Analysis of zz-www.sudokuoftheday.co.uk-20060807-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: 1.9......7...6.......35...9.9.1....38..7....5.1...42...64...5....8..7.6........42 initial
Autosolve
position: 1.9.7....7...6.......35...9.9.1....38..7....5.1...42...64.1.5....8.47.61.71....42 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 2,6 => CTR => A3: 4 * DIS # C4: 2,6 => CTR => C4: 5,7 * DIS # D1: 2,8 => CTR => D1: 4 * DIS # F3: 2,8 => CTR => F3: 1 * DIS # B1: 2,8 => CTR => B1: 3,5 * DIS # H1: 2,8 => CTR => H1: 3,5 * DIS # G4: 7,8 => CTR => G4: 4,6 * DIS # H6: 7,8 => CTR => H6: 9 * DIS # H3: 7,8 => CTR => H3: 1,2 * PRF # H7: 7,8 => SOL * DIS # G5: 1,9 => CTR => G5: 4,6 * PRF # H7: 7,8 => SOL * PRF # G9: 3,9 => SOL * CNT 13 HDP CHAINS / 41 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 2,6 => CTR => A3: 4 * DIS A3: 4 # D1: 2,8 => CTR => D1: 4 * DIS A3: 4 + D1: 4 # F3: 2,8 => CTR => F3: 1 * DIS A3: 4 + D1: 4 + F3: 1 # B1: 2,8 => CTR => B1: 3,5 * DIS A3: 4 + D1: 4 + F3: 1 + B1: 3,5 # H1: 2,8 => CTR => H1: 3,5 * DIS A3: 4 + D1: 4 + F3: 1 + B1: 3,5 + H1: 3,5 # H6: 7,8 => CTR => H6: 9 * PRF A3: 4 + D1: 4 + F3: 1 + B1: 3,5 + H1: 3,5 + H6: 9 => SOL * STA A3: 4 + D1: 4 + F3: 1 + B1: 3,5 + H1: 3,5 + H6: 9 * CNT 7 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.9......7...6.......35...9.9.1....38..7....5.1...42...64...5....8..7.6........42 | initial |
| 1.9.7....7...6.......35...9.9.1....38..7....5.1...42...64.1.5....8.47.61.71....42 | autosolve |
| 159472836723968154486351729697125483842739615315684297964213578238547961571896342 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) C3: 2,6 F1: 2,8 I2: 4,8 E4: 2,8 H4: 7,8 H5: 1,9 I7: 7,8 G8: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F2,F3: 1.. / F2 = 1 => 0 pairs (X) / F3 = 1 => 9 pairs (_) G5,H5: 1.. / G5 = 1 => 0 pairs (X) / H5 = 1 => 7 pairs (_) E4,E5: 2.. / E4 = 2 => 8 pairs (_) / E5 = 2 => 13 pairs (_) A3,B3: 4.. / A3 = 4 => 9 pairs (_) / B3 = 4 => 0 pairs (X) D1,D2: 4.. / D1 = 4 => 8 pairs (_) / D2 = 4 => 0 pairs (X) I1,I2: 4.. / I1 = 4 => 0 pairs (X) / I2 = 4 => 8 pairs (_) A4,B5: 4.. / A4 = 4 => 0 pairs (X) / B5 = 4 => 9 pairs (_) G4,G5: 4.. / G4 = 4 => 9 pairs (_) / G5 = 4 => 0 pairs (X) D1,I1: 4.. / D1 = 4 => 8 pairs (_) / I1 = 4 => 0 pairs (X) D2,I2: 4.. / D2 = 4 => 0 pairs (X) / I2 = 4 => 8 pairs (_) A4,G4: 4.. / A4 = 4 => 0 pairs (X) / G4 = 4 => 9 pairs (_) B5,G5: 4.. / B5 = 4 => 9 pairs (_) / G5 = 4 => 0 pairs (X) A3,A4: 4.. / A3 = 4 => 9 pairs (_) / A4 = 4 => 0 pairs (X) B3,B5: 4.. / B3 = 4 => 0 pairs (X) / B5 = 4 => 9 pairs (_) H1,H2: 5.. / H1 = 5 => 8 pairs (_) / H2 = 5 => 14 pairs (_) F4,D6: 5.. / F4 = 5 => 8 pairs (_) / D6 = 5 => 12 pairs (_) B1,H1: 5.. / B1 = 5 => 14 pairs (_) / H1 = 5 => 8 pairs (_) F4,F9: 5.. / F4 = 5 => 8 pairs (_) / F9 = 5 => 12 pairs (_) A3,C3: 6.. / A3 = 6 => 0 pairs (X) / C3 = 6 => 9 pairs (_) G1,I1: 6.. / G1 = 6 => 20 pairs (_) / I1 = 6 => 12 pairs (_) D9,F9: 6.. / D9 = 6 => 8 pairs (_) / F9 = 6 => 19 pairs (_) D6,D9: 6.. / D6 = 6 => 19 pairs (_) / D9 = 6 => 8 pairs (_) I1,I6: 6.. / I1 = 6 => 12 pairs (_) / I6 = 6 => 20 pairs (_) G3,H3: 7.. / G3 = 7 => 8 pairs (_) / H3 = 7 => 0 pairs (X) C4,C6: 7.. / C4 = 7 => 12 pairs (_) / C6 = 7 => 9 pairs (_) H7,I7: 7.. / H7 = 7 => 0 pairs (*) / I7 = 7 => 0 pairs (X) G3,G4: 7.. / G3 = 7 => 8 pairs (_) / G4 = 7 => 0 pairs (X) I6,I7: 7.. / I6 = 7 => 0 pairs (*) / I7 = 7 => 0 pairs (X) D2,F2: 9.. / D2 = 9 => 12 pairs (_) / F2 = 9 => 10 pairs (_) * DURATION: 0:00:29.852192 START: 01:37:29.299164 END: 01:37:59.151356 2019-05-01 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C3,E4,F1,G8,H4,H5,I2,I7) * 1.9.7....7...6.......35...9.9.1....38..7....5.1...42...64.1.5....8.47.61.71....42 * PAIR C3: 2,6 BLK 1 A3: 2,6,4 # reduction candidate for 2,6 A3: 2,6 => CTR * 1.9.7....7...6.....4.35...949.1....38.6793415317584296.64.1.537.38247961.71635842 A3: 4 # 9 pairs * PAIR C3: 2,6 COL C C4: 2,6,5,7 # reduction candidate for 2,6 C4: 2,6 => CTR * 1.9.7..567.5.6..34...35..29.921....38.37....5.17.34298.64.13587.58.47.61.71.8..42 C4: 5,7 # 9 pairs C5: 2,6,3 # reduction candidate for 2,6 C5: 2,6 # 11 pairs * PAIR F1: 2,8 BLK 2 D1: 2,8,4 # reduction candidate for 2,8 D1: 2,8 => CTR * 159.7.63472346915848635172969.1.54.384273691531.9.42.6.64.1.5.7..8547.61571693842 D1: 4 # 8 pairs D2: 2,8,4,9 # reduction candidate for 2,8 D2: 2,8 # 11 pairs F2: 2,8,1,9 # reduction candidate for 2,8 F2: 2,8 # 14 pairs F3: 2,8,1 # reduction candidate for 2,8 F3: 2,8 => CTR * 139472658785961324...358..9.9.1....38..7....5.1...42.6.64819537358247961971635842 F3: 1 # 9 pairs * PAIR F1: 2,8 ROW 1 B1: 2,8,3,5 # reduction candidate for 2,8 B1: 2,8 => CTR * 1.947.3567...6.1.4...3517.9.9.18..738..729.15.17.34298.64.1.537..8.47961.71.93842 B1: 3,5 # 9 pairs H1: 2,8,3,5 # reduction candidate for 2,8 H1: 2,8 => CTR * 15947.3.67...6.154...3517.9.9.18..738..729.15.17.34298.64.1.537..8.47961.71.93842 H1: 3,5 # 9 pairs * PAIR F1: 2,8 COL F F7: 2,8,3,9 # reduction candidate for 2,8 F7: 2,8 # 14 pairs F7: 3,9 # 10 pairs * PAIR I2: 4,8 BLK 3 I1: 4,8,6 # reduction candidate for 4,8 I1: 4,8 # 20 pairs I1: 6 # 12 pairs * PAIR I2: 4,8 ROW 2 D2: 4,8,2,9 # reduction candidate for 4,8 D2: 4,8 # 12 pairs D2: 2,9 # 10 pairs * PAIR H4: 7,8 BLK 6 G4: 7,8,4,6 # reduction candidate for 7,8 G4: 7,8 => CTR * 139.7265878596132464235817949612578382.7..415.17..4296.6481.537..8.47961.716..842 G4: 4,6 # 9 pairs H6: 7,8,9 # reduction candidate for 7,8 H6: 7,8 => CTR * 1.9.7.6..7...69...4.635172969.1.54.384.7.6..5315984276.64.1.537.38547961571693842 H6: 9 # 9 pairs I6: 7,8,6 # reduction candidate for 7,8 I6: 7,8 # 12 pairs * PAIR H4: 7,8 COL H H3: 7,8,1,2 # reduction candidate for 7,8 H3: 7,8 => CTR * 1.9.7....7...6.......35...9.9.1....38..793.15317584296.64.1.537.38247961.71635842 H3: 1,2 # 9 pairs H7: 7,8,3,9 # reduction candidate for 7,8 H7: 7,8 => SOLVED * 159472836723968154486351729697125483842739615315684297964213578238547961571896342 H7: 3,9 # 14 pairs * PAIR H5: 1,9 BLK 6 G5: 1,9,4,6 # reduction candidate for 1,9 G5: 1,9 => CTR * 1.9.7.6..7...69...48635172969.1.54.384.7.6..5315984276.64.1.537.38547961571693842 G5: 4,6 # 9 pairs * PAIR I7: 7,8 BLK 9 H7: 7,8,3,9 # reduction candidate for 7,8 H7: 7,8 => SOLVED * 159472836723968154486351729697125483842739615315684297964213578238547961571896342 H7: 3,9 # 14 pairs * PAIR I7: 7,8 COL I I6: 7,8,6 # reduction candidate for 7,8 I6: 6 # 20 pairs I6: 7,8 # 12 pairs * PAIR G8: 3,9 BLK 9 H7: 3,9,7,8 # reduction candidate for 3,9 H7: 3,9 # 14 pairs G9: 3,9,8 # reduction candidate for 3,9 G9: 3,9 => SOLVED * 159472836723968154486351729697125483842739615315684297964213578238547961571896342 G9: 8 # 14 pairs * PAIR G8: 3,9 ROW 8 A8: 3,9,2,5 # reduction candidate for 3,9 A8: 3,9 # 12 pairs A8: 2,5 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060807-absurd-base-pr-000.dot * REASONING * DIS # A3: 2,6 => CTR => A3: 4 * DIS # C4: 2,6 => CTR => C4: 5,7 * DIS # D1: 2,8 => CTR => D1: 4 * DIS # F3: 2,8 => CTR => F3: 1 * DIS # B1: 2,8 => CTR => B1: 3,5 * DIS # H1: 2,8 => CTR => H1: 3,5 * DIS # G4: 7,8 => CTR => G4: 4,6 * DIS # H6: 7,8 => CTR => H6: 9 * DIS # H3: 7,8 => CTR => H3: 1,2 * PRF # H7: 7,8 => SOL * DIS # G5: 1,9 => CTR => G5: 4,6 * PRF # H7: 7,8 => SOL * PRF # G9: 3,9 => SOL * CNT 13 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C3,E4,F1,G8,H4,H5,I2,I7) * 1.9.7....7...6.......35...9.9.1....38..7....5.1...42...64.1.5....8.47.61.71....42 * PAIR C3: 2,6 BLK 1 A3: 2,6,4 # reduction candidate for 2,6 A3: 2,6 => CTR * 1.9.7....7...6.....4.35...949.1....38.6793415317584296.64.1.537.38247961.71635842 * PAIR F1: 2,8 BLK 2 D1: 2,8,4 # reduction candidate for 2,8 D1: 2,8 => CTR * 159.7.63472346915848635172969.1.54.384273691531.9.42.6.64.1.5.7..8547.61571693842 D2: 2,8,9 # reduction candidate for 2,8 D2: 2,8 # 12 pairs F2: 2,8,1,9 # reduction candidate for 2,8 F2: 2,8 # 15 pairs F3: 2,8,1 # reduction candidate for 2,8 F3: 2,8 => CTR * 1.947.6.87..9613.44.635871969.1.54.384.7.6195.1.894276.64.1.5.7..8.47.61.716...42 * PAIR F1: 2,8 ROW 1 B1: 2,8,3,5 # reduction candidate for 2,8 B1: 2,8 => CTR * 1.947.3567...6.1.44.63517.9.9.18.47384.729615.17.34298.64.1.537..8.47961.71.93842 H1: 2,8,3,5 # reduction candidate for 2,8 H1: 2,8 => CTR * 15947.3.67...6.1544.63517.9.9518647384.729615617534298.64.1.537538247961.71...842 * PAIR RESTART * PAIR H4: 7,8 BLK 6 H6: 7,8,9 # reduction candidate for 7,8 H6: 7,8 => CTR * 15947263872386915448635172969.1.54.384273691531.9.42.6.64.1.5.7..8547.61571693842 H6: 9 => SOLVED * 159472836723968154486351729697125483842739615315684297964213578238547961571896342 * DURATION: 0:00:07.774291 START: 01:38:23.457071 END: 01:38:31.231362 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060807-absurd-base-pr-001.dot * REASONING * DIS # A3: 2,6 => CTR => A3: 4 * DIS A3: 4 # D1: 2,8 => CTR => D1: 4 * DIS A3: 4 + D1: 4 # F3: 2,8 => CTR => F3: 1 * DIS A3: 4 + D1: 4 + F3: 1 # B1: 2,8 => CTR => B1: 3,5 * DIS A3: 4 + D1: 4 + F3: 1 + B1: 3,5 # H1: 2,8 => CTR => H1: 3,5 * DIS A3: 4 + D1: 4 + F3: 1 + B1: 3,5 + H1: 3,5 # H6: 7,8 => CTR => H6: 9 * PRF A3: 4 + D1: 4 + F3: 1 + B1: 3,5 + H1: 3,5 + H6: 9 => SOL * STA A3: 4 + D1: 4 + F3: 1 + B1: 3,5 + H1: 3,5 + H6: 9 * CNT 7 HDP CHAINS / 8 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060807, absurd
Solution
position: 159472836723968154486351729697125483842739615315684297964213578238547961571896342 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 # A3: 2,6 => CTR => A3: 4 * INC # A3: 4 => UNS * DIS # C4: 2,6 => CTR => C4: 5,7 * INC # C4: 5,7 => UNS * INC # C5: 2,6 => UNS * DIS # D1: 2,8 => CTR => D1: 4 * INC # D1: 4 => UNS * INC # D2: 2,8 => UNS * INC # F2: 2,8 => UNS * DIS # F3: 2,8 => CTR => F3: 1 * INC # F3: 1 => UNS * DIS # B1: 2,8 => CTR => B1: 3,5 * INC # B1: 3,5 => UNS * DIS # H1: 2,8 => CTR => H1: 3,5 * INC # H1: 3,5 => UNS * INC # F7: 2,8 => UNS * INC # F7: 3,9 => UNS * INC # I1: 4,8 => UNS * INC # I1: 6 => UNS * INC # D2: 4,8 => UNS * INC # D2: 2,9 => UNS * DIS # G4: 7,8 => CTR => G4: 4,6 * INC # G4: 4,6 => UNS * DIS # H6: 7,8 => CTR => H6: 9 * INC # H6: 9 => UNS * INC # I6: 7,8 => UNS * DIS # H3: 7,8 => CTR => H3: 1,2 * INC # H3: 1,2 => UNS * PRF # H7: 7,8 => SOL * INC # H7: 3,9 => UNS * DIS # G5: 1,9 => CTR => G5: 4,6 * INC # G5: 4,6 => UNS * PRF # H7: 7,8 => SOL * INC # H7: 3,9 => UNS * INC # I6: 7,8 => UNS * INC # I6: 6 => UNS * INC # H7: 3,9 => UNS * PRF # G9: 3,9 => SOL * INC # G9: 8 => UNS * INC # A8: 3,9 => UNS * INC # A8: 2,5 => UNS * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A3: 2,6 => CTR => A3: 4 * DIS A3: 4 # D1: 2,8 => CTR => D1: 4 * INC A3: 4 + D1: 4 # D2: 2,8 => UNS * INC A3: 4 + D1: 4 # F2: 2,8 => UNS * DIS A3: 4 + D1: 4 # F3: 2,8 => CTR => F3: 1 * DIS A3: 4 + D1: 4 + F3: 1 # B1: 2,8 => CTR => B1: 3,5 * DIS A3: 4 + D1: 4 + F3: 1 + B1: 3,5 # H1: 2,8 => CTR => H1: 3,5 * DIS A3: 4 + D1: 4 + F3: 1 + B1: 3,5 + H1: 3,5 # H6: 7,8 => CTR => H6: 9 * PRF A3: 4 + D1: 4 + F3: 1 + B1: 3,5 + H1: 3,5 + H6: 9 => SOL * STA A3: 4 + D1: 4 + F3: 1 + B1: 3,5 + H1: 3,5 + H6: 9 * CNT 9 HDP CHAINS / 8 HYP OPENED