Analysis of zz-www.sudokuoftheday.co.uk-20190109-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019
level: medium
position: 7...8..1...8.26...4.....2..5...7.4....6..2......64..2....7....8..5..1.9......9.6. initial
Autosolve
position: 7..48.61...8.26.4746...728.5...78436.46..2.7...764..2.2..764.58685231794.74859.62 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D2: 3,5 => CTR => D2: 1,9 * DIS # B1: 3,5 => CTR => B1: 2,9 * PRF # B1: 2,9 => SOL * PRF # I1: 3,5 => SOL * DIS # I1: 9 => CTR => I1: 3,5 * DIS # D3: 1,9 => CTR => D3: 3,5 * DIS # C3: 3 => CTR => C3: 1,9 * DIS # I3: 5,9 => CTR => I3: 3 * PRF # B2: 5,9 => SOL * DIS # B2: 1,3 => CTR => B2: 5,9 * DIS # D2: 5,9 => CTR => D2: 1,3 * PRF # B4: 1,9 => SOL * DIS # D3: 1,9 => CTR => D3: 3,5 * DIS # D2: 3,5 => CTR => D2: 1,9 * DIS # A5: 1,9 => CTR => A5: 3,8 * DIS # B7: 1,3 => CTR => B7: 9 * PRF # A2: 1,3 => SOL * DIS # A2: 9 => CTR => A2: 1,3 * DIS # A5: 1,3 => CTR => A5: 8,9 * DIS # A6: 1,3 => CTR => A6: 8,9 * DIS # B7: 1,3 => CTR => B7: 9 * CNT 21 HDP CHAINS / 45 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D2: 3,5 => CTR => D2: 1,9 * PRF D2: 1,9 # I1: 3,5 => SOL * STA D2: 1,9 + I1: 3,5 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7...8..1...8.26...4.....2..5...7.4....6..2......64..2....7....8..5..1.9......9.6. | initial |
| 7..48.61...8.26.4746...728.5...78436.46..2.7...764..2.2..764.58685231794.74859.62 | autosolve |
| 729483615358126947461597283512978436846312579937645821293764158685231794174859362 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) F1: 3,5 E3: 1,9 G2: 5,9 D4: 1,9 D5: 3,5 E5: 1,9 F6: 3,5 A9: 1,3 G7: 1,3 G9: 1,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D4,E5: 1.. / D4 = 1 => 0 pairs (X) / E5 = 1 => 13 pairs (_) I5,I6: 1.. / I5 = 1 => 0 pairs (X) / I6 = 1 => 12 pairs (_) G7,G9: 1.. / G7 = 1 => 10 pairs (_) / G9 = 1 => 0 pairs (X) A9,G9: 1.. / A9 = 1 => 10 pairs (_) / G9 = 1 => 0 pairs (X) E3,E5: 1.. / E3 = 1 => 0 pairs (X) / E5 = 1 => 13 pairs (_) B1,C1: 2.. / B1 = 2 => 0 pairs (*) / C1 = 2 => 0 pairs (X) B4,C4: 2.. / B4 = 2 => 11 pairs (_) / C4 = 2 => 0 pairs (*) B1,B4: 2.. / B1 = 2 => 0 pairs (*) / B4 = 2 => 0 pairs (X) C1,C4: 2.. / C1 = 2 => 11 pairs (_) / C4 = 2 => 0 pairs (*) I1,I3: 3.. / I1 = 3 => 0 pairs (X) / I3 = 3 => 15 pairs (_) D5,F6: 3.. / D5 = 3 => 15 pairs (_) / F6 = 3 => 0 pairs (X) G7,G9: 3.. / G7 = 3 => 0 pairs (X) / G9 = 3 => 10 pairs (_) A5,D5: 3.. / A5 = 3 => 0 pairs (X) / D5 = 3 => 15 pairs (_) A9,G9: 3.. / A9 = 3 => 0 pairs (X) / G9 = 3 => 10 pairs (_) F1,F6: 3.. / F1 = 3 => 15 pairs (_) / F6 = 3 => 0 pairs (X) B1,B2: 5.. / B1 = 5 => 0 pairs (X) / B2 = 5 => 0 pairs (_) D5,F6: 5.. / D5 = 5 => 0 pairs (X) / F6 = 5 => 15 pairs (_) D3,I3: 5.. / D3 = 5 => 15 pairs (_) / I3 = 5 => 0 pairs (X) F1,F6: 5.. / F1 = 5 => 0 pairs (X) / F6 = 5 => 15 pairs (_) A5,A6: 8.. / A5 = 8 => 15 pairs (_) / A6 = 8 => 11 pairs (_) G5,G6: 8.. / G5 = 8 => 11 pairs (_) / G6 = 8 => 15 pairs (_) A5,G5: 8.. / A5 = 8 => 15 pairs (_) / G5 = 8 => 11 pairs (_) A6,G6: 8.. / A6 = 8 => 11 pairs (_) / G6 = 8 => 15 pairs (_) D4,E5: 9.. / D4 = 9 => 13 pairs (_) / E5 = 9 => 0 pairs (X) B7,C7: 9.. / B7 = 9 => 13 pairs (_) / C7 = 9 => 0 pairs (X) E3,E5: 9.. / E3 = 9 => 13 pairs (_) / E5 = 9 => 0 pairs (X) * DURATION: 0:00:35.558978 START: 02:49:22.570561 END: 02:49:58.129539 2019-05-01 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,D4,D5,E3,E5,F1,F6,G2,G7,G9) * 7..48.61...8.26.4746...728.5...78436.46..2.7...764..2.2..764.58685231794.74859.62 * PAIR F1: 3,5 BLK 2 D2: 3,5,1,9 # reduction candidate for 3,5 D2: 3,5 => CTR * 7..48.613..8326947463..72855...784363465.287...764..2.2..764.58685231794.74859.62 D2: 1,9 # 16 pairs D3: 3,5,1,9 # reduction candidate for 3,5 D3: 3,5 # 16 pairs * PAIR F1: 3,5 ROW 1 B1: 3,5,2,9 # reduction candidate for 3,5 B1: 3,5 => CTR * 752483619.189265474695.728352..78436.463.2.75..7645.212.3764158685231794174859362 B1: 2,9 => SOLVED * 729483615358126947461597283512978436846312579937645821293764158685231794174859362 I1: 3,5,9 # reduction candidate for 3,5 I1: 3,5 => SOLVED * 729483615358126947461597283512978436846312579937645821293764158685231794174859362 I1: 9 => CTR * 752483619.189265474695.728352..78436.463.2.75..7645.212.3764158685231794174859362 * PAIR E3: 1,9 BLK 2 D2: 1,9,3,5 # reduction candidate for 1,9 D2: 1,9 # 16 pairs D3: 1,9,3,5 # reduction candidate for 1,9 D3: 1,9 => CTR * 7..48.613..8326947463..72855...784363465.287...764..2.2..764.58685231794.74859.62 D3: 3,5 # 16 pairs * PAIR E3: 1,9 ROW 3 C3: 1,9,3 # reduction candidate for 1,9 C3: 3 => CTR * 79.48.613..8326.47463..728.5...784363465.287.8.7643.2.239764158685231794174859362 C3: 1,9 # 16 pairs * PAIR G2: 5,9 BLK 3 I1: 5,9,3 # reduction candidate for 5,9 I1: 5,9 # 15 pairs I3: 5,9,3 # reduction candidate for 5,9 I3: 5,9 => CTR * 7..485613.58.2694746...72855...784363465.287...7643.2.2..764.58685231794.74859.62 I3: 3 # 15 pairs * PAIR G2: 5,9 ROW 2 B2: 5,9,1,3 # reduction candidate for 5,9 B2: 5,9 => SOLVED * 729483615358126947461597283512978436846312579937645821293764158685231794174859362 B2: 1,3 => CTR * 752483619.189265474695.728352..78436.463.2.75..7645.212.3764158685231794174859362 D2: 5,9,1,3 # reduction candidate for 5,9 D2: 5,9 => CTR * 7..48.61...8.26.47469.1728.5..178436.46.92.7.9.764.82.29.764.58685231794.74859.62 D2: 1,3 # 13 pairs * PAIR G2: 5,9 COL G G5: 5,9,8 # reduction candidate for 5,9 G5: 5,9 # 15 pairs G6: 5,9,8 # reduction candidate for 5,9 G6: 5,9 # 11 pairs * PAIR D4: 1,9 ROW 4 B4: 1,9,2 # reduction candidate for 1,9 B4: 1,9 => SOLVED * 729483615358126947461597283512978436846312579937645821293764158685231794174859362 B4: 2 # 11 pairs C4: 1,9,2 # reduction candidate for 1,9 C4: 1,9 # 11 pairs * PAIR D4: 1,9 COL D D2: 1,9,3,5 # reduction candidate for 1,9 D2: 1,9 # 16 pairs D3: 1,9,3,5 # reduction candidate for 1,9 D3: 1,9 => CTR * 7..48.613..8326947463..72855...784363465.287...764..2.2..764.58685231794.74859.62 D3: 3,5 # 16 pairs * PAIR D5: 3,5 COL D D2: 3,5,1,9 # reduction candidate for 3,5 D2: 3,5 => CTR * 7..48.613..8326947463..72855...784363465.287...764..2.2..764.58685231794.74859.62 D2: 1,9 # 16 pairs D3: 3,5,1,9 # reduction candidate for 3,5 D3: 3,5 # 16 pairs * PAIR E5: 1,9 ROW 5 A5: 1,9,3,8 # reduction candidate for 1,9 A5: 1,9 => CTR * 7524836193.8.2654746.5.728352..784369463128758376459212.3764158685231794174859362 A5: 3,8 # 11 pairs I5: 1,9,5 # reduction candidate for 1,9 I5: 1,9 # 13 pairs * PAIR A9: 1,3 BLK 7 B7: 1,3,9 # reduction candidate for 1,3 B7: 1,3 => CTR * 7..48561.9.8326.4746...728.5...784363465.287.8.7643.2.239764158685231794174859362 B7: 9 # 13 pairs C7: 1,3,9 # reduction candidate for 1,3 C7: 1,3 # 13 pairs * PAIR A9: 1,3 COL A A2: 1,3,9 # reduction candidate for 1,3 A2: 1,3 => SOLVED * 729483615358126947461597283512978436846312579937645821293764158685231794174859362 A2: 9 => CTR * 75.48.61.9.8.2654746.5972835..978436.46312.75.976458212.9764.58685231794174859362 A5: 1,3,8,9 # reduction candidate for 1,3 A5: 1,3 => CTR * 7..48.61.9.8.2654746.5972835...78436.46..287.8.764..2.2..764.58685231794.74859.62 A5: 8,9 # 15 pairs A6: 1,3,8,9 # reduction candidate for 1,3 A6: 1,3 => CTR * 7..48361.938126547461597283512.784368463.2.7...764582.2..764.58685231794.74859.62 A6: 8,9 # 11 pairs * PAIR G7: 1,3 ROW 7 B7: 1,3,9 # reduction candidate for 1,3 B7: 1,3 => CTR * 7..48561.9.8326.4746...728.5...784363465.287.8.7643.2.239764158685231794174859362 B7: 9 # 13 pairs C7: 1,3,9 # reduction candidate for 1,3 C7: 1,3 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190109-absurd-base-pr-000.dot * REASONING * DIS # D2: 3,5 => CTR => D2: 1,9 * DIS # B1: 3,5 => CTR => B1: 2,9 * PRF # B1: 2,9 => SOL * PRF # I1: 3,5 => SOL * DIS # I1: 9 => CTR => I1: 3,5 * DIS # D3: 1,9 => CTR => D3: 3,5 * DIS # C3: 3 => CTR => C3: 1,9 * DIS # I3: 5,9 => CTR => I3: 3 * PRF # B2: 5,9 => SOL * DIS # B2: 1,3 => CTR => B2: 5,9 * DIS # D2: 5,9 => CTR => D2: 1,3 * PRF # B4: 1,9 => SOL * DIS # D3: 1,9 => CTR => D3: 3,5 * DIS # D2: 3,5 => CTR => D2: 1,9 * DIS # A5: 1,9 => CTR => A5: 3,8 * DIS # B7: 1,3 => CTR => B7: 9 * PRF # A2: 1,3 => SOL * DIS # A2: 9 => CTR => A2: 1,3 * DIS # A5: 1,3 => CTR => A5: 8,9 * DIS # A6: 1,3 => CTR => A6: 8,9 * DIS # B7: 1,3 => CTR => B7: 9 * CNT 21 HDP CHAINS / 45 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,D4,D5,E3,E5,F1,F6,G2,G7,G9) * 7..48.61...8.26.4746...728.5...78436.46..2.7...764..2.2..764.58685231794.74859.62 * PAIR F1: 3,5 BLK 2 D2: 3,5,1,9 # reduction candidate for 3,5 D2: 3,5 => CTR * 7..48.613..8326947463..72855...784363465.287...764..2.2..764.58685231794.74859.62 * RESTART * PAIR F1: 3,5 ROW 1 I1: 3,5,9 # reduction candidate for 3,5 I1: 3,5 => SOLVED * 729483615358126947461597283512978436846312579937645821293764158685231794174859362 * DURATION: 0:00:02.627689 START: 02:50:33.924827 END: 02:50:36.552516 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190109-absurd-base-pr-001.dot * REASONING * DIS # D2: 3,5 => CTR => D2: 1,9 * PRF D2: 1,9 # I1: 3,5 => SOL * STA D2: 1,9 + I1: 3,5 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190109, absurd
Solution
position: 729483615358126947461597283512978436846312579937645821293764158685231794174859362 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 # D2: 3,5 => CTR => D2: 1,9 * INC # D2: 1,9 => UNS * INC # D3: 3,5 => UNS * DIS # B1: 3,5 => CTR => B1: 2,9 * PRF # B1: 2,9 => SOL * PRF # I1: 3,5 => SOL * DIS # I1: 9 => CTR => I1: 3,5 * INC # D2: 1,9 => UNS * DIS # D3: 1,9 => CTR => D3: 3,5 * INC # D3: 3,5 => UNS * INC # C3: 1,9 => UNS * DIS # C3: 3 => CTR => C3: 1,9 * INC # I1: 5,9 => UNS * DIS # I3: 5,9 => CTR => I3: 3 * INC # I3: 3 => UNS * PRF # B2: 5,9 => SOL * DIS # B2: 1,3 => CTR => B2: 5,9 * DIS # D2: 5,9 => CTR => D2: 1,3 * INC # D2: 1,3 => UNS * INC # G5: 5,9 => UNS * INC # G6: 5,9 => UNS * PRF # B4: 1,9 => SOL * INC # B4: 2 => UNS * INC # C4: 1,9 => UNS * INC # D2: 1,9 => UNS * DIS # D3: 1,9 => CTR => D3: 3,5 * INC # D3: 3,5 => UNS * DIS # D2: 3,5 => CTR => D2: 1,9 * INC # D2: 1,9 => UNS * INC # D3: 3,5 => UNS * DIS # A5: 1,9 => CTR => A5: 3,8 * INC # A5: 3,8 => UNS * INC # I5: 1,9 => UNS * DIS # B7: 1,3 => CTR => B7: 9 * INC # B7: 9 => UNS * INC # C7: 1,3 => UNS * PRF # A2: 1,3 => SOL * DIS # A2: 9 => CTR => A2: 1,3 * DIS # A5: 1,3 => CTR => A5: 8,9 * INC # A5: 8,9 => UNS * DIS # A6: 1,3 => CTR => A6: 8,9 * INC # A6: 8,9 => UNS * DIS # B7: 1,3 => CTR => B7: 9 * INC # B7: 9 => UNS * INC # C7: 1,3 => UNS * CNT 45 HDP CHAINS / 45 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D2: 3,5 => CTR => D2: 1,9 * PRF D2: 1,9 # I1: 3,5 => SOL * STA D2: 1,9 + I1: 3,5 * CNT 2 HDP CHAINS / 2 HYP OPENED