Analysis of zz-www.sudokuoftheday.co.uk-20060820-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: 3.7...........47.8..1.6......6..9..3....7.124.....568...2.9.....73.2.4..4.5..6... initial
Autosolve
position: 3.7........9..47.8..1.6......6849573..8673124734215689..249.....7352.4..4.5..6... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 5,8 => CTR => B3: 4 * DIS # H1: 1,9 => CTR => H1: 4,5,6 * DIS # H2: 5,6 => CTR => H2: 1,3 * DIS # D9: 1,3 => CTR => D9: 7 * PRF # D9: 7 => SOL * DIS # H2: 3,5 => CTR => H2: 1,6 * PRF # G3: 2,9 => SOL * DIS # G3: 3 => CTR => G3: 2,9 * DIS # G9: 2,9 => CTR => G9: 8 * PRF # G9: 8 => SOL * DIS # I1: 2,5 => CTR => I1: 1,6 * PRF # F7: 1,8 => SOL * DIS # F7: 7 => CTR => F7: 1,8 * DIS # A8: 1,8 => CTR => A8: 6,9 * DIS # F1: 1,8 => CTR => F1: 2 * PRF # F1: 2 => SOL * DIS # H7: 1,6 => CTR => H7: 3,5 * DIS # I7: 1,6 => CTR => I7: 5,7 * DIS # A8: 1,6 => CTR => A8: 8,9 * DIS # I1: 2,5 => CTR => I1: 1,6 * DIS # H8: 1,9 => CTR => H8: 6 * DIS # B9: 8 => CTR => B9: 1,9 * DIS # H1: 1,9 => CTR => H1: 4,5,6 * CNT 23 HDP CHAINS / 40 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 5,8 => CTR => B3: 4 * PRF B3: 4 # G3: 2,9 => SOL * STA B3: 4 + G3: 2,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 3.7...........47.8..1.6......6..9..3....7.124.....568...2.9.....73.2.4..4.5..6... | initial |
| 3.7........9..47.8..1.6......6849573..8673124734215689..249.....7352.4..4.5..6... | autosolve |
| 357182946269354718841967235126849573598673124734215689682491357973528461415736892 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) A3: 5,8 D1: 1,9 E1: 5,8 D2: 1,3 E2: 3,5 G1: 2,9 I3: 2,5 A4: 1,2 B4: 1,2 A5: 5,9 B5: 5,9 F8: 1,8 E9: 3,8 G7: 3,8 I8: 1,6 H9: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A4,B4: 1.. / A4 = 1 => 17 pairs (_) / B4 = 1 => 17 pairs (_) D2,H2: 1.. / D2 = 1 => 0 pairs (X) / H2 = 1 => 22 pairs (_) A2,B2: 2.. / A2 = 2 => 17 pairs (_) / B2 = 2 => 17 pairs (_) F1,F3: 2.. / F1 = 2 => 0 pairs (*) / F3 = 2 => 0 pairs (X) A4,B4: 2.. / A4 = 2 => 17 pairs (_) / B4 = 2 => 17 pairs (_) G9,I9: 2.. / G9 = 2 => 0 pairs (X) / I9 = 2 => 0 pairs (_) A2,A4: 2.. / A2 = 2 => 17 pairs (_) / A4 = 2 => 17 pairs (_) B2,B4: 2.. / B2 = 2 => 17 pairs (_) / B4 = 2 => 17 pairs (_) D9,E9: 3.. / D9 = 3 => 0 pairs (X) / E9 = 3 => 22 pairs (_) G7,H7: 3.. / G7 = 3 => 0 pairs (*) / H7 = 3 => 0 pairs (X) E2,E9: 3.. / E2 = 3 => 0 pairs (X) / E9 = 3 => 22 pairs (_) G3,G7: 3.. / G3 = 3 => 0 pairs (X) / G7 = 3 => 0 pairs (_) B1,B3: 4.. / B1 = 4 => 0 pairs (X) / B3 = 4 => 20 pairs (_) H1,H3: 4.. / H1 = 4 => 20 pairs (_) / H3 = 4 => 0 pairs (X) B1,H1: 4.. / B1 = 4 => 0 pairs (X) / H1 = 4 => 20 pairs (_) B3,H3: 4.. / B3 = 4 => 20 pairs (_) / H3 = 4 => 0 pairs (X) E1,E2: 5.. / E1 = 5 => 0 pairs (X) / E2 = 5 => 22 pairs (_) A5,B5: 5.. / A5 = 5 => 22 pairs (_) / B5 = 5 => 0 pairs (X) H7,I7: 5.. / H7 = 5 => 0 pairs (*) / I7 = 5 => 0 pairs (X) D3,F3: 7.. / D3 = 7 => 0 pairs (X) / F3 = 7 => 0 pairs (_) F7,D9: 7.. / F7 = 7 => 0 pairs (X) / D9 = 7 => 0 pairs (_) I7,I9: 7.. / I7 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) F7,I7: 7.. / F7 = 7 => 0 pairs (X) / I7 = 7 => 0 pairs (_) D9,I9: 7.. / D9 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) D3,D9: 7.. / D3 = 7 => 0 pairs (X) / D9 = 7 => 0 pairs (_) F3,F7: 7.. / F3 = 7 => 0 pairs (*) / F7 = 7 => 0 pairs (X) G7,G9: 8.. / G7 = 8 => 0 pairs (X) / G9 = 8 => 0 pairs (_) A8,F8: 8.. / A8 = 8 => 0 pairs (X) / F8 = 8 => 22 pairs (_) E1,E9: 8.. / E1 = 8 => 22 pairs (_) / E9 = 8 => 0 pairs (X) D1,D3: 9.. / D1 = 9 => 0 pairs (X) / D3 = 9 => 0 pairs (_) A5,B5: 9.. / A5 = 9 => 0 pairs (X) / B5 = 9 => 22 pairs (_) A8,B9: 9.. / A8 = 9 => 22 pairs (_) / B9 = 9 => 0 pairs (X) A8,H8: 9.. / A8 = 9 => 22 pairs (_) / H8 = 9 => 0 pairs (X) A5,A8: 9.. / A5 = 9 => 0 pairs (X) / A8 = 9 => 22 pairs (_) B5,B9: 9.. / B5 = 9 => 22 pairs (_) / B9 = 9 => 0 pairs (X) * DURATION: 0:00:43.119976 START: 01:56:16.867990 END: 01:56:59.987966 2019-05-01 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A5,B4,B5,D1,D2,E1,E2,E9,F8,G1,G7,H9,I3,I8) * 3.7........9..47.8..1.6......6849573..8673124734215689..249.....7352.4..4.5..6... * PAIR A3: 5,8 BLK 1 B1: 5,8,4,6 # reduction candidate for 5,8 B1: 5,8 # 20 pairs B3: 5,8,4 # reduction candidate for 5,8 B3: 5,8 => CTR * 347.829.5..9.547.8..1967342..6849573..8673124734215689..249.8.7.7352.4..4.57362.1 B3: 4 # 20 pairs * PAIR D1: 1,9 ROW 1 H1: 1,9,4,5,6 # reduction candidate for 1,9 H1: 1,9 => CTR * 347.58..6..9..47.8..1.6..4...6849573..8673124734215689..249.....7352.4.14.5..6.9. H1: 4,5,6 # 16 pairs * PAIR E1: 5,8 ROW 1 B1: 5,8,4,6 # reduction candidate for 5,8 B1: 5,8 # 20 pairs B1: 4,6 # 18 pairs * PAIR D2: 1,3 ROW 2 H2: 1,3,5,6 # reduction candidate for 1,3 H2: 5,6 => CTR * 3.795.2....91347.8..1762..5..6849573..8673124734215689..24978...7352.4..4.5386..7 H2: 1,3 # 22 pairs * PAIR D2: 1,3 COL D D9: 1,3,7 # reduction candidate for 1,3 D9: 1,3 => CTR * 3.79..2....9..47.8..1762..5..6849573..8673124734215689..2497.5..7352.4..4.5..6..7 D9: 7 => SOLVED * 357182946269354718841967235126849573598673124734215689682491357973528461415736892 * PAIR E2: 3,5 ROW 2 H2: 3,5,1,6 # reduction candidate for 3,5 H2: 3,5 => CTR * 3.79..2....91.47.8..1.62..5..6849573..8673124734215689..2497.5..7352.4..4.5..6... H2: 1,6 # 24 pairs * PAIR G1: 2,9 BLK 3 G3: 2,9,3 # reduction candidate for 2,9 G3: 2,9 => SOLVED * 357182946269354718841967235126849573598673124734215689682491357973528461415736892 G3: 3 => CTR * 3.7........9..47.8..176.392..6849573..8673124734215689..249.835.7352.4..4.5..6..7 * PAIR G1: 2,9 COL G G9: 2,9,8 # reduction candidate for 2,9 G9: 2,9 => CTR * 3.7........9..47.8..176.392..6849573..8673124734215689..249.835.7352.4..4.5..6..7 G9: 8 => SOLVED * 357182946269354718841967235126849573598673124734215689682491357973528461415736892 * PAIR I3: 2,5 BLK 3 I1: 2,5,1,6 # reduction candidate for 2,5 I1: 2,5 => CTR * 3.7........9..47.8..1.6......6849573..8673124734215689..249.....7352.4..4.5..6... I1: 1,6 # 19 pairs * PAIR F8: 1,8 BLK 8 F7: 1,8,7 # reduction candidate for 1,8 F7: 1,8 => SOLVED * 357182946269354718841967235126849573598673124734215689682491357973528461415736892 F7: 7 => CTR * 3.79.......9..47.8..176......6849573..8673124734215689..2497....7352.4..4.5..62.7 * PAIR F8: 1,8 ROW 8 A8: 1,8,6,9 # reduction candidate for 1,8 A8: 1,8 => CTR * 3.79..2.1..91.47.8..1.629.5..6849573958673124734215689..2497....7352.496495..6.1. A8: 6,9 # 22 pairs * PAIR F8: 1,8 COL F F1: 1,8,2 # reduction candidate for 1,8 F1: 1,8 => CTR * 3.7.....2..9..47.8841762..5..6849573..8673124734215689..249735..735284..4.51.6..7 F1: 2 => SOLVED * 357182946269354718841967235126849573598673124734215689682491357973528461415736892 * PAIR I8: 1,6 BLK 9 H7: 1,6,3,5 # reduction candidate for 1,6 H7: 1,6 => CTR * 3.7........9..47.8..1.6......6849573..8673124734215689..249.3.5.7352.4..4.5..68.. H7: 3,5 # 17 pairs I7: 1,6,5,7 # reduction candidate for 1,6 I7: 1,6 => CTR * 3.7........9..47.8..176......6849573..8673124734215689..249735..7352.4..4.5..6..7 I7: 5,7 # 17 pairs H8: 1,6,9 # reduction candidate for 1,6 H8: 1,6 # 22 pairs * PAIR I8: 1,6 ROW 8 A8: 1,6,8,9 # reduction candidate for 1,6 A8: 1,6 => CTR * 3.7.8...1..91547385.1.6......6849573958673124734215689..249.....7352849.495.36812 A8: 8,9 # 17 pairs * PAIR I8: 1,6 COL I I1: 1,6,2,5 # reduction candidate for 1,6 I1: 2,5 => CTR * 3.7........9..47.8..1.6......6849573..8673124734215689..249.....7352.4..4.5..6... I1: 1,6 # 19 pairs * PAIR H9: 1,9 BLK 9 H8: 1,9,6 # reduction candidate for 1,9 H8: 1,9 => CTR * 3.79..2.1..91.47.8..1.629.5..6849573..8673124734215689..2497....7352.4.64.5..6... H8: 6 # 22 pairs * PAIR H9: 1,9 ROW 9 B9: 1,9,8 # reduction candidate for 1,9 B9: 8 => CTR * 3.7.8......93547188.1762.....6849573598673124734215689..249.8359735284..485.36..7 B9: 1,9 # 21 pairs * PAIR H9: 1,9 COL H H1: 1,9,4,5,6 # reduction candidate for 1,9 H1: 1,9 => CTR * 347.58..6..9..47.8..1.6..4...6849573..8673124734215689..249.....7352.4.14.5..6.9. H1: 4,5,6 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060820-absurd-base-pr-000.dot * REASONING * DIS # B3: 5,8 => CTR => B3: 4 * DIS # H1: 1,9 => CTR => H1: 4,5,6 * DIS # H2: 5,6 => CTR => H2: 1,3 * DIS # D9: 1,3 => CTR => D9: 7 * PRF # D9: 7 => SOL * DIS # H2: 3,5 => CTR => H2: 1,6 * PRF # G3: 2,9 => SOL * DIS # G3: 3 => CTR => G3: 2,9 * DIS # G9: 2,9 => CTR => G9: 8 * PRF # G9: 8 => SOL * DIS # I1: 2,5 => CTR => I1: 1,6 * PRF # F7: 1,8 => SOL * DIS # F7: 7 => CTR => F7: 1,8 * DIS # A8: 1,8 => CTR => A8: 6,9 * DIS # F1: 1,8 => CTR => F1: 2 * PRF # F1: 2 => SOL * DIS # H7: 1,6 => CTR => H7: 3,5 * DIS # I7: 1,6 => CTR => I7: 5,7 * DIS # A8: 1,6 => CTR => A8: 8,9 * DIS # I1: 2,5 => CTR => I1: 1,6 * DIS # H8: 1,9 => CTR => H8: 6 * DIS # B9: 8 => CTR => B9: 1,9 * DIS # H1: 1,9 => CTR => H1: 4,5,6 * CNT 23 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A5,B4,B5,D1,D2,E1,E2,E9,F8,G1,G7,H9,I3,I8) * 3.7........9..47.8..1.6......6849573..8673124734215689..249.....7352.4..4.5..6... * PAIR A3: 5,8 BLK 1 B1: 5,8,4,6 # reduction candidate for 5,8 B1: 5,8 # 20 pairs B3: 5,8,4 # reduction candidate for 5,8 B3: 5,8 => CTR * 347.829.5..9.547.8..1967342..6849573..8673124734215689..249.8.7.7352.4..4.57362.1 * PAIR RESTART * PAIR G1: 2,9 BLK 3 G3: 2,9,3 # reduction candidate for 2,9 G3: 2,9 => SOLVED * 357182946269354718841967235126849573598673124734215689682491357973528461415736892 * DURATION: 0:00:03.650853 START: 01:57:26.212021 END: 01:57:29.862874 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060820-absurd-base-pr-001.dot * REASONING * DIS # B3: 5,8 => CTR => B3: 4 * PRF B3: 4 # G3: 2,9 => SOL * STA B3: 4 + G3: 2,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060820, absurd
Solution
position: 357182946269354718841967235126849573598673124734215689682491357973528461415736892 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: 5,8 => UNS * DIS # B3: 5,8 => CTR => B3: 4 * INC # B3: 4 => UNS * DIS # H1: 1,9 => CTR => H1: 4,5,6 * INC # H1: 4,5,6 => UNS * INC # B1: 5,8 => UNS * INC # B1: 4,6 => UNS * INC # H2: 1,3 => UNS * DIS # H2: 5,6 => CTR => H2: 1,3 * DIS # D9: 1,3 => CTR => D9: 7 * PRF # D9: 7 => SOL * DIS # H2: 3,5 => CTR => H2: 1,6 * INC # H2: 1,6 => UNS * PRF # G3: 2,9 => SOL * DIS # G3: 3 => CTR => G3: 2,9 * DIS # G9: 2,9 => CTR => G9: 8 * PRF # G9: 8 => SOL * DIS # I1: 2,5 => CTR => I1: 1,6 * INC # I1: 1,6 => UNS * PRF # F7: 1,8 => SOL * DIS # F7: 7 => CTR => F7: 1,8 * DIS # A8: 1,8 => CTR => A8: 6,9 * INC # A8: 6,9 => UNS * DIS # F1: 1,8 => CTR => F1: 2 * PRF # F1: 2 => SOL * DIS # H7: 1,6 => CTR => H7: 3,5 * INC # H7: 3,5 => UNS * DIS # I7: 1,6 => CTR => I7: 5,7 * INC # I7: 5,7 => UNS * INC # H8: 1,6 => UNS * DIS # A8: 1,6 => CTR => A8: 8,9 * INC # A8: 8,9 => UNS * INC # I1: 1,6 => UNS * DIS # I1: 2,5 => CTR => I1: 1,6 * DIS # H8: 1,9 => CTR => H8: 6 * INC # H8: 6 => UNS * INC # B9: 1,9 => UNS * DIS # B9: 8 => CTR => B9: 1,9 * DIS # H1: 1,9 => CTR => H1: 4,5,6 * INC # H1: 4,5,6 => UNS * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 5,8 => UNS * DIS # B3: 5,8 => CTR => B3: 4 * PRF B3: 4 # G3: 2,9 => SOL * STA B3: 4 + G3: 2,9 * CNT 3 HDP CHAINS / 3 HYP OPENED