Analysis of zz-www.sudokuoftheday.co.uk-20190402-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019
level: medium
position: 32..64....1..9......9..3.1.....36...9.....4..5..7..8.........6.7.1...24...43.5..7 initial
Autosolve
position: 32.1649.8.1..9......9..3.1.148936...9.....43.5..74.89.28.4...697.168924.694325187 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 5,7 => CTR => C2: 6 * DIS # D2: 2,8 => CTR => D2: 5 * DIS # D5: 5 => CTR => D5: 2,8 * DIS # G3: 5,7 => CTR => G3: 6 * PRF # G2: 5,7 => SOL * DIS # H2: 5,7 => CTR => H2: 2 * DIS # G3: 5,7 => CTR => G3: 6 * DIS # H4: 2 => CTR => H4: 5,7 * DIS # I2: 2,4 => CTR => I2: 3,5 * DIS # C5: 6,7 => CTR => C5: 2 * DIS # B3: 6,7 => CTR => B3: 5 * PRF # B3: 5 => SOL * DIS # C6: 2 => CTR => C6: 3,6 * DIS # H4: 2 => CTR => H4: 5,7 * PRF # G2: 5,7 => SOL * DIS # G3: 5,7 => CTR => G3: 6 * PRF # H4: 7 => SOL * DIS # I2: 2,5 => CTR => I2: 3,4 * PRF # G2: 6,7 => SOL * DIS # I2: 2,4 => CTR => I2: 3,5 * CNT 20 HDP CHAINS / 43 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 5,7 => CTR => C2: 6 * DIS C2: 6 # D2: 2,8 => CTR => D2: 5 * PRF C2: 6 + D2: 5 => SOL * STA C2: 6 + D2: 5 * CNT 3 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 32..64....1..9......9..3.1.....36...9.....4..5..7..8.........6.7.1...24...43.5..7 | initial |
| 32.1649.8.1..9......9..3.1.148936...9.....43.5..74.89.28.4...697.168924.694325187 | autosolve |
| 327164958416598723859273614148936572972851436563742891285417369731689245694325187 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (21) C1: 5,7 A2: 4,8 A3: 4,8 D3: 2,8 E3: 5,7 H1: 5,7 I3: 2,4 B5: 6,7 B6: 3,6 E5: 1,5 F6: 1,2 G4: 5,7 I4: 2,5 I5: 1,6 I6: 1,6 C7: 3,5 B8: 3,5 E7: 1,7 F7: 1,7 G7: 3,5 I8: 3,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I5,I6: 1.. / I5 = 1 => 0 pairs (X) / I6 = 1 => 22 pairs (_) E7,F7: 1.. / E7 = 1 => 23 pairs (_) / F7 = 1 => 0 pairs (X) F6,I6: 1.. / F6 = 1 => 0 pairs (X) / I6 = 1 => 22 pairs (_) E5,E7: 1.. / E5 = 1 => 0 pairs (X) / E7 = 1 => 23 pairs (_) C5,C6: 2.. / C5 = 2 => 22 pairs (_) / C6 = 2 => 0 pairs (X) H4,I4: 2.. / H4 = 2 => 0 pairs (X) / I4 = 2 => 21 pairs (_) D3,I3: 2.. / D3 = 2 => 20 pairs (_) / I3 = 2 => 0 pairs (X) C6,F6: 2.. / C6 = 2 => 0 pairs (X) / F6 = 2 => 22 pairs (_) H2,H4: 2.. / H2 = 2 => 21 pairs (_) / H4 = 2 => 0 pairs (X) G2,I2: 3.. / G2 = 3 => 0 pairs (X) / I2 = 3 => 0 pairs (_) B6,C6: 3.. / B6 = 3 => 0 pairs (X) / C6 = 3 => 0 pairs (_) C7,B8: 3.. / C7 = 3 => 0 pairs (X) / B8 = 3 => 0 pairs (_) G7,I8: 3.. / G7 = 3 => 0 pairs (*) / I8 = 3 => 0 pairs (X) C7,G7: 3.. / C7 = 3 => 0 pairs (X) / G7 = 3 => 0 pairs (_) B8,I8: 3.. / B8 = 3 => 0 pairs (*) / I8 = 3 => 0 pairs (X) B6,B8: 3.. / B6 = 3 => 0 pairs (X) / B8 = 3 => 0 pairs (_) C6,C7: 3.. / C6 = 3 => 0 pairs (*) / C7 = 3 => 0 pairs (X) G2,G7: 3.. / G2 = 3 => 0 pairs (X) / G7 = 3 => 0 pairs (_) I2,I8: 3.. / I2 = 3 => 0 pairs (*) / I8 = 3 => 0 pairs (X) A2,A3: 4.. / A2 = 4 => 20 pairs (_) / A3 = 4 => 0 pairs (X) I2,I3: 4.. / I2 = 4 => 0 pairs (X) / I3 = 4 => 20 pairs (_) A2,I2: 4.. / A2 = 4 => 20 pairs (_) / I2 = 4 => 0 pairs (X) A3,I3: 4.. / A3 = 4 => 0 pairs (X) / I3 = 4 => 20 pairs (_) D2,E3: 5.. / D2 = 5 => 23 pairs (_) / E3 = 5 => 0 pairs (X) D5,E5: 5.. / D5 = 5 => 0 pairs (X) / E5 = 5 => 23 pairs (_) C7,B8: 5.. / C7 = 5 => 0 pairs (*) / B8 = 5 => 0 pairs (X) G7,I8: 5.. / G7 = 5 => 0 pairs (X) / I8 = 5 => 0 pairs (_) C1,H1: 5.. / C1 = 5 => 0 pairs (X) / H1 = 5 => 24 pairs (_) C7,G7: 5.. / C7 = 5 => 0 pairs (*) / G7 = 5 => 0 pairs (X) B8,I8: 5.. / B8 = 5 => 0 pairs (X) / I8 = 5 => 0 pairs (_) B3,B8: 5.. / B3 = 5 => 0 pairs (*) / B8 = 5 => 0 pairs (X) D2,D5: 5.. / D2 = 5 => 23 pairs (_) / D5 = 5 => 0 pairs (X) E3,E5: 5.. / E3 = 5 => 0 pairs (X) / E5 = 5 => 23 pairs (_) C2,B3: 6.. / C2 = 6 => 24 pairs (_) / B3 = 6 => 0 pairs (X) G2,G3: 6.. / G2 = 6 => 0 pairs (X) / G3 = 6 => 24 pairs (_) I5,I6: 6.. / I5 = 6 => 22 pairs (_) / I6 = 6 => 0 pairs (X) C2,G2: 6.. / C2 = 6 => 24 pairs (_) / G2 = 6 => 0 pairs (X) B3,G3: 6.. / B3 = 6 => 0 pairs (X) / G3 = 6 => 24 pairs (_) F2,E3: 7.. / F2 = 7 => 0 pairs (X) / E3 = 7 => 23 pairs (_) B5,C5: 7.. / B5 = 7 => 22 pairs (_) / C5 = 7 => 0 pairs (X) G4,H4: 7.. / G4 = 7 => 22 pairs (_) / H4 = 7 => 0 pairs (*) E7,F7: 7.. / E7 = 7 => 0 pairs (X) / F7 = 7 => 23 pairs (_) C1,H1: 7.. / C1 = 7 => 24 pairs (_) / H1 = 7 => 0 pairs (X) B3,B5: 7.. / B3 = 7 => 0 pairs (X) / B5 = 7 => 22 pairs (_) E3,E7: 7.. / E3 = 7 => 23 pairs (_) / E7 = 7 => 0 pairs (X) F2,F7: 7.. / F2 = 7 => 0 pairs (X) / F7 = 7 => 23 pairs (_) A2,A3: 8.. / A2 = 8 => 0 pairs (X) / A3 = 8 => 20 pairs (_) D5,F5: 8.. / D5 = 8 => 19 pairs (_) / F5 = 8 => 23 pairs (_) A3,D3: 8.. / A3 = 8 => 20 pairs (_) / D3 = 8 => 0 pairs (X) F2,F5: 8.. / F2 = 8 => 19 pairs (_) / F5 = 8 => 23 pairs (_) * DURATION: 0:01:06.374914 START: 05:00:09.913904 END: 05:01:16.288818 2019-05-01 * CP COUNT: (50) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,B5,B6,B8,C1,C7,D3,E3,E5,E7,F6,F7,G4,G7,H1,I3,I4,I5,I6,I8) * 32.1649.8.1..9......9..3.1.148936...9.....43.5..74.89.28.4...697.168924.694325187 * PAIR C1: 5,7 BLK 1 C2: 5,7,6 # reduction candidate for 5,7 C2: 5,7 => CTR * 32.1649.8.1..9.6.3.69..3.14148936..297....43.5..74.89.28.4...697.168924.694325187 C2: 6 # 24 pairs B3: 5,7,6 # reduction candidate for 5,7 B3: 5,7 # 24 pairs * PAIR D3: 2,8 BLK 2 D2: 2,8,5 # reduction candidate for 2,8 D2: 2,8 => CTR * 32.1649.8.1..973....9.5361.1489367..97.5184365..74289128.471.69751689243694325187 D2: 5 # 23 pairs F2: 2,8,7 # reduction candidate for 2,8 F2: 2,8 # 23 pairs * PAIR D3: 2,8 COL D D5: 2,8,5 # reduction candidate for 2,8 D5: 5 => CTR * 327164958.15.97.....9.53.1.148936...9725184365..74289128.471.69751689243694325187 D5: 2,8 # 23 pairs * PAIR E3: 5,7 ROW 3 B3: 5,7,6 # reduction candidate for 5,7 B3: 5,7 # 24 pairs G3: 5,7,6 # reduction candidate for 5,7 G3: 5,7 => CTR * 32.1649.8.1..9.6.3.69..3.14148936..297....43.5..74.89.28.4...697.168924.694325187 G3: 6 # 24 pairs * PAIR H1: 5,7 BLK 3 G2: 5,7,3,6 # reduction candidate for 5,7 G2: 5,7 => SOLVED * 327164958416598723859273614148936572972851436563742891285417369731689245694325187 G2: 3,6 # 22 pairs H2: 5,7,2 # reduction candidate for 5,7 H2: 5,7 => CTR * 32.1649.8.1..9.3....9.5361.1489367259..5184365..74.89.28.4..569751689243694325187 H2: 2 # 21 pairs G3: 5,7,6 # reduction candidate for 5,7 G3: 5,7 => CTR * 32.1649.8.1..9.6.3.69..3.14148936..297....43.5..74.89.28.4...697.168924.694325187 G3: 6 # 24 pairs * PAIR H1: 5,7 COL H H4: 5,7,2 # reduction candidate for 5,7 H4: 2 => CTR * 32.1649.8.1..9.3....9.5361.1489367259..5184365..74.89.28.4..569751689243694325187 H4: 5,7 # 21 pairs * PAIR I3: 2,4 BLK 3 I2: 2,4,3,5 # reduction candidate for 2,4 I2: 2,4 => CTR * 32.1649.8.16.9.3...79.5361.1489367.596751.43.5..74.89.2834..569751689243694325187 I2: 3,5 # 21 pairs * PAIR B5: 6,7 BLK 4 C5: 6,7,2 # reduction candidate for 6,7 C5: 6,7 => CTR * 32.1649.8.1..9......9..3.1.148936...9.....43.5.2741896283417569751689243694325187 C5: 2 # 22 pairs * PAIR B5: 6,7 COL B B3: 6,7,5 # reduction candidate for 6,7 B3: 6,7 => CTR * 32.1649.8.16.9.3...79.5361.1489367..96751.43.53.74.89.2834..569751689243694325187 B3: 5 => SOLVED * 327164958416598723859273614148936572972851436563742891285417369731689245694325187 * PAIR B6: 3,6 BLK 4 C6: 3,6,2 # reduction candidate for 3,6 C6: 2 => CTR * 32.1649.8.1..9......9..3.1.148936...9.....43.532741896283417569751689243694325187 C6: 3,6 # 22 pairs * PAIR F6: 1,2 BLK 5 F5: 1,2,8 # reduction candidate for 1,2 F5: 8 # 23 pairs F5: 1,2 # 19 pairs * PAIR G4: 5,7 BLK 6 H4: 5,7,2 # reduction candidate for 5,7 H4: 2 => CTR * 32.1649.8.1..9.3....9.5361.1489367259..5184365..74.89.28.4..569751689243694325187 H4: 5,7 # 21 pairs * PAIR G4: 5,7 COL G G2: 5,7,3,6 # reduction candidate for 5,7 G2: 5,7 => SOLVED * 327164958416598723859273614148936572972851436563742891285417369731689245694325187 G2: 3,6 # 22 pairs G3: 5,7,6 # reduction candidate for 5,7 G3: 5,7 => CTR * 32.1649.8.1..9.6.3.69..3.14148936..297....43.5..74.89.28.4...697.168924.694325187 G3: 6 # 24 pairs * PAIR I4: 2,5 BLK 6 H4: 2,5,7 # reduction candidate for 2,5 H4: 7 => SOLVED * 327164958416598723859273614148936572972851436563742891285417369731689245694325187 H4: 2,5 # 22 pairs * PAIR I4: 2,5 COL I I2: 2,5,3,4 # reduction candidate for 2,5 I2: 2,5 => CTR * 32.1649.8416.9.3..8792536141489367..96751.43.5..74.89.2834..569751689243694325187 I2: 3,4 # 22 pairs * PAIR G7: 3,5 COL G G2: 3,5,6,7 # reduction candidate for 3,5 G2: 6,7 => SOLVED * 327164958416598723859273614148936572972851436563742891285417369731689245694325187 G2: 3,5 # 25 pairs * PAIR I8: 3,5 COL I I2: 3,5,2,4 # reduction candidate for 3,5 I2: 2,4 => CTR * 32.1649.8.16.9.3...79.5361.1489367.596751.43.5..74.89.2834..569751689243694325187 I2: 3,5 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190402-absurd-base-pr-000.dot * REASONING * DIS # C2: 5,7 => CTR => C2: 6 * DIS # D2: 2,8 => CTR => D2: 5 * DIS # D5: 5 => CTR => D5: 2,8 * DIS # G3: 5,7 => CTR => G3: 6 * PRF # G2: 5,7 => SOL * DIS # H2: 5,7 => CTR => H2: 2 * DIS # G3: 5,7 => CTR => G3: 6 * DIS # H4: 2 => CTR => H4: 5,7 * DIS # I2: 2,4 => CTR => I2: 3,5 * DIS # C5: 6,7 => CTR => C5: 2 * DIS # B3: 6,7 => CTR => B3: 5 * PRF # B3: 5 => SOL * DIS # C6: 2 => CTR => C6: 3,6 * DIS # H4: 2 => CTR => H4: 5,7 * PRF # G2: 5,7 => SOL * DIS # G3: 5,7 => CTR => G3: 6 * PRF # H4: 7 => SOL * DIS # I2: 2,5 => CTR => I2: 3,4 * PRF # G2: 6,7 => SOL * DIS # I2: 2,4 => CTR => I2: 3,5 * CNT 20 HDP CHAINS / 43 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,B5,B6,B8,C1,C7,D3,E3,E5,E7,F6,F7,G4,G7,H1,I3,I4,I5,I6,I8) * 32.1649.8.1..9......9..3.1.148936...9.....43.5..74.89.28.4...697.168924.694325187 * PAIR C1: 5,7 BLK 1 C2: 5,7,6 # reduction candidate for 5,7 C2: 5,7 => CTR * 32.1649.8.1..9.6.3.69..3.14148936..297....43.5..74.89.28.4...697.168924.694325187 * RESTART * PAIR D3: 2,8 BLK 2 D2: 2,8,5 # reduction candidate for 2,8 D2: 2,8 => CTR * 32.1649.8.16.9......9.5361.148936...9..5184365637428912854...697.168924.694325187 D2: 5 => SOLVED * 327164958416598723859273614148936572972851436563742891285417369731689245694325187 * DURATION: 0:00:02.066255 START: 05:01:48.303578 END: 05:01:50.369833 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190402-absurd-base-pr-001.dot * REASONING * DIS # C2: 5,7 => CTR => C2: 6 * DIS C2: 6 # D2: 2,8 => CTR => D2: 5 * PRF C2: 6 + D2: 5 => SOL * STA C2: 6 + D2: 5 * CNT 3 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190402, absurd
Solution
position: 327164958416598723859273614148936572972851436563742891285417369731689245694325187 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 # C2: 5,7 => CTR => C2: 6 * INC # C2: 6 => UNS * INC # B3: 5,7 => UNS * DIS # D2: 2,8 => CTR => D2: 5 * INC # D2: 5 => UNS * INC # F2: 2,8 => UNS * INC # D5: 2,8 => UNS * DIS # D5: 5 => CTR => D5: 2,8 * INC # B3: 5,7 => UNS * DIS # G3: 5,7 => CTR => G3: 6 * INC # G3: 6 => UNS * PRF # G2: 5,7 => SOL * INC # G2: 3,6 => UNS * DIS # H2: 5,7 => CTR => H2: 2 * INC # H2: 2 => UNS * DIS # G3: 5,7 => CTR => G3: 6 * INC # G3: 6 => UNS * INC # H4: 5,7 => UNS * DIS # H4: 2 => CTR => H4: 5,7 * DIS # I2: 2,4 => CTR => I2: 3,5 * INC # I2: 3,5 => UNS * DIS # C5: 6,7 => CTR => C5: 2 * INC # C5: 2 => UNS * DIS # B3: 6,7 => CTR => B3: 5 * PRF # B3: 5 => SOL * INC # C6: 3,6 => UNS * DIS # C6: 2 => CTR => C6: 3,6 * INC # F5: 1,2 => UNS * INC # F5: 8 => UNS * INC # H4: 5,7 => UNS * DIS # H4: 2 => CTR => H4: 5,7 * PRF # G2: 5,7 => SOL * INC # G2: 3,6 => UNS * DIS # G3: 5,7 => CTR => G3: 6 * INC # G3: 6 => UNS * INC # H4: 2,5 => UNS * PRF # H4: 7 => SOL * DIS # I2: 2,5 => CTR => I2: 3,4 * INC # I2: 3,4 => UNS * INC # G2: 3,5 => UNS * PRF # G2: 6,7 => SOL * INC # I2: 3,5 => UNS * DIS # I2: 2,4 => CTR => I2: 3,5 * CNT 43 HDP CHAINS / 43 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C2: 5,7 => CTR => C2: 6 * DIS C2: 6 # D2: 2,8 => CTR => D2: 5 * PRF C2: 6 + D2: 5 => SOL * STA C2: 6 + D2: 5 * CNT 3 HDP CHAINS / 2 HYP OPENED