Analysis of zz-www.sudokuoftheday.co.uk-20060407-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006
level: medium
position: 4.....6.725.6....4....1..5.8..23.5..3.........97..4..27.9.2..3....7..49.68....... initial
Autosolve
position: 4.....6.725.6..9.497641..538..23.5..3.........97..43.2749.2..3....7..49.68..4.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B8: 2 => CTR => B8: 1,3 * DIS # F2: 7,8 => CTR => F2: 3 * DIS # F1: 3,5,9 => CTR => F1: 2,8 * DIS # H1: 2 => CTR => H1: 1,8 * DIS # C2: 3 => CTR => C2: 1,8 * DIS # H1: 1 => CTR => H1: 2,8 * DIS # B5: 1,6 => CTR => B5: 2 * DIS # C5: 1,4 => CTR => C5: 2,5 * PRF # C5: 1,5 => SOL * PRF # D6: 8 => SOL * PRF # I5: 8 => SOL * PRF # F4: 1,9 => SOL * DIS # H5: 6,8 => CTR => H5: 4,7 * PRF # E6: 5 => SOL * DIS # C8: 1,5 => CTR => C8: 2,3 * PRF # I8: 1,5 => SOL * DIS # G5: 7 => CTR => G5: 1,8 * DIS # I7: 1,5 => CTR => I7: 6,8 * PRF # I8: 1,5 => SOL * DIS # D9: 1,5 => CTR => D9: 3,9 * DIS # F9: 1,5 => CTR => F9: 3,9 * CNT 21 HDP CHAINS / 55 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B8: 2 => CTR => B8: 1,3 * DIS B8: 1,3 # F2: 7,8 => CTR => F2: 3 * DIS B8: 1,3 + F2: 3 # F1: 5 => CTR => F1: 2,8 * PRF B8: 1,3 + F2: 3 + F1: 2,8 # D6: 8 => SOL * STA B8: 1,3 + F2: 3 + F1: 2,8 + D6: 8 * CNT 4 HDP CHAINS / 11 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 4.....6.725.6....4....1..5.8..23.5..3.........97..4..27.9.2..3....7..49.68....... | initial |
| 4.....6.725.6..9.497641..538..23.5..3.........97..43.2749.2..3....7..49.68..4.... | autosolve |
| 413592687258673914976418253864231579325967148197854362749125836532786491681349725 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) B1: 1,3 E2: 7,8 F3: 2,8 H2: 1,8 G3: 2,8 B4: 1,6 C4: 1,4 A6: 1,5 I4: 1,9 H6: 6,8 A8: 1,5 G7: 1,8 G9: 2,7 H9: 2,7 I9: 1,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H1,H2: 1.. / H1 = 1 => 0 pairs (X) / H2 = 1 => 16 pairs (_) C2,H2: 1.. / C2 = 1 => 0 pairs (X) / H2 = 1 => 16 pairs (_) A6,D6: 1.. / A6 = 1 => 0 pairs (*) / D6 = 1 => 0 pairs (X) A6,A8: 1.. / A6 = 1 => 0 pairs (*) / A8 = 1 => 0 pairs (X) G5,G7: 1.. / G5 = 1 => 0 pairs (*) / G7 = 1 => 0 pairs (X) F1,F3: 2.. / F1 = 2 => 26 pairs (_) / F3 = 2 => 0 pairs (X) H1,G3: 2.. / H1 = 2 => 0 pairs (X) / G3 = 2 => 26 pairs (_) B5,C5: 2.. / B5 = 2 => 16 pairs (_) / C5 = 2 => 0 pairs (X) B8,C8: 2.. / B8 = 2 => 0 pairs (X) / C8 = 2 => 16 pairs (_) G9,H9: 2.. / G9 = 2 => 0 pairs (X) / H9 = 2 => 26 pairs (_) F1,H1: 2.. / F1 = 2 => 26 pairs (_) / H1 = 2 => 0 pairs (X) F3,G3: 2.. / F3 = 2 => 0 pairs (X) / G3 = 2 => 26 pairs (_) B5,B8: 2.. / B5 = 2 => 16 pairs (_) / B8 = 2 => 0 pairs (X) C5,C8: 2.. / C5 = 2 => 0 pairs (X) / C8 = 2 => 16 pairs (_) G3,G9: 2.. / G3 = 2 => 26 pairs (_) / G9 = 2 => 0 pairs (X) H1,H9: 2.. / H1 = 2 => 0 pairs (X) / H9 = 2 => 26 pairs (_) C2,F2: 3.. / C2 = 3 => 0 pairs (X) / F2 = 3 => 19 pairs (_) B1,B8: 3.. / B1 = 3 => 0 pairs (X) / B8 = 3 => 19 pairs (_) D1,D9: 3.. / D1 = 3 => 0 pairs (X) / D9 = 3 => 19 pairs (_) C4,C5: 4.. / C4 = 4 => 15 pairs (_) / C5 = 4 => 0 pairs (X) H4,H5: 4.. / H4 = 4 => 0 pairs (X) / H5 = 4 => 15 pairs (_) C4,H4: 4.. / C4 = 4 => 15 pairs (_) / H4 = 4 => 0 pairs (X) C5,H5: 4.. / C5 = 4 => 0 pairs (X) / H5 = 4 => 15 pairs (_) C5,A6: 5.. / C5 = 5 => 0 pairs (*) / A6 = 5 => 0 pairs (X) A6,A8: 5.. / A6 = 5 => 17 pairs (_) / A8 = 5 => 0 pairs (*) B4,B5: 6.. / B4 = 6 => 16 pairs (_) / B5 = 6 => 0 pairs (X) I7,I8: 6.. / I7 = 6 => 16 pairs (_) / I8 = 6 => 17 pairs (_) E6,H6: 6.. / E6 = 6 => 0 pairs (X) / H6 = 6 => 16 pairs (_) F7,I7: 6.. / F7 = 6 => 17 pairs (_) / I7 = 6 => 16 pairs (_) E2,F2: 7.. / E2 = 7 => 15 pairs (_) / F2 = 7 => 0 pairs (X) G9,H9: 7.. / G9 = 7 => 26 pairs (_) / H9 = 7 => 0 pairs (X) F4,H4: 7.. / F4 = 7 => 20 pairs (_) / H4 = 7 => 26 pairs (_) E2,E5: 7.. / E2 = 7 => 15 pairs (_) / E5 = 7 => 0 pairs (X) G5,G9: 7.. / G5 = 7 => 0 pairs (X) / G9 = 7 => 26 pairs (_) C1,C2: 8.. / C1 = 8 => 18 pairs (_) / C2 = 8 => 19 pairs (_) F3,G3: 8.. / F3 = 8 => 26 pairs (_) / G3 = 8 => 0 pairs (X) I4,I5: 9.. / I4 = 9 => 16 pairs (_) / I5 = 9 => 0 pairs (X) D9,F9: 9.. / D9 = 9 => 0 pairs (X) / F9 = 9 => 16 pairs (_) F4,I4: 9.. / F4 = 9 => 0 pairs (X) / I4 = 9 => 16 pairs (_) E1,E5: 9.. / E1 = 9 => 15 pairs (_) / E5 = 9 => 20 pairs (_) * DURATION: 0:00:46.039146 START: 22:12:49.551754 END: 22:13:35.590900 2019-04-30 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A8,B1,B4,C4,E2,F3,G3,G7,G9,H2,H6,H9,I4,I9) * 4.....6.725.6..9.497641..538..23.5..3.........97..43.2749.2..3....7..49.68..4.... * PAIR B1: 1,3 BLK 1 C1: 1,3,8 # reduction candidate for 1,3 C1: 1,3 # 19 pairs C2: 1,3,8 # reduction candidate for 1,3 C2: 1,3 # 18 pairs * PAIR B1: 1,3 COL B B8: 1,3,2 # reduction candidate for 1,3 B8: 2 => CTR * 43....6.725.6739.497641..538.423.5.93.2...148597184362749.218361237.8495685349721 B8: 1,3 # 16 pairs * PAIR E2: 7,8 BLK 2 F2: 7,8,3 # reduction candidate for 7,8 F2: 7,8 => CTR * 418...6272536..91497641285386.23754932........97..43.2749.2.13..327..49.68..4.275 F2: 3 # 19 pairs * PAIR E2: 7,8 COL E E5: 7,8,5,6,9 # reduction candidate for 7,8 E5: 7,8 # 18 pairs E5: 5,6,9 # 15 pairs * PAIR F3: 2,8 BLK 2 F1: 2,8,3,5,9 # reduction candidate for 2,8 F1: 3,5,9 => CTR * 431...627258673914976412853814237569362...741597164382749.2.13.12578649.683941275 F1: 2,8 # 22 pairs * PAIR H2: 1,8 BLK 3 H1: 1,8,2 # reduction candidate for 1,8 H1: 2 => CTR * 431...627258673914976412853814237569362...741597164382749.2.13.12578649.683941275 H1: 1,8 # 26 pairs * PAIR H2: 1,8 ROW 2 C2: 1,8,3 # reduction candidate for 1,8 C2: 3 => CTR * 418...6272536..91497641285386.23754932........97..43.2749.2.13..327..49.68..4.275 C2: 1,8 # 19 pairs * PAIR G3: 2,8 BLK 3 H1: 2,8,1 # reduction candidate for 2,8 H1: 1 => CTR * 438..26172516739849764182538.423.5793.2.67148.97..4362749.2.83...378.49.685349721 H1: 2,8 # 16 pairs * PAIR B4: 1,6 BLK 4 B5: 1,6,2 # reduction candidate for 1,6 B5: 1,6 => CTR * 43....6.725.6739.497641..5381423.5.9362...148597184362749.21836123768495685349721 B5: 2 # 16 pairs * PAIR B4: 1,6 ROW 4 F4: 1,6,7,9 # reduction candidate for 1,6 F4: 1,6 # 26 pairs F4: 7,9 # 16 pairs * PAIR C4: 1,4 BLK 4 C5: 1,4,2,5 # reduction candidate for 1,4 C5: 1,4 => CTR * 41....6.725.6..91497641..5386123.549324...178597184362749.218361327.8495685.4.721 C5: 2,5 # 16 pairs * PAIR A6: 1,5 BLK 4 C5: 1,5,2,4 # reduction candidate for 1,5 C5: 1,5 => SOLVED * 413592687258673914976418253864231579325967148197854362749125836532786491681349725 C5: 2,4 # 18 pairs * PAIR A6: 1,5 ROW 6 D6: 1,5,8 # reduction candidate for 1,5 D6: 8 => SOLVED * 413592687258673914976418253864231579325967148197854362749125836532786491681349725 D6: 1,5 # 17 pairs * PAIR I4: 1,9 BLK 6 I5: 1,9,8 # reduction candidate for 1,9 I5: 8 => SOLVED * 413592687258673914976418253864231579325967148197854362749125836532786491681349725 I5: 1,9 # 23 pairs * PAIR I4: 1,9 ROW 4 F4: 1,9,6,7 # reduction candidate for 1,9 F4: 1,9 => SOLVED * 413592687258673914976418253864231579325967148197854362749125836532786491681349725 F4: 6,7 # 20 pairs * PAIR H6: 6,8 BLK 6 H5: 6,8,4,7 # reduction candidate for 6,8 H5: 6,8 => CTR * 4.....6.725.6..9.497641..538..23.54.3.4...7..5971.43.2749.2.13.1.27..49.685.4.... H5: 4,7 # 16 pairs * PAIR H6: 6,8 ROW 6 E6: 6,8,5 # reduction candidate for 6,8 E6: 5 => SOLVED * 413592687258673914976418253864231579325967148197854362749125836532786491681349725 E6: 6,8 # 17 pairs * PAIR A8: 1,5 BLK 7 C8: 1,5,2,3 # reduction candidate for 1,5 C8: 1,5 => CTR * 4.....6.725.6..9.497641..538..23.5..3.2....4.5971.43.2749.2..3.1257.349.683.4.... C8: 2,3 # 16 pairs C9: 1,5,3 # reduction candidate for 1,5 C9: 1,5 # 20 pairs * PAIR A8: 1,5 ROW 8 F8: 1,5,3,6,8 # reduction candidate for 1,5 F8: 1,5 # 23 pairs I8: 1,5,6,8 # reduction candidate for 1,5 I8: 1,5 => SOLVED * 413592687258673914976418253864231579325967148197854362749125836532786491681349725 I8: 6,8 # 16 pairs * PAIR G7: 1,8 BLK 9 I7: 1,8,5,6 # reduction candidate for 1,8 I7: 1,8 # 22 pairs I8: 1,8,5,6 # reduction candidate for 1,8 I8: 1,8 # 19 pairs * PAIR G7: 1,8 ROW 7 D7: 1,8,5 # reduction candidate for 1,8 D7: 1,8 # 18 pairs F7: 1,8,5,6 # reduction candidate for 1,8 F7: 1,8 # 18 pairs * PAIR G7: 1,8 COL G G5: 1,8,7 # reduction candidate for 1,8 G5: 7 => CTR * 431...627258673914976412853814237569362...741597164382749.2.13.12578649.683941275 G5: 1,8 # 26 pairs * PAIR I9: 1,5 BLK 9 I7: 1,5,6,8 # reduction candidate for 1,5 I7: 1,5 => CTR * 4...926.725.6739.497641825386.2315.93...6.1.8.97854362749.2683.5..78.49668..4.72. I7: 6,8 # 17 pairs I8: 1,5,6,8 # reduction candidate for 1,5 I8: 1,5 => SOLVED * 413592687258673914976418253864231579325967148197854362749125836532786491681349725 I8: 6,8 # 16 pairs * PAIR I9: 1,5 ROW 9 C9: 1,5,3 # reduction candidate for 1,5 C9: 1,5 # 20 pairs D9: 1,5,3,9 # reduction candidate for 1,5 D9: 1,5 => CTR * 4..3..6.72536..91497641..538..23.5..3..9......97..43.2749.2..3..327..49.68..4.... D9: 3,9 # 16 pairs F9: 1,5,3,9 # reduction candidate for 1,5 F9: 1,5 => CTR * 4..3..6.72536..91497641..538..23.5..3.........97..43.2749.2..3..327..49.68.94.... F9: 3,9 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060407-absurd-base-pr-000.dot * REASONING * DIS # B8: 2 => CTR => B8: 1,3 * DIS # F2: 7,8 => CTR => F2: 3 * DIS # F1: 3,5,9 => CTR => F1: 2,8 * DIS # H1: 2 => CTR => H1: 1,8 * DIS # C2: 3 => CTR => C2: 1,8 * DIS # H1: 1 => CTR => H1: 2,8 * DIS # B5: 1,6 => CTR => B5: 2 * DIS # C5: 1,4 => CTR => C5: 2,5 * PRF # C5: 1,5 => SOL * PRF # D6: 8 => SOL * PRF # I5: 8 => SOL * PRF # F4: 1,9 => SOL * DIS # H5: 6,8 => CTR => H5: 4,7 * PRF # E6: 5 => SOL * DIS # C8: 1,5 => CTR => C8: 2,3 * PRF # I8: 1,5 => SOL * DIS # G5: 7 => CTR => G5: 1,8 * DIS # I7: 1,5 => CTR => I7: 6,8 * PRF # I8: 1,5 => SOL * DIS # D9: 1,5 => CTR => D9: 3,9 * DIS # F9: 1,5 => CTR => F9: 3,9 * CNT 21 HDP CHAINS / 55 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A8,B1,B4,C4,E2,F3,G3,G7,G9,H2,H6,H9,I4,I9) * 4.....6.725.6..9.497641..538..23.5..3.........97..43.2749.2..3....7..49.68..4.... * PAIR B1: 1,3 BLK 1 C1: 1,3,8 # reduction candidate for 1,3 C1: 1,3 # 19 pairs C2: 1,3,8 # reduction candidate for 1,3 C2: 1,3 # 18 pairs * PAIR B1: 1,3 COL B B8: 1,3,2 # reduction candidate for 1,3 B8: 2 => CTR * 43....6.725.6739.497641..538.423.5.93.2...148597184362749.218361237.8495685349721 * PAIR RESTART * PAIR B1: 1,3 BLK 1 C1: 1,3,8 # reduction candidate for 1,3 C1: 1,3 # 16 pairs C2: 1,3,8 # reduction candidate for 1,3 C2: 1,3 # 19 pairs * PAIR E2: 7,8 BLK 2 F2: 7,8,3 # reduction candidate for 7,8 F2: 7,8 => CTR * 418...6272536..91497641285386.23754932........97..43.2749.2.13..327..49.68..4.275 * PAIR F3: 2,8 BLK 2 F1: 2,8,5 # reduction candidate for 2,8 F1: 5 => CTR * 413..562725867391497641285386.23.5.932........97..43.2749.2.13..327.149.681349275 * PAIR A6: 1,5 ROW 6 D6: 1,5,8 # reduction candidate for 1,5 D6: 8 => SOLVED * 413592687258673914976418253864231579325967148197854362749125836532786491681349725 * DURATION: 0:00:08.930144 START: 22:14:09.904751 END: 22:14:18.834895 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060407-absurd-base-pr-001.dot * REASONING * DIS # B8: 2 => CTR => B8: 1,3 * DIS B8: 1,3 # F2: 7,8 => CTR => F2: 3 * DIS B8: 1,3 + F2: 3 # F1: 5 => CTR => F1: 2,8 * PRF B8: 1,3 + F2: 3 + F1: 2,8 # D6: 8 => SOL * STA B8: 1,3 + F2: 3 + F1: 2,8 + D6: 8 * CNT 4 HDP CHAINS / 11 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060407, absurd
Solution
position: 413592687258673914976418253864231579325967148197854362749125836532786491681349725 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 # C1: 1,3 => UNS * INC # C2: 1,3 => UNS * INC # B8: 1,3 => UNS * DIS # B8: 2 => CTR => B8: 1,3 * DIS # F2: 7,8 => CTR => F2: 3 * INC # F2: 3 => UNS * INC # E5: 7,8 => UNS * INC # E5: 5,6,9 => UNS * INC # F1: 2,8 => UNS * DIS # F1: 3,5,9 => CTR => F1: 2,8 * INC # H1: 1,8 => UNS * DIS # H1: 2 => CTR => H1: 1,8 * INC # C2: 1,8 => UNS * DIS # C2: 3 => CTR => C2: 1,8 * INC # H1: 2,8 => UNS * DIS # H1: 1 => CTR => H1: 2,8 * DIS # B5: 1,6 => CTR => B5: 2 * INC # B5: 2 => UNS * INC # F4: 1,6 => UNS * INC # F4: 7,9 => UNS * DIS # C5: 1,4 => CTR => C5: 2,5 * INC # C5: 2,5 => UNS * PRF # C5: 1,5 => SOL * INC # C5: 2,4 => UNS * INC # D6: 1,5 => UNS * PRF # D6: 8 => SOL * INC # I5: 1,9 => UNS * PRF # I5: 8 => SOL * PRF # F4: 1,9 => SOL * INC # F4: 6,7 => UNS * DIS # H5: 6,8 => CTR => H5: 4,7 * INC # H5: 4,7 => UNS * INC # E6: 6,8 => UNS * PRF # E6: 5 => SOL * DIS # C8: 1,5 => CTR => C8: 2,3 * INC # C8: 2,3 => UNS * INC # C9: 1,5 => UNS * INC # F8: 1,5 => UNS * PRF # I8: 1,5 => SOL * INC # I8: 6,8 => UNS * INC # I7: 1,8 => UNS * INC # I8: 1,8 => UNS * INC # D7: 1,8 => UNS * INC # F7: 1,8 => UNS * INC # G5: 1,8 => UNS * DIS # G5: 7 => CTR => G5: 1,8 * DIS # I7: 1,5 => CTR => I7: 6,8 * INC # I7: 6,8 => UNS * PRF # I8: 1,5 => SOL * INC # I8: 6,8 => UNS * INC # C9: 1,5 => UNS * DIS # D9: 1,5 => CTR => D9: 3,9 * INC # D9: 3,9 => UNS * DIS # F9: 1,5 => CTR => F9: 3,9 * INC # F9: 3,9 => UNS * CNT 55 HDP CHAINS / 55 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 1,3 => UNS * INC # C2: 1,3 => UNS * INC # B8: 1,3 => UNS * DIS # B8: 2 => CTR => B8: 1,3 * INC B8: 1,3 # C1: 1,3 => UNS * INC B8: 1,3 # C2: 1,3 => UNS * DIS B8: 1,3 # F2: 7,8 => CTR => F2: 3 * INC B8: 1,3 + F2: 3 # F1: 2,8 => UNS * DIS B8: 1,3 + F2: 3 # F1: 5 => CTR => F1: 2,8 * INC B8: 1,3 + F2: 3 + F1: 2,8 # D6: 1,5 => UNS * PRF B8: 1,3 + F2: 3 + F1: 2,8 # D6: 8 => SOL * STA B8: 1,3 + F2: 3 + F1: 2,8 + D6: 8 * CNT 11 HDP CHAINS / 11 HYP OPENED