Analysis of zz-www.sudokuoftheday.co.uk-20060719-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006
level: medium
position: ....1........9258...8..549.54.3..6.....6..3.8.......4..7..6.1..1..5....2..91.7... initial
Autosolve
position: ...816......49258...873549.54.3..6.....6.43.8.....1.4..7..6.1..1..5....2..91.78.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C7: 4,5 => CTR => C7: 2,3 * PRF # C7: 2,3 => SOL * PRF # H1: 3 => SOL * DIS # G6: 9 => CTR => G6: 2,7 * DIS # H1: 2 => CTR => H1: 3,7 * DIS # B6: 3,6 => CTR => B6: 8 * DIS # C2: 3,6 => CTR => C2: 1,7 * DIS # C8: 3,6 => CTR => C8: 4 * PRF # C8: 4 => SOL * PRF # G6: 7 => SOL * DIS # I6: 7,9 => CTR => I6: 5 * DIS # I7: 3,5 => CTR => I7: 4,9 * DIS # H9: 3,5 => CTR => H9: 6 * DIS # G6: 2 => CTR => G6: 7,9 * CNT 14 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 # C7: 4,5 => CTR => C7: 2,3 * PRF C7: 2,3 => SOL * STA C7: 2,3 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....1........9258...8..549.54.3..6.....6..3.8.......4..7..6.1..1..5....2..91.7... | initial |
| ...816......49258...873549.54.3..6.....6.43.8.....1.4..7..6.1..1..5....2..91.78.. | autosolve |
| 495816237731492586628735491542378619917654328386921745873269154164583972259147863 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) A1: 4,9 B1: 5,9 C1: 4,5 A3: 2,6 G1: 2,7 I1: 3,7 I2: 1,6 I3: 1,6 C6: 3,6 F4: 8,9 D6: 2,9 I4: 7,9 D7: 2,9 E8: 4,8 E9: 2,4 H7: 3,5 G8: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I2,I3: 1.. / I2 = 1 => 19 pairs (_) / I3 = 1 => 18 pairs (_) H4,H5: 1.. / H4 = 1 => 18 pairs (_) / H5 = 1 => 22 pairs (_) B3,I3: 1.. / B3 = 1 => 19 pairs (_) / I3 = 1 => 18 pairs (_) C4,H4: 1.. / C4 = 1 => 22 pairs (_) / H4 = 1 => 18 pairs (_) A3,B3: 2.. / A3 = 2 => 21 pairs (_) / B3 = 2 => 18 pairs (_) G1,H1: 2.. / G1 = 2 => 24 pairs (_) / H1 = 2 => 0 pairs (X) D7,E9: 2.. / D7 = 2 => 0 pairs (*) / E9 = 2 => 0 pairs (X) D6,D7: 2.. / D6 = 2 => 0 pairs (X) / D7 = 2 => 0 pairs (_) G1,G6: 2.. / G1 = 2 => 24 pairs (_) / G6 = 2 => 0 pairs (X) H1,I1: 3.. / H1 = 3 => 0 pairs (*) / I1 = 3 => 0 pairs (X) F7,F8: 3.. / F7 = 3 => 22 pairs (_) / F8 = 3 => 22 pairs (_) A1,C1: 4.. / A1 = 4 => 17 pairs (_) / C1 = 4 => 0 pairs (X) E8,E9: 4.. / E8 = 4 => 0 pairs (X) / E9 = 4 => 0 pairs (_) I7,I9: 4.. / I7 = 4 => 21 pairs (_) / I9 = 4 => 0 pairs (X) C8,E8: 4.. / C8 = 4 => 0 pairs (*) / E8 = 4 => 0 pairs (X) B1,C1: 5.. / B1 = 5 => 0 pairs (X) / C1 = 5 => 17 pairs (_) E5,E6: 5.. / E5 = 5 => 19 pairs (_) / E6 = 5 => 0 pairs (X) H5,I6: 5.. / H5 = 5 => 0 pairs (X) / I6 = 5 => 19 pairs (_) C7,B9: 5.. / C7 = 5 => 0 pairs (X) / B9 = 5 => 17 pairs (_) E5,H5: 5.. / E5 = 5 => 19 pairs (_) / H5 = 5 => 0 pairs (X) E6,I6: 5.. / E6 = 5 => 0 pairs (X) / I6 = 5 => 19 pairs (_) B1,B9: 5.. / B1 = 5 => 0 pairs (X) / B9 = 5 => 17 pairs (_) C1,C7: 5.. / C1 = 5 => 17 pairs (_) / C7 = 5 => 0 pairs (X) I2,I3: 6.. / I2 = 6 => 18 pairs (_) / I3 = 6 => 19 pairs (_) H8,H9: 6.. / H8 = 6 => 0 pairs (X) / H9 = 6 => 18 pairs (_) A2,C2: 7.. / A2 = 7 => 18 pairs (_) / C2 = 7 => 0 pairs (X) G8,H8: 7.. / G8 = 7 => 0 pairs (X) / H8 = 7 => 20 pairs (_) A2,A5: 7.. / A2 = 7 => 18 pairs (_) / A5 = 7 => 0 pairs (X) A6,B6: 8.. / A6 = 8 => 0 pairs (X) / B6 = 8 => 20 pairs (_) E4,F4: 8.. / E4 = 8 => 0 pairs (X) / F4 = 8 => 0 pairs (_) A7,B8: 8.. / A7 = 8 => 20 pairs (_) / B8 = 8 => 0 pairs (X) A7,F7: 8.. / A7 = 8 => 20 pairs (_) / F7 = 8 => 0 pairs (X) A6,A7: 8.. / A6 = 8 => 0 pairs (X) / A7 = 8 => 20 pairs (_) B6,B8: 8.. / B6 = 8 => 20 pairs (_) / B8 = 8 => 0 pairs (X) E4,E8: 8.. / E4 = 8 => 0 pairs (X) / E8 = 8 => 0 pairs (_) A1,B1: 9.. / A1 = 9 => 0 pairs (X) / B1 = 9 => 17 pairs (_) A5,B5: 9.. / A5 = 9 => 17 pairs (_) / B5 = 9 => 0 pairs (X) F4,D6: 9.. / F4 = 9 => 0 pairs (X) / D6 = 9 => 0 pairs (_) I7,G8: 9.. / I7 = 9 => 0 pairs (X) / G8 = 9 => 20 pairs (_) F4,I4: 9.. / F4 = 9 => 0 pairs (X) / I4 = 9 => 0 pairs (_) F8,G8: 9.. / F8 = 9 => 0 pairs (X) / G8 = 9 => 20 pairs (_) A1,A5: 9.. / A1 = 9 => 0 pairs (X) / A5 = 9 => 17 pairs (_) B1,B5: 9.. / B1 = 9 => 17 pairs (_) / B5 = 9 => 0 pairs (X) D6,D7: 9.. / D6 = 9 => 0 pairs (*) / D7 = 9 => 0 pairs (X) G6,G8: 9.. / G6 = 9 => 0 pairs (X) / G8 = 9 => 20 pairs (_) * DURATION: 0:00:58.434119 START: 00:48:24.774506 END: 00:49:23.208625 2019-05-01 * CP COUNT: (45) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B1,C1,C6,D6,D7,E8,E9,F4,G1,G8,H7,I1,I2,I3,I4) * ...816......49258...873549.54.3..6.....6.43.8.....1.4..7..6.1..1..5....2..91.78.. * PAIR C1: 4,5 COL C C7: 4,5,2,3 # reduction candidate for 4,5 C7: 4,5 => CTR * ...816......49258..2873549154.3896.7...6.43.8...27194527.9681..18.543762..91278.. C7: 2,3 => SOLVED * 495816237731492586628735491542378619917654328386921745873269154164583972259147863 * PAIR A3: 2,6 BLK 1 B3: 2,6,1 # reduction candidate for 2,6 B3: 1 # 19 pairs B3: 2,6 # 18 pairs * PAIR A3: 2,6 COL A A9: 2,6,3,4 # reduction candidate for 2,6 A9: 2,6 # 21 pairs A9: 3,4 # 18 pairs * PAIR G1: 2,7 BLK 3 H1: 2,7,3 # reduction candidate for 2,7 H1: 3 => SOLVED * 495816237731492586628735491542378619917654328386921745873269154164583972259147863 H1: 2,7 # 22 pairs * PAIR G1: 2,7 COL G G6: 2,7,9 # reduction candidate for 2,7 G6: 9 => CTR * ...8162.....49258...873549.54.3..6.....6.43.8.....194..7.96.1..1..5..7.2..91278.. G6: 2,7 # 20 pairs * PAIR I1: 3,7 BLK 3 H1: 3,7,2 # reduction candidate for 3,7 H1: 2 => CTR * .54816723...49258...873549.54.3..61..916.4358...95124747.26.1..1..5..972..9147865 H1: 3,7 # 24 pairs * PAIR I2: 1,6 ROW 2 B2: 1,6,3 # reduction candidate for 1,6 B2: 1,6 # 21 pairs C2: 1,6,3,7 # reduction candidate for 1,6 C2: 1,6 # 23 pairs * PAIR I3: 1,6 ROW 3 B3: 1,6,2 # reduction candidate for 1,6 B3: 1,6 # 21 pairs B3: 2 # 18 pairs * PAIR C6: 3,6 BLK 4 A6: 3,6,8 # reduction candidate for 3,6 A6: 3,6 # 20 pairs B6: 3,6,8 # reduction candidate for 3,6 B6: 3,6 => CTR * ...816......49258...873549.54.3896.7...6.43.88..2.1.4..7..681..18.543972..912786. B6: 8 # 20 pairs * PAIR C6: 3,6 COL C C2: 3,6,1,7 # reduction candidate for 3,6 C2: 3,6 => CTR * ...816...7..49258...873549.54.3..6.....6.43.8.....1.4..7296.1..1.458...2..91.78.. C2: 1,7 # 18 pairs C8: 3,6,4 # reduction candidate for 3,6 C8: 3,6 => CTR * ...816......49258...873549.54.3896.7...6.43.8...271945.7.96.1..1..54.7.2..91278.. C8: 4 => SOLVED * 495816237731492586628735491542378619917654328386921745873269154164583972259147863 * PAIR F4: 8,9 COL F F7: 8,9,3 # reduction candidate for 8,9 F7: 8,9 # 22 pairs F8: 8,9,3 # reduction candidate for 8,9 F8: 8,9 # 22 pairs * PAIR D6: 2,9 ROW 6 G6: 2,9,7 # reduction candidate for 2,9 G6: 7 => SOLVED * 495816237731492586628735491542378619917654328386921745873269154164583972259147863 G6: 2,9 # 20 pairs * PAIR I4: 7,9 BLK 6 G6: 7,9,2 # reduction candidate for 7,9 G6: 7,9 # 24 pairs I6: 7,9,5 # reduction candidate for 7,9 I6: 7,9 => CTR * .54816723...49258...873549.54.3.8619.916.4358.8.951247.7.26913.1..583972..9147865 I6: 5 # 19 pairs * PAIR E9: 2,4 ROW 9 A9: 2,4,3,6 # reduction candidate for 2,4 A9: 2,4 # 23 pairs A9: 3,6 # 18 pairs * PAIR H7: 3,5 BLK 9 I7: 3,5,4,9 # reduction candidate for 3,5 I7: 3,5 => CTR * .95816......49258...873549.54.3896.79.76543.8...2.1.4..7..6.1..1..54.972.59127864 I7: 4,9 # 18 pairs H9: 3,5,6 # reduction candidate for 3,5 H9: 3,5 => CTR * ...8162.....49258...873549.54.3..6.....6.43.8.....194..7.96.1..1..5..762..91278.. H9: 6 # 18 pairs I9: 3,5,4 # reduction candidate for 3,5 I9: 3,5 # 21 pairs * PAIR H7: 3,5 ROW 7 C7: 3,5,2,4 # reduction candidate for 3,5 C7: 3,5 # 28 pairs C7: 2,4 # 18 pairs * PAIR G8: 7,9 COL G G6: 7,9,2 # reduction candidate for 7,9 G6: 2 => CTR * ...816723...49258...873549.54.3..61....6.4358...951247.7.2691341.4583972..9147865 G6: 7,9 # 24 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060719-absurd-base-pr-000.dot * REASONING * DIS # C7: 4,5 => CTR => C7: 2,3 * PRF # C7: 2,3 => SOL * PRF # H1: 3 => SOL * DIS # G6: 9 => CTR => G6: 2,7 * DIS # H1: 2 => CTR => H1: 3,7 * DIS # B6: 3,6 => CTR => B6: 8 * DIS # C2: 3,6 => CTR => C2: 1,7 * DIS # C8: 3,6 => CTR => C8: 4 * PRF # C8: 4 => SOL * PRF # G6: 7 => SOL * DIS # I6: 7,9 => CTR => I6: 5 * DIS # I7: 3,5 => CTR => I7: 4,9 * DIS # H9: 3,5 => CTR => H9: 6 * DIS # G6: 2 => CTR => G6: 7,9 * CNT 14 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B1,C1,C6,D6,D7,E8,E9,F4,G1,G8,H7,I1,I2,I3,I4) * ...816......49258...873549.54.3..6.....6.43.8.....1.4..7..6.1..1..5....2..91.78.. * PAIR C1: 4,5 COL C C7: 4,5,2,3 # reduction candidate for 4,5 C7: 4,5 => CTR * ...816......49258..2873549154.3896.7...6.43.8...27194527.9681..18.543762..91278.. C7: 2,3 => SOLVED * 495816237731492586628735491542378619917654328386921745873269154164583972259147863 * DURATION: 0:00:02.574734 START: 00:49:52.098626 END: 00:49:54.673360 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060719-absurd-base-pr-001.dot * REASONING * DIS # C7: 4,5 => CTR => C7: 2,3 * PRF C7: 2,3 => SOL * STA C7: 2,3 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060719, absurd
Solution
position: 495816237731492586628735491542378619917654328386921745873269154164583972259147863 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 # C7: 4,5 => CTR => C7: 2,3 * PRF # C7: 2,3 => SOL * INC # B3: 2,6 => UNS * INC # B3: 1 => UNS * INC # A9: 2,6 => UNS * INC # A9: 3,4 => UNS * INC # H1: 2,7 => UNS * PRF # H1: 3 => SOL * INC # G6: 2,7 => UNS * DIS # G6: 9 => CTR => G6: 2,7 * INC # H1: 3,7 => UNS * DIS # H1: 2 => CTR => H1: 3,7 * INC # B2: 1,6 => UNS * INC # C2: 1,6 => UNS * INC # B3: 1,6 => UNS * INC # B3: 2 => UNS * INC # A6: 3,6 => UNS * DIS # B6: 3,6 => CTR => B6: 8 * INC # B6: 8 => UNS * DIS # C2: 3,6 => CTR => C2: 1,7 * INC # C2: 1,7 => UNS * DIS # C8: 3,6 => CTR => C8: 4 * PRF # C8: 4 => SOL * INC # F7: 8,9 => UNS * INC # F8: 8,9 => UNS * INC # G6: 2,9 => UNS * PRF # G6: 7 => SOL * INC # G6: 7,9 => UNS * DIS # I6: 7,9 => CTR => I6: 5 * INC # I6: 5 => UNS * INC # A9: 2,4 => UNS * INC # A9: 3,6 => UNS * DIS # I7: 3,5 => CTR => I7: 4,9 * INC # I7: 4,9 => UNS * DIS # H9: 3,5 => CTR => H9: 6 * INC # H9: 6 => UNS * INC # I9: 3,5 => UNS * INC # C7: 3,5 => UNS * INC # C7: 2,4 => UNS * INC # G6: 7,9 => UNS * DIS # G6: 2 => CTR => G6: 7,9 * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C7: 4,5 => CTR => C7: 2,3 * PRF C7: 2,3 => SOL * STA C7: 2,3 * CNT 2 HDP CHAINS / 1 HYP OPENED