Analysis of zz-www.sudokuoftheday.co.uk-20190425-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: ..7..........5..9..8..4.3...3..8.24..1.4...5.4...629.3.........1.5..37..3...9.... initial
Autosolve
position: ..731......3.5..9..81.4.3...3..8.24..1.43..5.458.629.38...7..39195.237.437..9.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 2,6 => CTR => B2: 4 * DIS # I2: 2,6 => CTR => I2: 1,7,8 * DIS # A5: 7 => CTR => A5: 2,6 * DIS # D3: 2,7 => CTR => D3: 9 * PRF # D3: 9 => SOL * DIS # I2: 2,7 => CTR => I2: 1,6,8 * DIS # A5: 6,7 => CTR => A5: 2 * PRF # I4: 6,7 => SOL * DIS # I4: 1 => CTR => I4: 6,7 * DIS # C5: 2 => CTR => C5: 6,9 * PRF # D4: 1,5 => SOL * DIS # D4: 7,9 => CTR => D4: 1,5 * DIS # F7: 1,5 => CTR => F7: 4 * DIS # D4: 7,9 => CTR => D4: 1,5 * PRF # D4: 1,5 => SOL * DIS # D4: 1,7 => CTR => D4: 5,9 * PRF # I5: 7 => SOL * DIS # G1: 6,8 => CTR => G1: 4,5 * DIS # G2: 6,8 => CTR => G2: 1,4 * PRF # I4: 6 => SOL * DIS # C7: 4 => CTR => C7: 2,6 * DIS # B2: 2,6 => CTR => B2: 4 * DIS # C7: 4,6 => CTR => C7: 2 * DIS # D9: 1,5 => CTR => D9: 6,8 * DIS # H9: 6,8 => CTR => H9: 1,2 * DIS # I9: 6,8 => CTR => I9: 1,2,5 * DIS # H1: 2 => CTR => H1: 6,8 * CNT 27 HDP CHAINS / 53 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 2,6 => CTR => B2: 4 * DIS B2: 4 # I2: 2,6 => CTR => I2: 1,7,8 * DIS B2: 4 + I2: 1,7,8 # A5: 7 => CTR => A5: 2,6 * DIS B2: 4 + I2: 1,7,8 + A5: 2,6 # D3: 2,7 => CTR => D3: 9 * PRF B2: 4 + I2: 1,7,8 + A5: 2,6 + D3: 9 => SOL * STA B2: 4 + I2: 1,7,8 + A5: 2,6 + D3: 9 * CNT 5 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..7..........5..9..8..4.3...3..8.24..1.4...5.4...629.3.........1.5..37..3...9.... | initial |
| ..731......3.5..9..81.4.3...3..8.24..1.43..5.458.629.38...7..39195.237.437..9.... | autosolve |
| 927318465643257198581946372739581246216439857458762913862174539195623784374895621 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) A1: 5,9 A2: 2,6 A3: 5,9 D2: 2,7 A4: 6,7 C4: 6,9 F4: 1,5 F5: 7,9 D6: 1,7 G5: 6,8 H6: 1,7 B7: 2,6 C9: 4,6 D8: 6,8 H8: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G2,I2: 1.. / G2 = 1 => 20 pairs (_) / I2 = 1 => 0 pairs (X) I4,H6: 1.. / I4 = 1 => 0 pairs (X) / H6 = 1 => 0 pairs (_) D6,H6: 1.. / D6 = 1 => 0 pairs (X) / H6 = 1 => 0 pairs (_) H6,H9: 1.. / H6 = 1 => 0 pairs (*) / H9 = 1 => 0 pairs (X) D2,D3: 2.. / D2 = 2 => 22 pairs (_) / D3 = 2 => 0 pairs (X) A5,C5: 2.. / A5 = 2 => 20 pairs (_) / C5 = 2 => 0 pairs (X) B7,C7: 2.. / B7 = 2 => 0 pairs (X) / C7 = 2 => 20 pairs (_) H9,I9: 2.. / H9 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) A2,A5: 2.. / A2 = 2 => 0 pairs (X) / A5 = 2 => 20 pairs (_) C5,C7: 2.. / C5 = 2 => 0 pairs (X) / C7 = 2 => 20 pairs (_) B1,B2: 4.. / B1 = 4 => 0 pairs (X) / B2 = 4 => 16 pairs (_) G1,G2: 4.. / G1 = 4 => 16 pairs (_) / G2 = 4 => 0 pairs (X) C7,C9: 4.. / C7 = 4 => 0 pairs (X) / C9 = 4 => 19 pairs (_) F7,F9: 4.. / F7 = 4 => 19 pairs (_) / F9 = 4 => 0 pairs (X) B1,G1: 4.. / B1 = 4 => 0 pairs (X) / G1 = 4 => 16 pairs (_) B2,G2: 4.. / B2 = 4 => 16 pairs (_) / G2 = 4 => 0 pairs (X) C7,F7: 4.. / C7 = 4 => 0 pairs (X) / F7 = 4 => 19 pairs (_) C9,F9: 4.. / C9 = 4 => 19 pairs (_) / F9 = 4 => 0 pairs (X) A1,A3: 5.. / A1 = 5 => 0 pairs (X) / A3 = 5 => 14 pairs (_) D4,F4: 5.. / D4 = 5 => 0 pairs (*) / F4 = 5 => 0 pairs (X) A3,I3: 5.. / A3 = 5 => 14 pairs (_) / I3 = 5 => 0 pairs (X) D8,H8: 6.. / D8 = 6 => 15 pairs (_) / H8 = 6 => 16 pairs (_) A4,A5: 7.. / A4 = 7 => 16 pairs (_) / A5 = 7 => 0 pairs (X) D6,H6: 7.. / D6 = 7 => 0 pairs (*) / H6 = 7 => 0 pairs (X) H3,H6: 7.. / H3 = 7 => 0 pairs (*) / H6 = 7 => 0 pairs (X) F1,F2: 8.. / F1 = 8 => 20 pairs (_) / F2 = 8 => 16 pairs (_) G5,I5: 8.. / G5 = 8 => 15 pairs (_) / I5 = 8 => 18 pairs (_) D8,D9: 8.. / D8 = 8 => 16 pairs (_) / D9 = 8 => 15 pairs (_) D8,H8: 8.. / D8 = 8 => 16 pairs (_) / H8 = 8 => 15 pairs (_) A1,A3: 9.. / A1 = 9 => 14 pairs (_) / A3 = 9 => 0 pairs (X) C4,C5: 9.. / C4 = 9 => 0 pairs (*) / C5 = 9 => 0 pairs (X) D4,F5: 9.. / D4 = 9 => 0 pairs (X) / F5 = 9 => 0 pairs (_) A1,F1: 9.. / A1 = 9 => 14 pairs (_) / F1 = 9 => 0 pairs (X) C4,D4: 9.. / C4 = 9 => 0 pairs (*) / D4 = 9 => 0 pairs (X) C5,F5: 9.. / C5 = 9 => 0 pairs (X) / F5 = 9 => 0 pairs (_) D3,D4: 9.. / D3 = 9 => 0 pairs (*) / D4 = 9 => 0 pairs (X) * DURATION: 0:00:42.745965 START: 05:35:25.488376 END: 05:36:08.234341 2019-05-01 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A3,A4,B7,C4,C9,D2,D6,D8,F4,F5,G5,H6,H8) * ..731......3.5..9..81.4.3...3..8.24..1.43..5.458.629.38...7..39195.237.437..9.... * PAIR A2: 2,6 BLK 1 B1: 2,6,4 # reduction candidate for 2,6 B1: 2,6 # 16 pairs B2: 2,6,4 # reduction candidate for 2,6 B2: 2,6 => CTR * .4731......3.58491.81.4.37..3..8.24..1.437.5.458.629138...7..39195.237.437..9.... B2: 4 # 16 pairs * PAIR A2: 2,6 ROW 2 I2: 2,6,1,7,8 # reduction candidate for 2,6 I2: 2,6 => CTR * ..731.4...4375819..8124.3...3.985241.19437.5.4581629738.2.7..39195.237.437..9.... I2: 1,7,8 # 15 pairs * PAIR A2: 2,6 COL A A5: 2,6,7 # reduction candidate for 2,6 A5: 7 => CTR * ..731....2.375..9..8124.3..639.8.24771.43..5.458.629.38...7..39195.237.437..9.... A5: 2,6 # 16 pairs * PAIR D2: 2,7 BLK 2 D3: 2,7,9 # reduction candidate for 2,7 D3: 2,7 => CTR * ..731......3.5..9..81.4.3...3.985241.19437.5.4581629738.2.74139195.237.4374.91... D3: 9 => SOLVED * 927318465643257198581946372739581246216439857458762913862174539195623784374895621 * PAIR D2: 2,7 ROW 2 I2: 2,7,1,6,8 # reduction candidate for 2,7 I2: 2,7 => CTR * .2731.4..643.5819..81.4.3..73.581246216439857458762913862174539195.237.4374.956.1 I2: 1,6,8 # 17 pairs * PAIR A4: 6,7 BLK 4 A5: 6,7,2 # reduction candidate for 6,7 A5: 6,7 => CTR * ..731....2.375..9..8124.3...3.985241.1.43..5.458.629.38...7..39195.237.437..9.... A5: 2 # 20 pairs * PAIR A4: 6,7 ROW 4 I4: 6,7,1 # reduction candidate for 6,7 I4: 6,7 => SOLVED * 927318465643257198581946372739581246216439857458762913862174539195623784374895621 I4: 1 => CTR * .6731.42.24375.19..8124.367.3..85241.1.43..5.4581629738.4.71.39195.237.4376.94.12 * PAIR C4: 6,9 BLK 4 C5: 6,9,2 # reduction candidate for 6,9 C5: 2 => CTR * 9.731....2.375..9..81.4.3...39.8.24..12439.5.458.629.382..7..39195.237.437..9.... C5: 6,9 # 20 pairs * PAIR F4: 1,5 BLK 5 D4: 1,5,7,9 # reduction candidate for 1,5 D4: 1,5 => SOLVED * 927318465643257198581946372739581246216439857458762913862174539195623784374895621 D4: 7,9 => CTR * .6731.42.24375.19..8124.367.3..85241.1.43..5.4581629738.4.71.39195.237.4376.94.12 * PAIR F4: 1,5 COL F F7: 1,5,4 # reduction candidate for 1,5 F7: 1,5 => CTR * 9.731....2.375..9..81.4.3...39.8.24..12439.5.458.629.3824.7..39195.237.4376.94... F7: 4 # 19 pairs F9: 1,5,4 # reduction candidate for 1,5 F9: 1,5 # 19 pairs * PAIR F5: 7,9 BLK 5 D4: 7,9,1,5 # reduction candidate for 7,9 D4: 7,9 => CTR * .6731.42.24375.19..8124.367.3..85241.1.43..5.4581629738.4.71.39195.237.4376.94.12 D4: 1,5 => SOLVED * 927318465643257198581946372739581246216439857458762913862174539195623784374895621 * PAIR F5: 7,9 COL F F3: 7,9,6 # reduction candidate for 7,9 F3: 6 # 18 pairs F3: 7,9 # 17 pairs * PAIR D6: 1,7 BLK 5 D4: 1,7,5,9 # reduction candidate for 1,7 D4: 1,7 => CTR * 92731.4.564325719.58194.3...39.8524.216439857458762913862.74.39195.237.4374.91... D4: 5,9 # 16 pairs * PAIR G5: 6,8 BLK 6 I5: 6,8,7 # reduction candidate for 6,8 I5: 7 => SOLVED * 927318465643257198581946372739581246216439857458762913862174539195623784374895621 I5: 6,8 # 19 pairs * PAIR G5: 6,8 COL G G1: 6,8,4,5 # reduction candidate for 6,8 G1: 6,8 => CTR * .4731......3.58491.81.4.37..3..8.24..1.437.5.458.629138...7..39195.237.437..9.... G1: 4,5 # 16 pairs G2: 6,8,1,4 # reduction candidate for 6,8 G2: 6,8 => CTR * ..731.4...43257891.81946372.39.8.24.21643..5.4587629138...7..39195.237.437..9.... G2: 1,4 # 16 pairs G9: 6,8,1,5 # reduction candidate for 6,8 G9: 6,8 # 20 pairs * PAIR H6: 1,7 BLK 6 I4: 1,7,6 # reduction candidate for 1,7 I4: 6 => SOLVED * 927318465643257198581946372739581246216439857458762913862174539195623784374895621 I4: 1,7 # 19 pairs * PAIR B7: 2,6 BLK 7 C7: 2,6,4 # reduction candidate for 2,6 C7: 4 => CTR * 9.731....2.375..9..81.4.3...3..8.24..12439.5.458.629.3824.7..39195.237.4376.94... C7: 2,6 # 19 pairs * PAIR B7: 2,6 COL B B1: 2,6,4 # reduction candidate for 2,6 B1: 2,6 # 16 pairs B2: 2,6,4 # reduction candidate for 2,6 B2: 2,6 => CTR * .4731......3.58491.81.4.37..3..8.24..1.437.5.458.629138...7..39195.237.437..9.... B2: 4 # 16 pairs * PAIR C9: 4,6 BLK 7 C7: 4,6,2 # reduction candidate for 4,6 C7: 4,6 => CTR * 9.731....2.375..9..81.4.3...3..8.24..12439.5.458.629.382..7..39195.237.437..9.... C7: 2 # 20 pairs * PAIR D8: 6,8 BLK 8 D9: 6,8,1,5 # reduction candidate for 6,8 D9: 1,5 => CTR * 9.731....2.375..9..81.4.3...39.8.24..12439.5.458.629.382467..39195823764376.94... D9: 6,8 # 17 pairs * PAIR H8: 6,8 BLK 9 G9: 6,8,1,5 # reduction candidate for 6,8 G9: 6,8 # 20 pairs H9: 6,8,1,2 # reduction candidate for 6,8 H9: 6,8 => CTR * ..731..2...3257891.81946375.3..8.24..1.43..5.4587629138...7..39195.237.437..9...2 H9: 1,2 # 16 pairs I9: 6,8,1,2,5 # reduction candidate for 6,8 I9: 6,8 => CTR * ..731......3257891.81946372.39.8.24.21643..5.4587629138...7..39195.237.437..9..2. I9: 1,2,5 # 15 pairs * PAIR H8: 6,8 COL H H1: 6,8,2 # reduction candidate for 6,8 H1: 2 => CTR * ..731..2...3.5..9..8124.3...3.985241.19437.5.4581629738.2.74139195.237.4374.91..2 H1: 6,8 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190425-absurd-base-pr-000.dot * REASONING * DIS # B2: 2,6 => CTR => B2: 4 * DIS # I2: 2,6 => CTR => I2: 1,7,8 * DIS # A5: 7 => CTR => A5: 2,6 * DIS # D3: 2,7 => CTR => D3: 9 * PRF # D3: 9 => SOL * DIS # I2: 2,7 => CTR => I2: 1,6,8 * DIS # A5: 6,7 => CTR => A5: 2 * PRF # I4: 6,7 => SOL * DIS # I4: 1 => CTR => I4: 6,7 * DIS # C5: 2 => CTR => C5: 6,9 * PRF # D4: 1,5 => SOL * DIS # D4: 7,9 => CTR => D4: 1,5 * DIS # F7: 1,5 => CTR => F7: 4 * DIS # D4: 7,9 => CTR => D4: 1,5 * PRF # D4: 1,5 => SOL * DIS # D4: 1,7 => CTR => D4: 5,9 * PRF # I5: 7 => SOL * DIS # G1: 6,8 => CTR => G1: 4,5 * DIS # G2: 6,8 => CTR => G2: 1,4 * PRF # I4: 6 => SOL * DIS # C7: 4 => CTR => C7: 2,6 * DIS # B2: 2,6 => CTR => B2: 4 * DIS # C7: 4,6 => CTR => C7: 2 * DIS # D9: 1,5 => CTR => D9: 6,8 * DIS # H9: 6,8 => CTR => H9: 1,2 * DIS # I9: 6,8 => CTR => I9: 1,2,5 * DIS # H1: 2 => CTR => H1: 6,8 * CNT 27 HDP CHAINS / 53 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A3,A4,B7,C4,C9,D2,D6,D8,F4,F5,G5,H6,H8) * ..731......3.5..9..81.4.3...3..8.24..1.43..5.458.629.38...7..39195.237.437..9.... * PAIR A2: 2,6 BLK 1 B1: 2,6,4 # reduction candidate for 2,6 B1: 2,6 # 16 pairs B2: 2,6,4 # reduction candidate for 2,6 B2: 2,6 => CTR * .4731......3.58491.81.4.37..3..8.24..1.437.5.458.629138...7..39195.237.437..9.... * RESTART * PAIR A2: 2,6 ROW 2 I2: 2,6,1,7,8 # reduction candidate for 2,6 I2: 2,6 => CTR * ..731.4...4375819..8124.3...3.985241.19437.5.4581629738.2.7..39195.237.437..9.... * PAIR A2: 2,6 COL A A5: 2,6,7 # reduction candidate for 2,6 A5: 7 => CTR * ..731.4..24375..9..8124.3..639.8.24771.43..5.458.629.38...7..39195.237.437..9.... * PAIR RESTART * PAIR D2: 2,7 BLK 2 D3: 2,7,9 # reduction candidate for 2,7 D3: 2,7 => CTR * ..731.4...43.5..9..81.4.3..73.985241.19437.5.4581629738.2.74139195.237.4374.915.. D3: 9 => SOLVED * 927318465643257198581946372739581246216439857458762913862174539195623784374895621 * DURATION: 0:00:06.437789 START: 05:36:43.993170 END: 05:36:50.430959 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190425-absurd-base-pr-001.dot * REASONING * DIS # B2: 2,6 => CTR => B2: 4 * DIS B2: 4 # I2: 2,6 => CTR => I2: 1,7,8 * DIS B2: 4 + I2: 1,7,8 # A5: 7 => CTR => A5: 2,6 * DIS B2: 4 + I2: 1,7,8 + A5: 2,6 # D3: 2,7 => CTR => D3: 9 * PRF B2: 4 + I2: 1,7,8 + A5: 2,6 + D3: 9 => SOL * STA B2: 4 + I2: 1,7,8 + A5: 2,6 + D3: 9 * CNT 5 HDP CHAINS / 6 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190425, absurd
Solution
position: 927318465643257198581946372739581246216439857458762913862174539195623784374895621 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 # B1: 2,6 => UNS * DIS # B2: 2,6 => CTR => B2: 4 * INC # B2: 4 => UNS * DIS # I2: 2,6 => CTR => I2: 1,7,8 * INC # I2: 1,7,8 => UNS * INC # A5: 2,6 => UNS * DIS # A5: 7 => CTR => A5: 2,6 * DIS # D3: 2,7 => CTR => D3: 9 * PRF # D3: 9 => SOL * DIS # I2: 2,7 => CTR => I2: 1,6,8 * INC # I2: 1,6,8 => UNS * DIS # A5: 6,7 => CTR => A5: 2 * INC # A5: 2 => UNS * PRF # I4: 6,7 => SOL * DIS # I4: 1 => CTR => I4: 6,7 * INC # C5: 6,9 => UNS * DIS # C5: 2 => CTR => C5: 6,9 * PRF # D4: 1,5 => SOL * DIS # D4: 7,9 => CTR => D4: 1,5 * DIS # F7: 1,5 => CTR => F7: 4 * INC # F7: 4 => UNS * INC # F9: 1,5 => UNS * DIS # D4: 7,9 => CTR => D4: 1,5 * PRF # D4: 1,5 => SOL * INC # F3: 7,9 => UNS * INC # F3: 6 => UNS * DIS # D4: 1,7 => CTR => D4: 5,9 * INC # D4: 5,9 => UNS * INC # I5: 6,8 => UNS * PRF # I5: 7 => SOL * DIS # G1: 6,8 => CTR => G1: 4,5 * INC # G1: 4,5 => UNS * DIS # G2: 6,8 => CTR => G2: 1,4 * INC # G2: 1,4 => UNS * INC # G9: 6,8 => UNS * INC # I4: 1,7 => UNS * PRF # I4: 6 => SOL * INC # C7: 2,6 => UNS * DIS # C7: 4 => CTR => C7: 2,6 * INC # B1: 2,6 => UNS * DIS # B2: 2,6 => CTR => B2: 4 * INC # B2: 4 => UNS * DIS # C7: 4,6 => CTR => C7: 2 * INC # C7: 2 => UNS * INC # D9: 6,8 => UNS * DIS # D9: 1,5 => CTR => D9: 6,8 * INC # G9: 6,8 => UNS * DIS # H9: 6,8 => CTR => H9: 1,2 * INC # H9: 1,2 => UNS * DIS # I9: 6,8 => CTR => I9: 1,2,5 * INC # I9: 1,2,5 => UNS * INC # H1: 6,8 => UNS * DIS # H1: 2 => CTR => H1: 6,8 * CNT 53 HDP CHAINS / 53 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 2,6 => UNS * DIS # B2: 2,6 => CTR => B2: 4 * DIS B2: 4 # I2: 2,6 => CTR => I2: 1,7,8 * INC B2: 4 + I2: 1,7,8 # A5: 2,6 => UNS * DIS B2: 4 + I2: 1,7,8 # A5: 7 => CTR => A5: 2,6 * DIS B2: 4 + I2: 1,7,8 + A5: 2,6 # D3: 2,7 => CTR => D3: 9 * PRF B2: 4 + I2: 1,7,8 + A5: 2,6 + D3: 9 => SOL * STA B2: 4 + I2: 1,7,8 + A5: 2,6 + D3: 9 * CNT 7 HDP CHAINS / 6 HYP OPENED