / E5 = 3 => 15 pairs (_) / E6 = 3 => 0 pairs (X) G4,H4: 3.. / G4 = 3 => 0 pairs (X) / H4 = 3 => 15 pairs (_) D9,F9: 3.. / D9 = 3 => 17 pairs (_) / F9 = 3 => 19 pairs (_) A5,E5: 3.. / A5 = 3 => 0 pairs (X) / E5 = 3 => 15 pairs (_) A6,E6: 3.. / A6 = 3 => 15 pairs (_) / E6 = 3 => 0 pairs (X) D3,D9: 3.. / D3 = 3 => 19 pairs (_) / D9 = 3 => 17 pairs (_) F3,F9: 3.. / F3 = 3 => 17 pairs (_) / F9 = 3 => 19 pairs (_) G2,G4: 3.. / G2 = 3 => 15 pairs (_) / G4 = 3 => 0 pairs (X) H2,H4: 3.. / H2 = 3 => 0 pairs (X) / H4 = 3 => 15 pairs (_) I1,I2: 4.. / I1 = 4 => 15 pairs (_) / I2 = 4 => 0 pairs (X) D4,D5: 4.. / D4 = 4 => 0 pairs (X) / D5 = 4 => 15 pairs (_) B7,B9: 4.. / B7 = 4 => 15 pairs (_) / B9 = 4 => 18 pairs (_) F7,F9: 4.. / F7 = 4 => 18 pairs (_) / F9 = 4 => 15 pairs (_) G8,H8: 4.. / G8 = 4 => 0 pairs (X) / H8 = 4 => 19 pairs (_) A2,I2: 4.. / A2 = 4 => 15 pairs (_) / I2 = 4 => 0 pairs (X) A6,G6: 4.. / A6 = 4 => 0 pairs (X) / G6 = 4 => 15 pairs (_) B7,F7: 4.. / B7 = 4 => 15 pairs (_) / F7 = 4 => 18 pairs (_) B9,F9: 4.. / B9 = 4 => 18 pairs (_) / F9 = 4 => 15 pairs (_) C1,C4: 4.. / C1 = 4 => 0 pairs (X) / C4 = 4 => 15 pairs (_) G5,H5: 5.. / G5 = 5 => 17 pairs (_) / H5 = 5 => 0 pairs (X) D7,F7: 5.. / D7 = 5 => 17 pairs (_) / F7 = 5 => 17 pairs (_) G3,G5: 5.. / G3 = 5 => 0 pairs (X) / G5 = 5 => 17 pairs (_) C1,C3: 6.. / C1 = 6 => 0 pairs (X) / C3 = 6 => 18 pairs (_) F4,E5: 6.. / F4 = 6 => 15 pairs (_) / E5 = 6 => 0 pairs (X) H4,H5: 6.. / H4 = 6 => 0 pairs (X) / H5 = 6 => 15 pairs (_) F2,I2: 6.. / F2 = 6 => 0 pairs (X) / I2 = 6 => 15 pairs (_) F4,H4: 6.. / F4 = 6 => 15 pairs (_) / H4 = 6 => 0 pairs (X) E5,H5: 6.. / E5 = 6 => 0 pairs (X) / H5 = 6 => 15 pairs (_) E1,E5: 6.. / E1 = 6 => 15 pairs (_) / E5 = 6 => 0 pairs (X) H7,G9: 7.. / H7 = 7 => 27 pairs (_) / G9 = 7 => 22 pairs (_) C9,G9: 7.. / C9 = 7 => 27 pairs (_) / G9 = 7 => 22 pairs (_) G3,G9: 7.. / G3 = 7 => 27 pairs (_) / G9 = 7 => 22 pairs (_) B7,B9: 8.. / B7 = 8 => 18 pairs (_) / B9 = 8 => 15 pairs (_) G2,H2: 9.. / G2 = 9 => 0 pairs (X) / H2 = 9 => 15 pairs (_) E6,F6: 9.. / E6 = 9 => 12 pairs (_) / F6 = 9 => 17 pairs (_) * DURATION: 0:01:09.437662 START: 21:51:02.718482 END: 21:52:12.156144 2019-04-30 * CP COUNT: (48) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,B7,B9,C4,C9,D2,D5,E5,E8,F6,G2,G5,G6,H2,I3) * .3....1...58.7.....1..4....87..5...9.92..8..7.657...18......6.35236.7..16...1..25 * PAIR A2: 2,4 BLK 1 A1: 2,4,7,9 # reduction candidate for 2,4 A1: 7,9 # 17 pairs A1: 2,4 # 15 pairs * PAIR A2: 2,4 ROW 2 I2: 2,4,6 # reduction candidate for 2,4 I2: 2,4 => CTR * .3....1...58.76....1..4....87..51.691924.8..7.657...18......6.35236.7..16...1..25 I2: 6 # 15 pairs * PAIR D2: 1,2 BLK 2 F2: 1,2,6 # reduction candidate for 1,2 F2: 6 => CTR * .3....1...58176....1..4....87.251.691924.8..7.657...18......6.35236.7..16...1..25 F2: 1,2 # 15 pairs * PAIR D2: 1,2 COL D D4: 1,2,4 # reduction candidate for 1,2 D4: 4 => CTR * 234...1...58271..6.1..4...287145...9.921.8..7.657...181.....6.35236.7..16...1..25 D4: 1,2 # 15 pairs * PAIR I3: 2,6 BLK 3 I1: 2,6,4 # reduction candidate for 2,6 I1: 2,6 => CTR * .3....1..258176..4.1..4....87.251.691924.8..7.657...18......6.35236.7..16...1..25 I1: 4 # 15 pairs I2: 2,6,4 # reduction candidate for 2,6 I2: 2,6 # 15 pairs * PAIR I3: 2,6 ROW 3 F3: 2,6,3,5,9 # reduction candidate for 2,6 F3: 2,6 => CTR * .3...51...58.7.....1.34....87..5...9392168..746573921818.5246.35236.7..164..13.25 F3: 3,5,9 # 16 pairs * PAIR C4: 1,4 BLK 4 A5: 1,4,3 # reduction candidate for 1,4 A5: 3 => CTR * .3....1...58.7.....1..4....871.5...9392168..74657392181.....6.35236.7..16...1..25 A5: 1,4 # 15 pairs * PAIR C4: 1,4 ROW 4 D4: 1,4,2 # reduction candidate for 1,4 D4: 2 => CTR * .3....1...58.7.....1..4....87.25...9.924.8567.657.9.18......6.35236.7..16...1..25 D4: 1,4 # 15 pairs * PAIR A6: 3,4 BLK 4 A5: 3,4,1 # reduction candidate for 3,4 A5: 3,4 => CTR * .34...1..258.7.....1..4....871.5...9.921.8..7.657...181.....6.35236.7..16...1..25 A5: 1 # 15 pairs * PAIR D5: 1,4 BLK 5 D4: 1,4,2 # reduction candidate for 1,4 D4: 2 => CTR * .3....1...58.7.....1..4....87.25...9.924.8567.657.9.18......6.35236.7..16...1..25 D4: 1,4 # 15 pairs * PAIR D5: 1,4 ROW 5 A5: 1,4,3 # reduction candidate for 1,4 A5: 3 => CTR * .3....1...58.7.....1..4....871.5...9392168..74657392181.....6.35236.7..16...1..25 A5: 1,4 # 15 pairs * PAIR F6: 2,9 BLK 5 E6: 2,9,3 # reduction candidate for 2,9 E6: 3 => CTR * .3....1...58.7.....1..4....87..5...9392168..74657392181.....6.35236.7..16...1..25 E6: 2,9 # 15 pairs * PAIR F6: 2,9 COL F F1: 2,9,5,6 # reduction candidate for 2,9 F1: 2,9 # 23 pairs F3: 2,9,3,5,6 # reduction candidate for 2,9 F3: 2,9 => CTR * .3.98517..58.7693.917342..687.2513691924.8..7.657...18.8.524693523697..1649813725 F3: 3,5,6 # 16 pairs F7: 2,9,4,5 # reduction candidate for 2,9 F7: 2,9 # 22 pairs * PAIR G5: 4,5 BLK 6 H5: 4,5,6 # reduction candidate for 4,5 H5: 4,5 => CTR * .3....1...58.7..3..1..4....87..5.369392168..74657392181.....6.35236.7..16...1..25 H5: 6 # 15 pairs * PAIR G6: 2,4 BLK 6 G4: 2,4,3 # reduction candidate for 2,4 G4: 3 => CTR * .34...1..258176934.16.4...2871.5.3.9.92..8..7465739218......6.35236.7..16...1..25 G4: 2,4 # 15 pairs * PAIR C9: 7,9 BLK 7 A7: 7,9,1 # reduction candidate for 7,9 A7: 7,9 # 15 pairs C7: 7,9,1 # reduction candidate for 7,9 C7: 7,9 => CTR * .34...1..258.7.....1..4....871.5...9.921.8..7.657...181.....6.35236.7..16...1..25 C7: 1 # 15 pairs * PAIR C9: 7,9 ROW 9 G9: 7,9,8 # reduction candidate for 7,9 G9: 8 # 28 pairs G9: 7,9 # 19 pairs * PAIR C9: 7,9 COL C C1: 7,9,4,6 # reduction candidate for 7,9 C1: 7,9 # 15 pairs C3: 7,9,6 # reduction candidate for 7,9 C3: 7,9 => CTR * .36...1...58.7.....1..4....874.5...91924.8..7.657...18......6.35236.7..16...1..25 C3: 6 # 18 pairs * PAIR E8: 8,9 BLK 8 D7: 8,9,5 # reduction candidate for 8,9 D7: 8,9 # 17 pairs E7: 8,9,2 # reduction candidate for 8,9 E7: 8,9 # 22 pairs D9: 8,9,3 # reduction candidate for 8,9 D9: 8,9 # 19 pairs * PAIR E8: 8,9 ROW 8 G8: 8,9,4 # reduction candidate for 8,9 G8: 8,9 # 19 pairs H8: 8,9,4 # reduction candidate for 8,9 H8: 8,9 => CTR * .34...1..258176..4.16.4...2871.5...9.92..85.7465739218......6.35236.74.16...1..25 H8: 4 # 19 pairs * PAIR E8: 8,9 COL E E1: 8,9,2,6 # reduction candidate for 8,9 E1: 8,9 => CTR * .3....1...58.7.....1..4....87..5..69392168..74657392181...2.6.35236.7..16...1..25 E1: 2,6 # 22 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060324-absurd-base-pr-000.dot * REASONING * DIS # I2: 2,4 => CTR => I2: 6 * DIS # F2: 6 => CTR => F2: 1,2 * DIS # D4: 4 => CTR => D4: 1,2 * DIS # I1: 2,6 => CTR => I1: 4 * DIS # F3: 2,6 => CTR => F3: 3,5,9 * DIS # A5: 3 => CTR => A5: 1,4 * DIS # D4: 2 => CTR => D4: 1,4 * DIS # A5: 3,4 => CTR => A5: 1 * DIS # D4: 2 => CTR => D4: 1,4 * DIS # A5: 3 => CTR => A5: 1,4 * DIS # E6: 3 => CTR => E6: 2,9 * DIS # F3: 2,9 => CTR => F3: 3,5,6 * DIS # H5: 4,5 => CTR => H5: 6 * DIS # G4: 3 => CTR => G4: 2,4 * DIS # C7: 7,9 => CTR => C7: 1 * DIS # C3: 7,9 => CTR => C3: 6 * DIS # H8: 8,9 => CTR => H8: 4 * DIS # E1: 8,9 => CTR => E1: 2,6 * CNT 18 HDP CHAINS / 49 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,B7,B9,C4,C9,D2,D5,E5,E8,F6,G2,G5,G6,H2,I3) * .3....1...58.7.....1..4....87..5...9.92..8..7.657...18......6.35236.7..16...1..25 * PAIR A2: 2,4 BLK 1 A1: 2,4,7,9 # reduction candidate for 2,4 A1: 7,9 # 17 pairs A1: 2,4 # 15 pairs * PAIR A2: 2,4 ROW 2 I2: 2,4,6 # reduction candidate for 2,4 I2: 2,4 => CTR * .3....1...58.76....1..4....87..51.691924.8..7.657...18......6.35236.7..16...1..25 * PAIR RESTART * PAIR F6: 2,9 COL F F7: 2,9,4,5 # reduction candidate for 2,9 F7: 2,9 # 15 pairs F7: 4,5 # 13 pairs * PAIR C9: 7,9 ROW 9 G9: 7,9,8 # reduction candidate for 7,9 G9: 8 => CTR * 23..6.1.4458271396.16.4.7.28741562391924385673657..4187.1...6835236.7.416...1..25 * PAIR RESTART * PAIR E8: 8,9 BLK 8 E7: 8,9,2 # reduction candidate for 8,9 E7: 2 => SOLVED * 237869154458271396916543872874156239192438567365792418741925683523687941689314725 * DURATION: 0:00:11.084413 START: 21:52:50.479502 END: 21:53:01.563915 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060324-absurd-base-pr-001.dot * REASONING * DIS # I2: 2,4 => CTR => I2: 6 * DIS I2: 6 # G9: 8 => CTR => G9: 7,9 * PRF I2: 6 + G9: 7,9 # E7: 2 => SOL * STA I2: 6 + G9: 7,9 + E7: 2 * CNT 3 HDP CHAINS / 9 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060324, absurd
Solution
position: 237869154458271396916543872874156239192438567365792418741925683523687941689314725 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: 2,4 => UNS * INC # A1: 7,9 => UNS * DIS # I2: 2,4 => CTR => I2: 6 * INC # I2: 6 => UNS * INC # F2: 1,2 => UNS * DIS # F2: 6 => CTR => F2: 1,2 * INC # D4: 1,2 => UNS * DIS # D4: 4 => CTR => D4: 1,2 * DIS # I1: 2,6 => CTR => I1: 4 * INC # I1: 4 => UNS * INC # I2: 2,6 => UNS * DIS # F3: 2,6 => CTR => F3: 3,5,9 * INC # F3: 3,5,9 => UNS * INC # A5: 1,4 => UNS * DIS # A5: 3 => CTR => A5: 1,4 * INC # D4: 1,4 => UNS * DIS # D4: 2 => CTR => D4: 1,4 * DIS # A5: 3,4 => CTR => A5: 1 * INC # A5: 1 => UNS * INC # D4: 1,4 => UNS * DIS # D4: 2 => CTR => D4: 1,4 * INC # A5: 1,4 => UNS * DIS # A5: 3 => CTR => A5: 1,4 * INC # E6: 2,9 => UNS * DIS # E6: 3 => CTR => E6: 2,9 * INC # F1: 2,9 => UNS * DIS # F3: 2,9 => CTR => F3: 3,5,6 * INC # F3: 3,5,6 => UNS * INC # F7: 2,9 => UNS * DIS # H5: 4,5 => CTR => H5: 6 * INC # H5: 6 => UNS * INC # G4: 2,4 => UNS * DIS # G4: 3 => CTR => G4: 2,4 * INC # A7: 7,9 => UNS * DIS # C7: 7,9 => CTR => C7: 1 * INC # C7: 1 => UNS * INC # G9: 7,9 => UNS * INC # G9: 8 => UNS * INC # C1: 7,9 => UNS * DIS # C3: 7,9 => CTR => C3: 6 * INC # C3: 6 => UNS * INC # D7: 8,9 => UNS * INC # E7: 8,9 => UNS * INC # D9: 8,9 => UNS * INC # G8: 8,9 => UNS * DIS # H8: 8,9 => CTR => H8: 4 * INC # H8: 4 => UNS * DIS # E1: 8,9 => CTR => E1: 2,6 * INC # E1: 2,6 => UNS * CNT 49 HDP CHAINS / 49 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 2,4 => UNS * INC # A1: 7,9 => UNS * DIS # I2: 2,4 => CTR => I2: 6 * INC I2: 6 # F7: 2,9 => UNS * INC I2: 6 # F7: 4,5 => UNS * INC I2: 6 # G9: 7,9 => UNS * DIS I2: 6 # G9: 8 => CTR => G9: 7,9 * INC I2: 6 + G9: 7,9 # E7: 8,9 => UNS * PRF I2: 6 + G9: 7,9 # E7: 2 => SOL * STA I2: 6 + G9: 7,9 + E7: 2 * CNT 9 HDP CHAINS / 9 HYP OPENED