Analysis of zz-www.sudokuoftheday.co.uk-20190415-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019
level: medium
position: 736..1...914...7.5..5....1......85.....4.78.1...39........8.3....17..4...9.2...8. initial
Autosolve
position: 736541928914862735..5973614...6185.3...4278.11.83952.....18.3....17..4...9.2..18. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B8: 5,6 => CTR => B8: 2,8 * PRF # A5: 5,6 => SOL * DIS # A5: 3 => CTR => A5: 5,6 * PRF # B7: 5,6 => SOL * DIS # B8: 5,6 => CTR => B8: 2,8 * PRF # H6: 6,7 => SOL * PRF # B6: 4 => SOL * DIS # B7: 2,7 => CTR => B7: 4,5,6 * DIS # C4: 2,7 => CTR => C4: 9 * PRF # C4: 9 => SOL * DIS # A8: 3,5 => CTR => A8: 2,6,8 * DIS # F7: 4 => CTR => F7: 6,9 * PRF # A9: 3,5 => SOL * DIS # A9: 4,6 => CTR => A9: 3,5 * DIS # F7: 9 => CTR => F7: 4,6 * DIS # A9: 4,6 => CTR => A9: 3,5 * PRF # A9: 3,5 => SOL * DIS # H7: 5,6 => CTR => H7: 7 * PRF # H7: 7 => SOL * DIS # B8: 5,6 => CTR => B8: 2,8 * DIS # H7: 5 => CTR => H7: 6,7 * CNT 21 HDP CHAINS / 39 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B8: 5,6 => CTR => B8: 2,8 * PRF B8: 2,8 # A5: 5,6 => SOL * STA B8: 2,8 + A5: 5,6 * CNT 2 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 736..1...914...7.5..5....1......85.....4.78.1...39........8.3....17..4...9.2...8. | initial |
| 736541928914862735..5973614...6185.3...4278.11.83952.....18.3....17..4...9.2..18. | autosolve |
| 736541928914862735825973614279618543563427891148395267452186379681739452397254186 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) A3: 2,8 B3: 2,8 A4: 2,4 B5: 5,6 C5: 3,9 H5: 6,9 I6: 6,7 C7: 2,7 C9: 3,7 E8: 3,5 F8: 6,9 E9: 3,5 F9: 4,6 I7: 2,9 H8: 5,6 I8: 2,9 I9: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A3,B3: 2.. / A3 = 2 => 18 pairs (_) / B3 = 2 => 16 pairs (_) I7,I8: 2.. / I7 = 2 => 0 pairs (X) / I8 = 2 => 15 pairs (_) C4,C7: 2.. / C4 = 2 => 0 pairs (X) / C7 = 2 => 15 pairs (_) A5,C5: 3.. / A5 = 3 => 0 pairs (X) / C5 = 3 => 0 pairs (_) E8,E9: 3.. / E8 = 3 => 15 pairs (_) / E9 = 3 => 0 pairs (X) A8,E8: 3.. / A8 = 3 => 0 pairs (X) / E8 = 3 => 15 pairs (_) C5,C9: 3.. / C5 = 3 => 0 pairs (*) / C9 = 3 => 0 pairs (X) H4,H6: 4.. / H4 = 4 => 0 pairs (*) / H6 = 4 => 0 pairs (X) F7,F9: 4.. / F7 = 4 => 0 pairs (X) / F9 = 4 => 17 pairs (_) B6,H6: 4.. / B6 = 4 => 0 pairs (*) / H6 = 4 => 0 pairs (X) A9,F9: 4.. / A9 = 4 => 0 pairs (X) / F9 = 4 => 17 pairs (_) A5,B5: 5.. / A5 = 5 => 0 pairs (*) / B5 = 5 => 0 pairs (X) E8,E9: 5.. / E8 = 5 => 0 pairs (X) / E9 = 5 => 15 pairs (_) H7,H8: 5.. / H7 = 5 => 0 pairs (X) / H8 = 5 => 15 pairs (_) A9,E9: 5.. / A9 = 5 => 0 pairs (X) / E9 = 5 => 15 pairs (_) I6,I9: 6.. / I6 = 6 => 0 pairs (X) / I9 = 6 => 0 pairs (_) H7,I9: 7.. / H7 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) C9,I9: 7.. / C9 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) I6,I9: 7.. / I6 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) A3,B3: 8.. / A3 = 8 => 16 pairs (_) / B3 = 8 => 18 pairs (_) A8,B8: 8.. / A8 = 8 => 18 pairs (_) / B8 = 8 => 16 pairs (_) A3,A8: 8.. / A3 = 8 => 16 pairs (_) / A8 = 8 => 18 pairs (_) B3,B8: 8.. / B3 = 8 => 18 pairs (_) / B8 = 8 => 16 pairs (_) C4,C5: 9.. / C4 = 9 => 0 pairs (*) / C5 = 9 => 0 pairs (X) H4,H5: 9.. / H4 = 9 => 0 pairs (X) / H5 = 9 => 0 pairs (_) F7,F8: 9.. / F7 = 9 => 0 pairs (X) / F8 = 9 => 15 pairs (_) I7,I8: 9.. / I7 = 9 => 15 pairs (_) / I8 = 9 => 0 pairs (X) C4,H4: 9.. / C4 = 9 => 0 pairs (*) / H4 = 9 => 0 pairs (X) C5,H5: 9.. / C5 = 9 => 0 pairs (X) / H5 = 9 => 0 pairs (_) F7,I7: 9.. / F7 = 9 => 0 pairs (X) / I7 = 9 => 15 pairs (_) F8,I8: 9.. / F8 = 9 => 15 pairs (_) / I8 = 9 => 0 pairs (X) * DURATION: 0:00:39.443373 START: 05:18:55.271902 END: 05:19:34.715275 2019-05-01 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B3,B5,C5,C7,C9,E8,E9,F8,F9,H5,H8,I6,I7,I8,I9) * 736541928914862735..5973614...6185.3...4278.11.83952.....18.3....17..4...9.2..18. * PAIR A3: 2,8 COL A A8: 2,8,3,5,6 # reduction candidate for 2,8 A8: 2,8 # 21 pairs A8: 3,5,6 # 14 pairs * PAIR B3: 2,8 COL B B8: 2,8,5,6 # reduction candidate for 2,8 B8: 5,6 => CTR * 7365419289148627352859736144..6185.3...4278.11.839524..4218.3798.1739452.97254186 B8: 2,8 # 19 pairs * PAIR A4: 2,4 BLK 4 B4: 2,4,7 # reduction candidate for 2,4 B4: 7 # 20 pairs B4: 2,4 # 18 pairs * PAIR A4: 2,4 COL A A7: 2,4,5,6 # reduction candidate for 2,4 A7: 5,6 # 18 pairs A7: 2,4 # 15 pairs * PAIR B5: 5,6 BLK 4 A5: 5,6,3 # reduction candidate for 5,6 A5: 5,6 => SOLVED * 736541928914862735825973614279618543563427891148395267452186379681739452397254186 A5: 3 => CTR * 736541928914862735..5973614...6185.3359427861168395247...18.37...173.45..9.2..18. * PAIR B5: 5,6 COL B B7: 5,6,2,4,7 # reduction candidate for 5,6 B7: 5,6 => SOLVED * 736541928914862735825973614279618543563427891148395267452186379681739452397254186 B7: 2,4,7 # 17 pairs B8: 5,6,2,8 # reduction candidate for 5,6 B8: 5,6 => CTR * 7365419289148627352859736144..6185.3...4278.11.839524..4218.3798.1739452.97254186 B8: 2,8 # 19 pairs * PAIR I6: 6,7 BLK 6 H6: 6,7,4 # reduction candidate for 6,7 H6: 6,7 => SOLVED * 736541928914862735825973614279618543563427891148395267452186379681739452397254186 H6: 4 # 19 pairs * PAIR I6: 6,7 ROW 6 B6: 6,7,4 # reduction candidate for 6,7 B6: 4 => SOLVED * 736541928914862735825973614279618543563427891148395267452186379681739452397254186 B6: 6,7 # 19 pairs * PAIR C7: 2,7 BLK 7 B7: 2,7,4,5,6 # reduction candidate for 2,7 B7: 2,7 => CTR * 736541928914862735825973614247618593...4278.11.83952...7218.3.9.817.94.2.9325.187 B7: 4,5,6 # 18 pairs * PAIR C7: 2,7 COL C C4: 2,7,9 # reduction candidate for 2,7 C4: 2,7 => CTR * 736541928914862735..5973614...618593..9427861168395247...18.37...17..45..9.2..18. C4: 9 => SOLVED * 736541928914862735825973614279618543563427891148395267452186379681739452397254186 * PAIR E8: 3,5 ROW 8 A8: 3,5,2,6,8 # reduction candidate for 3,5 A8: 3,5 => CTR * 736541928914862735825973614...6185.3...4278911.83952.6...18.359.817.9462.932..187 A8: 2,6,8 # 15 pairs * PAIR F8: 6,9 BLK 8 F7: 6,9,4 # reduction candidate for 6,9 F7: 4 => CTR * 736541928914862735..59736142..6185.3...4278.11.83952.6..21843.9..17394.2493256187 F7: 6,9 # 17 pairs * PAIR E9: 3,5 ROW 9 A9: 3,5,4,6 # reduction candidate for 3,5 A9: 3,5 => SOLVED * 736541928914862735825973614279618543563427891148395267452186379681739452397254186 A9: 4,6 => CTR * 736541928914862735..5973614...6185.33594278611.83952.....18.3....173.4...9325.187 * PAIR F9: 4,6 BLK 8 F7: 4,6,9 # reduction candidate for 4,6 F7: 9 => CTR * 736541928914862735..5973614..2618593..94278611683952476..1893.2..17.6459.9.25418. F7: 4,6 # 15 pairs * PAIR F9: 4,6 ROW 9 A9: 4,6,3,5 # reduction candidate for 4,6 A9: 4,6 => CTR * 736541928914862735..5973614...6185.33594278611.83952.....18.3....173.4...9325.187 A9: 3,5 => SOLVED * 736541928914862735825973614279618543563427891148395267452186379681739452397254186 * PAIR H8: 5,6 BLK 9 H7: 5,6,7 # reduction candidate for 5,6 H7: 5,6 => CTR * 736541928914862735..5973614...6185.3...4278.11.83952.6...18.3....17..4...9325.187 H7: 7 => SOLVED * 736541928914862735825973614279618543563427891148395267452186379681739452397254186 * PAIR H8: 5,6 ROW 8 A8: 5,6,2,3,8 # reduction candidate for 5,6 A8: 5,6 # 13 pairs B8: 5,6,2,8 # reduction candidate for 5,6 B8: 5,6 => CTR * 7365419289148627352859736144..6185.3...4278.11.839524..4218.3798.1739452.97254186 B8: 2,8 # 19 pairs * PAIR I9: 6,7 BLK 9 H7: 6,7,5 # reduction candidate for 6,7 H7: 5 => CTR * 736541928914862735..5973614...6185.3...4278911.83952.6...18.35...17.9462.932..187 H7: 6,7 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190415-absurd-base-pr-000.dot * REASONING * DIS # B8: 5,6 => CTR => B8: 2,8 * PRF # A5: 5,6 => SOL * DIS # A5: 3 => CTR => A5: 5,6 * PRF # B7: 5,6 => SOL * DIS # B8: 5,6 => CTR => B8: 2,8 * PRF # H6: 6,7 => SOL * PRF # B6: 4 => SOL * DIS # B7: 2,7 => CTR => B7: 4,5,6 * DIS # C4: 2,7 => CTR => C4: 9 * PRF # C4: 9 => SOL * DIS # A8: 3,5 => CTR => A8: 2,6,8 * DIS # F7: 4 => CTR => F7: 6,9 * PRF # A9: 3,5 => SOL * DIS # A9: 4,6 => CTR => A9: 3,5 * DIS # F7: 9 => CTR => F7: 4,6 * DIS # A9: 4,6 => CTR => A9: 3,5 * PRF # A9: 3,5 => SOL * DIS # H7: 5,6 => CTR => H7: 7 * PRF # H7: 7 => SOL * DIS # B8: 5,6 => CTR => B8: 2,8 * DIS # H7: 5 => CTR => H7: 6,7 * CNT 21 HDP CHAINS / 39 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B3,B5,C5,C7,C9,E8,E9,F8,F9,H5,H8,I6,I7,I8,I9) * 736541928914862735..5973614...6185.3...4278.11.83952.....18.3....17..4...9.2..18. * PAIR A3: 2,8 COL A A8: 2,8,3,5,6 # reduction candidate for 2,8 A8: 2,8 # 21 pairs A8: 3,5,6 # 14 pairs * PAIR B3: 2,8 COL B B8: 2,8,5,6 # reduction candidate for 2,8 B8: 5,6 => CTR * 7365419289148627352859736144..6185.3...4278.11.839524..4218.3798.1739452.97254186 * PAIR RESTART * PAIR A4: 2,4 COL A A7: 2,4,5,6 # reduction candidate for 2,4 A7: 5,6 # 20 pairs A7: 2,4 # 15 pairs * PAIR B5: 5,6 BLK 4 A5: 5,6,3 # reduction candidate for 5,6 A5: 5,6 => SOLVED * 736541928914862735825973614279618543563427891148395267452186379681739452397254186 * DURATION: 0:00:06.255122 START: 05:20:05.573472 END: 05:20:11.828594 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190415-absurd-base-pr-001.dot * REASONING * DIS # B8: 5,6 => CTR => B8: 2,8 * PRF B8: 2,8 # A5: 5,6 => SOL * STA B8: 2,8 + A5: 5,6 * CNT 2 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190415, absurd
Solution
position: 736541928914862735825973614279618543563427891148395267452186379681739452397254186 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 # A8: 2,8 => UNS * INC # A8: 3,5,6 => UNS * INC # B8: 2,8 => UNS * DIS # B8: 5,6 => CTR => B8: 2,8 * INC # B4: 2,4 => UNS * INC # B4: 7 => UNS * INC # A7: 2,4 => UNS * INC # A7: 5,6 => UNS * PRF # A5: 5,6 => SOL * DIS # A5: 3 => CTR => A5: 5,6 * PRF # B7: 5,6 => SOL * INC # B7: 2,4,7 => UNS * DIS # B8: 5,6 => CTR => B8: 2,8 * INC # B8: 2,8 => UNS * PRF # H6: 6,7 => SOL * INC # H6: 4 => UNS * INC # B6: 6,7 => UNS * PRF # B6: 4 => SOL * DIS # B7: 2,7 => CTR => B7: 4,5,6 * INC # B7: 4,5,6 => UNS * DIS # C4: 2,7 => CTR => C4: 9 * PRF # C4: 9 => SOL * DIS # A8: 3,5 => CTR => A8: 2,6,8 * INC # A8: 2,6,8 => UNS * INC # F7: 6,9 => UNS * DIS # F7: 4 => CTR => F7: 6,9 * PRF # A9: 3,5 => SOL * DIS # A9: 4,6 => CTR => A9: 3,5 * INC # F7: 4,6 => UNS * DIS # F7: 9 => CTR => F7: 4,6 * DIS # A9: 4,6 => CTR => A9: 3,5 * PRF # A9: 3,5 => SOL * DIS # H7: 5,6 => CTR => H7: 7 * PRF # H7: 7 => SOL * INC # A8: 5,6 => UNS * DIS # B8: 5,6 => CTR => B8: 2,8 * INC # B8: 2,8 => UNS * INC # H7: 6,7 => UNS * DIS # H7: 5 => CTR => H7: 6,7 * CNT 39 HDP CHAINS / 39 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A8: 2,8 => UNS * INC # A8: 3,5,6 => UNS * INC # B8: 2,8 => UNS * DIS # B8: 5,6 => CTR => B8: 2,8 * INC B8: 2,8 # A7: 2,4 => UNS * INC B8: 2,8 # A7: 5,6 => UNS * PRF B8: 2,8 # A5: 5,6 => SOL * STA B8: 2,8 + A5: 5,6 * CNT 7 HDP CHAINS / 7 HYP OPENED