Analysis of zz-sudoku-de-665801-base.sdk
Contents
Original Sudoku
level: medium
position: ...9..5..29.....3...4..7.6..4783..2.1.......8.3..5417..6.7..4...2.....17..9..6... initial
Autosolve
position: 71.9..58429....731.84.17269647831925152679348938254176.617..49..2..9.617.791.685. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A7: 3,5 => SOL * DIS # A7: 8 => CTR => A7: 3,5 * DIS # A8: 3,5 => CTR => A8: 4,8 * DIS # F7: 2,3 => CTR => F7: 5,8 * PRF # F7: 5,8 => SOL * PRF # D8: 4,5 => SOL * DIS # D8: 3 => CTR => D8: 4,5 * PRF # F7: 5,8 => SOL * DIS # F7: 2,3 => CTR => F7: 5,8 * DIS # F8: 5,8 => CTR => F8: 3 * PRF # F8: 3 => SOL * DIS # D8: 3,5 => CTR => D8: 4 * PRF # D8: 4 => SOL * PRF # A7: 3,5 => SOL * DIS # A7: 8 => CTR => A7: 3,5 * DIS # A8: 3,5 => CTR => A8: 4,8 * DIS # D8: 3,5 => CTR => D8: 4 * PRF # D8: 4 => SOL * PRF # F8: 3,5 => SOL * DIS # F8: 8 => CTR => F8: 3,5 * DIS # A8: 3,4 => CTR => A8: 5,8 * PRF # A8: 5,8 => SOL * DIS # F7: 2,8 => CTR => F7: 3,5 * PRF # F7: 3,5 => SOL * DIS # F7: 2,3 => CTR => F7: 5,8 * PRF # F7: 5,8 => SOL * CNT 26 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A7: 3,5 => SOL * STA A7: 3,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...9..5..29.....3...4..7.6..4783..2.1.......8.3..5417..6.7..4...2.....17..9..6... | initial |
| 71.9..58429....731.84.17269647831925152679348938254176.617..49..2..9.617.791.685. | autosolve |
| 713962584296548731584317269647831925152679348938254176361785492825493617479126853 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) C1: 3,6 C2: 5,6 A3: 3,5 E1: 2,6 F1: 2,3 D2: 4,5 F2: 5,8 D3: 3,5 C8: 3,5 A9: 3,4 E7: 2,8 E9: 2,4 I7: 2,3 I9: 2,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,F1: 2.. / E1 = 2 => 0 pairs (X) / F1 = 2 => 0 pairs (_) I7,I9: 2.. / I7 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) E9,I9: 2.. / E9 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) F1,F7: 2.. / F1 = 2 => 0 pairs (*) / F7 = 2 => 0 pairs (X) C1,A3: 3.. / C1 = 3 => 0 pairs (*) / A3 = 3 => 0 pairs (X) F1,D3: 3.. / F1 = 3 => 0 pairs (X) / D3 = 3 => 0 pairs (_) I7,I9: 3.. / I7 = 3 => 0 pairs (X) / I9 = 3 => 0 pairs (_) C1,F1: 3.. / C1 = 3 => 0 pairs (*) / F1 = 3 => 0 pairs (X) A3,D3: 3.. / A3 = 3 => 0 pairs (X) / D3 = 3 => 0 pairs (_) A9,I9: 3.. / A9 = 3 => 0 pairs (X) / I9 = 3 => 0 pairs (_) C1,C8: 3.. / C1 = 3 => 0 pairs (*) / C8 = 3 => 0 pairs (X) D3,D8: 3.. / D3 = 3 => 0 pairs (*) / D8 = 3 => 0 pairs (X) D2,E2: 4.. / D2 = 4 => 0 pairs (X) / E2 = 4 => 0 pairs (_) A8,A9: 4.. / A8 = 4 => 0 pairs (X) / A9 = 4 => 0 pairs (_) D8,E9: 4.. / D8 = 4 => 0 pairs (*) / E9 = 4 => 0 pairs (X) A8,D8: 4.. / A8 = 4 => 0 pairs (X) / D8 = 4 => 0 pairs (_) A9,E9: 4.. / A9 = 4 => 0 pairs (*) / E9 = 4 => 0 pairs (X) D2,D8: 4.. / D2 = 4 => 0 pairs (X) / D8 = 4 => 0 pairs (_) E2,E9: 4.. / E2 = 4 => 0 pairs (*) / E9 = 4 => 0 pairs (X) C2,A3: 5.. / C2 = 5 => 0 pairs (X) / A3 = 5 => 0 pairs (_) A3,D3: 5.. / A3 = 5 => 0 pairs (*) / D3 = 5 => 0 pairs (X) A7,F7: 5.. / A7 = 5 => 0 pairs (X) / F7 = 5 => 0 pairs (_) C2,C8: 5.. / C2 = 5 => 0 pairs (X) / C8 = 5 => 0 pairs (_) C1,C2: 6.. / C1 = 6 => 0 pairs (X) / C2 = 6 => 0 pairs (_) E1,E2: 6.. / E1 = 6 => 0 pairs (*) / E2 = 6 => 0 pairs (X) C1,E1: 6.. / C1 = 6 => 0 pairs (X) / E1 = 6 => 0 pairs (_) C2,E2: 6.. / C2 = 6 => 0 pairs (*) / E2 = 6 => 0 pairs (X) E2,F2: 8.. / E2 = 8 => 0 pairs (X) / F2 = 8 => 0 pairs (_) A7,A8: 8.. / A7 = 8 => 0 pairs (X) / A8 = 8 => 0 pairs (_) A8,F8: 8.. / A8 = 8 => 0 pairs (*) / F8 = 8 => 0 pairs (X) E2,E7: 8.. / E2 = 8 => 0 pairs (X) / E7 = 8 => 0 pairs (_) * DURATION: 0:00:54.318146 START: 07:41:54.800668 END: 07:42:49.118814 2017-05-01 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A9,C1,C2,C8,D2,D3,E1,E7,E9,F1,F2,I7,I9) * 71.9..58429....731.84.17269647831925152679348938254176.617..49..2..9.617.791.685. * PAIR A3: 3,5 COL A A7: 3,5,8 # reduction candidate for 3,5 A7: 3,5 => SOLVED * 713962584296548731584317269647831925152679348938254176361785492825493617479126853 A7: 8 => CTR * 71.9..58429....731.84.17269647831925152679348938254176861725493.2..98617.791.685. A8: 3,5,4,8 # reduction candidate for 3,5 A8: 3,5 => CTR * 71.9..58429....731.84.17269647831925152679348938254176861725493.2.49.617.791.685. A8: 4,8 # 15 pairs * PAIR F1: 2,3 COL F F7: 2,3,5,8 # reduction candidate for 2,3 F7: 2,3 => CTR * 71.9..58429....731.84.1726964783192515267934893825417656178.49.82349.617.791.685. F7: 5,8 => SOLVED * 713962584296548731584317269647831925152679348938254176361785492825493617479126853 * PAIR D2: 4,5 COL D D8: 4,5,3 # reduction candidate for 4,5 D8: 4,5 => SOLVED * 713962584296548731584317269647831925152679348938254176361785492825493617479126853 D8: 3 => CTR * 71.9..58429.4..731.84517269647831925152679348938254176.617..49.42.398617.791.685. * PAIR F2: 5,8 COL F F7: 5,8,2,3 # reduction candidate for 5,8 F7: 5,8 => SOLVED * 713962584296548731584317269647831925152679348938254176361785492825493617479126853 F7: 2,3 => CTR * 71.9..58429....731.84.1726964783192515267934893825417656178.49.82349.617.791.685. F8: 5,8,3 # reduction candidate for 5,8 F8: 5,8 => CTR * 71.9..58429....731.84.1726964783192515267934893825417656178.49.82349.617.791.685. F8: 3 => SOLVED * 713962584296548731584317269647831925152679348938254176361785492825493617479126853 * PAIR D3: 3,5 COL D D8: 3,5,4 # reduction candidate for 3,5 D8: 3,5 => CTR * 713962584296485731584.17269647831925152679348938254176.617..49.42..98617379146852 D8: 4 => SOLVED * 713962584296548731584317269647831925152679348938254176361785492825493617479126853 * PAIR C8: 3,5 BLK 7 A7: 3,5,8 # reduction candidate for 3,5 A7: 3,5 => SOLVED * 713962584296548731584317269647831925152679348938254176361785492825493617479126853 A7: 8 => CTR * 71.9..58429....731.84.17269647831925152679348938254176861725493.2..98617.791.685. A8: 3,5,4,8 # reduction candidate for 3,5 A8: 3,5 => CTR * 71.9..58429....731.84.17269647831925152679348938254176861725493.2.49.617.791.685. A8: 4,8 # 15 pairs * PAIR C8: 3,5 ROW 8 D8: 3,5,4 # reduction candidate for 3,5 D8: 3,5 => CTR * 713962584296485731584.17269647831925152679348938254176.617..49.42..98617379146852 D8: 4 => SOLVED * 713962584296548731584317269647831925152679348938254176361785492825493617479126853 F8: 3,5,8 # reduction candidate for 3,5 F8: 3,5 => SOLVED * 713962584296548731584317269647831925152679348938254176361785492825493617479126853 F8: 8 => CTR * 71.9..58429..85731584.17269647831925152679348938254176.617..49..2..98617.791.685. * PAIR A9: 3,4 BLK 7 A8: 3,4,5,8 # reduction candidate for 3,4 A8: 3,4 => CTR * 71.9..58429....731.84.17269647831925152679348938254176861725493.25.98617.791.685. A8: 5,8 => SOLVED * 713962584296548731584317269647831925152679348938254176361785492825493617479126853 * PAIR E7: 2,8 BLK 8 F7: 2,8,3,5 # reduction candidate for 2,8 F7: 2,8 => CTR * 71.9..58429....731.84.172696478319251526793489382541765617..493823.9.617.791.685. F7: 3,5 => SOLVED * 713962584296548731584317269647831925152679348938254176361785492825493617479126853 * PAIR I7: 2,3 ROW 7 F7: 2,3,5,8 # reduction candidate for 2,3 F7: 2,3 => CTR * 71.9..58429....731.84.1726964783192515267934893825417656178.49.82349.617.791.685. F7: 5,8 => SOLVED * 713962584296548731584317269647831925152679348938254176361785492825493617479126853 * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-665801-base-pr-000.dot * REASONING * PRF # A7: 3,5 => SOL * DIS # A7: 8 => CTR => A7: 3,5 * DIS # A8: 3,5 => CTR => A8: 4,8 * DIS # F7: 2,3 => CTR => F7: 5,8 * PRF # F7: 5,8 => SOL * PRF # D8: 4,5 => SOL * DIS # D8: 3 => CTR => D8: 4,5 * PRF # F7: 5,8 => SOL * DIS # F7: 2,3 => CTR => F7: 5,8 * DIS # F8: 5,8 => CTR => F8: 3 * PRF # F8: 3 => SOL * DIS # D8: 3,5 => CTR => D8: 4 * PRF # D8: 4 => SOL * PRF # A7: 3,5 => SOL * DIS # A7: 8 => CTR => A7: 3,5 * DIS # A8: 3,5 => CTR => A8: 4,8 * DIS # D8: 3,5 => CTR => D8: 4 * PRF # D8: 4 => SOL * PRF # F8: 3,5 => SOL * DIS # F8: 8 => CTR => F8: 3,5 * DIS # A8: 3,4 => CTR => A8: 5,8 * PRF # A8: 5,8 => SOL * DIS # F7: 2,8 => CTR => F7: 3,5 * PRF # F7: 3,5 => SOL * DIS # F7: 2,3 => CTR => F7: 5,8 * PRF # F7: 5,8 => SOL * CNT 26 HDP CHAINS / 28 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A9,C1,C2,C8,D2,D3,E1,E7,E9,F1,F2,I7,I9) * 71.9..58429....731.84.17269647831925152679348938254176.617..49..2..9.617.791.685. * PAIR A3: 3,5 COL A A7: 3,5,8 # reduction candidate for 3,5 A7: 3,5 => SOLVED * 713962584296548731584317269647831925152679348938254176361785492825493617479126853 * DURATION: 0:00:01.975912 START: 07:43:21.515885 END: 07:43:23.491797 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-665801-base-pr-001.dot * REASONING * PRF # A7: 3,5 => SOL * STA A7: 3,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokus.de/665801.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: 71.9..58429....731.84.17269647831925152679348938254176.617..49..2..9.617.791.685. C1: 3,6 C2: 5,6 A3: 3,5 A7: 3,5,8 # reduction candidate for 3,5 A7: 3,5 => SOLVED * 713962584296548731584317269647831925152679348938254176361785492825493617479126853 * SOLVED! -------------------------------------------------- * AUTO .. G2 = 7 # set value F4 = 1 # set value B5 = 5 # set value E5 = 7 # set value G5 = 3 # set value H5 = 4 # set value H1: 8 # naked single G8 = 6 # set value G4: 9 # naked single F5: 9.. # hidden single I4: 5.. # hidden single H7: 9.. # hidden single H1 = 8 # set value H9: 5 # naked single G4 = 9 # set value I6: 6 # naked single G3: 2 # naked single A4: 6 # naked single I4 = 5 # set value F5 = 9 # set value I6 = 6 # set value D6: 2 # naked single H7 = 9 # set value H9 = 5 # set value I3: 9.. # hidden single A6: 9.. # hidden single D5: 6.. # hidden single E8: 9.. # hidden single G9: 8.. # hidden single G3 = 2 # set value G9: 8 # naked single I3 = 9 # set value A4 = 6 # set value C5: 2 # naked single C5 = 2 # set value C6: 8 # naked single D5: 6 # naked single D5 = 6 # set value A6 = 9 # set value C6 = 8 # set value D6 = 2 # set value E8 = 9 # set value G9 = 8 # set value B3: 8.. # hidden single B3 = 8 # set value E3: 1 # naked single E3 = 1 # set value D9: 1.. # hidden single C7: 1.. # hidden single C7 = 1 # set value B9: 7 # naked single B9 = 7 # set value B1: 1 # naked single D9 = 1 # set value A1: 7.. # hidden single I2: 1.. # hidden single A1 = 7 # set value B1 = 1 # set value I1: 4 # naked single I1 = 4 # set value I2: 1 # naked single I2 = 1 # set value * UNSOLVED! |:step:| 00 -------------------------------------------------- * DISABLE VALUE:: A7 != 8 |:step:| 01 --------------------------------------------------
Solution
position: 713962584296548731584317269647831925152679348938254176361785492825493617479126853 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:
* PRF # A7: 3,5 => SOL * DIS # A7: 8 => CTR => A7: 3,5 * DIS # A8: 3,5 => CTR => A8: 4,8 * INC # A8: 4,8 => UNS * DIS # F7: 2,3 => CTR => F7: 5,8 * PRF # F7: 5,8 => SOL * PRF # D8: 4,5 => SOL * DIS # D8: 3 => CTR => D8: 4,5 * PRF # F7: 5,8 => SOL * DIS # F7: 2,3 => CTR => F7: 5,8 * DIS # F8: 5,8 => CTR => F8: 3 * PRF # F8: 3 => SOL * DIS # D8: 3,5 => CTR => D8: 4 * PRF # D8: 4 => SOL * PRF # A7: 3,5 => SOL * DIS # A7: 8 => CTR => A7: 3,5 * DIS # A8: 3,5 => CTR => A8: 4,8 * INC # A8: 4,8 => UNS * DIS # D8: 3,5 => CTR => D8: 4 * PRF # D8: 4 => SOL * PRF # F8: 3,5 => SOL * DIS # F8: 8 => CTR => F8: 3,5 * DIS # A8: 3,4 => CTR => A8: 5,8 * PRF # A8: 5,8 => SOL * DIS # F7: 2,8 => CTR => F7: 3,5 * PRF # F7: 3,5 => SOL * DIS # F7: 2,3 => CTR => F7: 5,8 * PRF # F7: 5,8 => SOL * CNT 28 HDP CHAINS / 28 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A7: 3,5 => SOL * STA A7: 3,5 * CNT 1 HDP CHAINS / 1 HYP OPENED