Analysis of zz-www.sudokuoftheday.co.uk-20060806-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006
level: medium
position: .12..5...7..9.6.4...3.7...6.3.....29.95.4...8........4.2...1..3...3........6..275 initial
Autosolve
position: 6124.5..77589.6.42943.7...6.34.6..29.95.43..8.....9..4.2...1..3...3....1381694275 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # G1: 3,8 => SOL * DIS # D3: 2,8 => CTR => D3: 1 * PRF # D3: 1 => SOL * DIS # F8: 2,8 => CTR => F8: 7 * PRF # G6: 5 => SOL * DIS # A6: 2 => CTR => A6: 1,8 * DIS # D4: 1,8 => CTR => D4: 5,7 * DIS # A6: 1,2 => CTR => A6: 8 * DIS # D5: 1,2 => CTR => D5: 7 * PRF # D5: 7 => SOL * DIS # C8: 6,7 => CTR => C8: 9 * DIS # D4: 7,8 => CTR => D4: 1,5 * DIS # F8: 2 => CTR => F8: 7,8 * PRF # G5: 1,6 => SOL * DIS # G5: 7 => CTR => G5: 1,6 * DIS # C8: 6,7 => CTR => C8: 9 * DIS # E8: 5,8 => CTR => E8: 2 * DIS # E6: 5,8 => CTR => E6: 1,2 * CNT 18 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # G1: 3,8 => SOL * STA G1: 3,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .12..5...7..9.6.4...3.7...6.3.....29.95.4...8........4.2...1..3...3........6..275 | initial |
| 6124.5..77589.6.42943.7...6.34.6..29.95.43..8.....9..4.2...1..3...3....1381694275 | autosolve |
| 612485397758936142943172856134568729295743618876219534427851963569327481381694275 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) E1: 3,8 E2: 1,3 F3: 2,8 G2: 1,3 A4: 1,8 A5: 1,2 B6: 6,7 C6: 6,7 F4: 7,8 H5: 1,6 A7: 4,5 A8: 4,5 B8: 6,7 E7: 5,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,D3: 1.. / E2 = 1 => 0 pairs (X) / D3 = 1 => 0 pairs (_) E2,G2: 1.. / E2 = 1 => 0 pairs (X) / G2 = 1 => 0 pairs (_) E2,E6: 1.. / E2 = 1 => 0 pairs (X) / E6 = 1 => 0 pairs (_) D3,F3: 2.. / D3 = 2 => 0 pairs (X) / F3 = 2 => 13 pairs (_) A5,A6: 2.. / A5 = 2 => 15 pairs (_) / A6 = 2 => 0 pairs (X) E8,F8: 2.. / E8 = 2 => 13 pairs (_) / F8 = 2 => 0 pairs (X) A5,D5: 2.. / A5 = 2 => 15 pairs (_) / D5 = 2 => 0 pairs (X) E6,E8: 2.. / E6 = 2 => 0 pairs (X) / E8 = 2 => 13 pairs (_) F3,F8: 2.. / F3 = 2 => 13 pairs (_) / F8 = 2 => 0 pairs (X) E1,E2: 3.. / E1 = 3 => 0 pairs (X) / E2 = 3 => 0 pairs (_) G6,H6: 3.. / G6 = 3 => 0 pairs (X) / H6 = 3 => 0 pairs (_) E2,G2: 3.. / E2 = 3 => 0 pairs (*) / G2 = 3 => 0 pairs (X) H1,H6: 3.. / H1 = 3 => 0 pairs (X) / H6 = 3 => 0 pairs (_) A7,A8: 4.. / A7 = 4 => 13 pairs (_) / A8 = 4 => 0 pairs (X) G7,G8: 4.. / G7 = 4 => 0 pairs (X) / G8 = 4 => 13 pairs (_) A7,G7: 4.. / A7 = 4 => 13 pairs (_) / G7 = 4 => 0 pairs (X) A8,G8: 4.. / A8 = 4 => 0 pairs (X) / G8 = 4 => 13 pairs (_) G3,H3: 5.. / G3 = 5 => 0 pairs (X) / H3 = 5 => 19 pairs (_) A7,A8: 5.. / A7 = 5 => 0 pairs (X) / A8 = 5 => 13 pairs (_) D4,G4: 5.. / D4 = 5 => 18 pairs (_) / G4 = 5 => 0 pairs (X) A8,E8: 5.. / A8 = 5 => 13 pairs (_) / E8 = 5 => 0 pairs (X) H3,H6: 5.. / H3 = 5 => 19 pairs (_) / H6 = 5 => 0 pairs (X) B6,C6: 6.. / B6 = 6 => 0 pairs (X) / C6 = 6 => 14 pairs (_) G5,H5: 6.. / G5 = 6 => 0 pairs (*) / H5 = 6 => 0 pairs (X) B6,B8: 6.. / B6 = 6 => 0 pairs (X) / B8 = 6 => 14 pairs (_) B6,C6: 7.. / B6 = 7 => 14 pairs (_) / C6 = 7 => 0 pairs (X) G4,G5: 7.. / G4 = 7 => 0 pairs (*) / G5 = 7 => 0 pairs (X) D7,F8: 7.. / D7 = 7 => 0 pairs (X) / F8 = 7 => 15 pairs (_) D5,G5: 7.. / D5 = 7 => 0 pairs (*) / G5 = 7 => 0 pairs (X) C7,D7: 7.. / C7 = 7 => 15 pairs (_) / D7 = 7 => 0 pairs (X) B6,B8: 7.. / B6 = 7 => 14 pairs (_) / B8 = 7 => 0 pairs (X) F4,F8: 7.. / F4 = 7 => 0 pairs (X) / F8 = 7 => 15 pairs (_) A4,A6: 8.. / A4 = 8 => 0 pairs (X) / A6 = 8 => 14 pairs (_) G1,H1: 9.. / G1 = 9 => 15 pairs (_) / H1 = 9 => 0 pairs (*) C7,C8: 9.. / C7 = 9 => 0 pairs (X) / C8 = 9 => 16 pairs (_) * DURATION: 0:00:47.493092 START: 01:36:05.668555 END: 01:36:53.161647 2019-05-01 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,A7,A8,B6,B8,C6,E1,E2,E7,F3,F4,G2,H5) * 6124.5..77589.6.42943.7...6.34.6..29.95.43..8.....9..4.2...1..3...3....1381694275 * PAIR E1: 3,8 ROW 1 G1: 3,8,9 # reduction candidate for 3,8 G1: 3,8 => SOLVED * 612485397758936142943172856134568729295743618876219534427851963569327481381694275 G1: 9 # 15 pairs H1: 3,8,9 # reduction candidate for 3,8 H1: 3,8 # 15 pairs * PAIR F3: 2,8 BLK 2 D3: 2,8,1 # reduction candidate for 2,8 D3: 2,8 => CTR * 612435..7758916342943.7.156.3456.729295743618...129534.278.1..3...3....1381694275 D3: 1 => SOLVED * 612485397758936142943172856134568729295743618876219534427851963569327481381694275 * PAIR F3: 2,8 COL F F8: 2,8,7 # reduction candidate for 2,8 F8: 2,8 => CTR * 6124.5937758936142943172856134867529295.43768.....9..4.2.7.1..3...3....1381694275 F8: 7 # 15 pairs * PAIR G2: 1,3 COL G G6: 1,3,5 # reduction candidate for 1,3 G6: 5 => SOLVED * 612485397758936142943172856134568729295743618876219534427851963569327481381694275 G6: 1,3 # 19 pairs * PAIR A4: 1,8 BLK 4 A6: 1,8,2 # reduction candidate for 1,8 A6: 2 => CTR * 612485937758936142943172856834567.291952437682....9..4.297516835..328491381694275 A6: 1,8 # 15 pairs * PAIR A4: 1,8 ROW 4 D4: 1,8,5,7 # reduction candidate for 1,8 D4: 1,8 => CTR * 6124.5.377589.6.42943.7..56.34.67529.95.43768...5.9.14.2.7.1..3...3....1381694275 D4: 5,7 # 15 pairs * PAIR A5: 1,2 BLK 4 A6: 1,2,8 # reduction candidate for 1,2 A6: 1,2 => CTR * 6124.5937758936142943172856834567.29.95.43768.....9..4.2.7.1..3...3....1381694275 A6: 8 # 14 pairs * PAIR A5: 1,2 ROW 5 D5: 1,2,7 # reduction candidate for 1,2 D5: 1,2 => CTR * 6124.5937758936142943172856134.6.529295.43768.....9..4.2...1..3...3....1381694275 D5: 7 => SOLVED * 612485397758936142943172856134568729295743618876219534427851963569327481381694275 * PAIR C6: 6,7 COL C C7: 6,7,9 # reduction candidate for 6,7 C7: 6,7 # 16 pairs C8: 6,7,9 # reduction candidate for 6,7 C8: 6,7 => CTR * 6124.5937758936142943172856134867529295.43768.....9..4.297.1683...3..491381694275 C8: 9 # 16 pairs * PAIR F4: 7,8 BLK 5 D4: 7,8,1,5 # reduction candidate for 7,8 D4: 7,8 => CTR * 6124.5.377589.6.42943.7..56134.6.5292951437688....9.14.2...1..3...3....1381694275 D4: 1,5 # 15 pairs * PAIR F4: 7,8 COL F F8: 7,8,2 # reduction candidate for 7,8 F8: 2 => CTR * 612435..7758916342943278..6.34.67.29295143768....29.34.2.7.1..3...3.2..1381694275 F8: 7,8 # 13 pairs * PAIR H5: 1,6 BLK 6 G5: 1,6,7 # reduction candidate for 1,6 G5: 1,6 => SOLVED * 612485397758936142943172856134568729295743618876219534427851963569327481381694275 G5: 7 => CTR * 6124.5937758936142943172856134.6.529295.43768.....9..4.2...1..3...3....1381694275 * PAIR B8: 6,7 BLK 7 C7: 6,7,9 # reduction candidate for 6,7 C7: 6,7 # 16 pairs C8: 6,7,9 # reduction candidate for 6,7 C8: 6,7 => CTR * 6124.5937758936142943172856134867529295.43768.....9..4.297.1683...3..491381694275 C8: 9 # 16 pairs * PAIR E7: 5,8 BLK 8 D7: 5,8,7 # reduction candidate for 5,8 D7: 5,8 # 15 pairs E8: 5,8,2 # reduction candidate for 5,8 E8: 5,8 => CTR * 6124.5..7758916342943278..6.34.67.29295143768....29.34.2.7.1..3...3.2..1381694275 E8: 2 # 13 pairs * PAIR E7: 5,8 COL E E6: 5,8,1,2 # reduction candidate for 5,8 E6: 5,8 => CTR * 612435..7758916342943872156.3456.729295743.18.....9534.2..51..35..32.4.1381694275 E6: 1,2 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060806-absurd-base-pr-000.dot * REASONING * PRF # G1: 3,8 => SOL * DIS # D3: 2,8 => CTR => D3: 1 * PRF # D3: 1 => SOL * DIS # F8: 2,8 => CTR => F8: 7 * PRF # G6: 5 => SOL * DIS # A6: 2 => CTR => A6: 1,8 * DIS # D4: 1,8 => CTR => D4: 5,7 * DIS # A6: 1,2 => CTR => A6: 8 * DIS # D5: 1,2 => CTR => D5: 7 * PRF # D5: 7 => SOL * DIS # C8: 6,7 => CTR => C8: 9 * DIS # D4: 7,8 => CTR => D4: 1,5 * DIS # F8: 2 => CTR => F8: 7,8 * PRF # G5: 1,6 => SOL * DIS # G5: 7 => CTR => G5: 1,6 * DIS # C8: 6,7 => CTR => C8: 9 * DIS # E8: 5,8 => CTR => E8: 2 * DIS # E6: 5,8 => CTR => E6: 1,2 * CNT 18 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,A7,A8,B6,B8,C6,E1,E2,E7,F3,F4,G2,H5) * 6124.5..77589.6.42943.7...6.34.6..29.95.43..8.....9..4.2...1..3...3....1381694275 * PAIR E1: 3,8 ROW 1 G1: 3,8,9 # reduction candidate for 3,8 G1: 3,8 => SOLVED * 612485397758936142943172856134568729295743618876219534427851963569327481381694275 * DURATION: 0:00:01.678576 START: 01:37:18.600376 END: 01:37:20.278952 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060806-absurd-base-pr-001.dot * REASONING * PRF # G1: 3,8 => SOL * STA G1: 3,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060806, absurd
Solution
position: 612485397758936142943172856134568729295743618876219534427851963569327481381694275 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:
* PRF # G1: 3,8 => SOL * INC # G1: 9 => UNS * INC # H1: 3,8 => UNS * DIS # D3: 2,8 => CTR => D3: 1 * PRF # D3: 1 => SOL * DIS # F8: 2,8 => CTR => F8: 7 * INC # F8: 7 => UNS * INC # G6: 1,3 => UNS * PRF # G6: 5 => SOL * INC # A6: 1,8 => UNS * DIS # A6: 2 => CTR => A6: 1,8 * DIS # D4: 1,8 => CTR => D4: 5,7 * INC # D4: 5,7 => UNS * DIS # A6: 1,2 => CTR => A6: 8 * INC # A6: 8 => UNS * DIS # D5: 1,2 => CTR => D5: 7 * PRF # D5: 7 => SOL * INC # C7: 6,7 => UNS * DIS # C8: 6,7 => CTR => C8: 9 * INC # C8: 9 => UNS * DIS # D4: 7,8 => CTR => D4: 1,5 * INC # D4: 1,5 => UNS * INC # F8: 7,8 => UNS * DIS # F8: 2 => CTR => F8: 7,8 * PRF # G5: 1,6 => SOL * DIS # G5: 7 => CTR => G5: 1,6 * INC # C7: 6,7 => UNS * DIS # C8: 6,7 => CTR => C8: 9 * INC # C8: 9 => UNS * INC # D7: 5,8 => UNS * DIS # E8: 5,8 => CTR => E8: 2 * INC # E8: 2 => UNS * DIS # E6: 5,8 => CTR => E6: 1,2 * INC # E6: 1,2 => UNS * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # G1: 3,8 => SOL * STA G1: 3,8 * CNT 1 HDP CHAINS / 1 HYP OPENED