Analysis of zz-sudoku-de-719598-base.sdk
Contents
Original Sudoku
level: medium
position: 3.47...9....36.1..2....5...4......271.5...3.478......9...5....3..3.89....4...36.2 initial
Autosolve
position: 3.471829....36214.2....573.43..518271.58.736478..3.519...5..9.3..3.894.1.4.1736.2 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 8,9 => CTR => C2: 7 * DIS # A9: 8,9 => CTR => A9: 5 * PRF # A9: 5 => SOL * PRF # D6: 2,6 => SOL * DIS # D6: 4 => CTR => D6: 2,6 * PRF # D6: 4,6 => SOL * DIS # D6: 2 => CTR => D6: 4,6 * PRF # B7: 2,7 => SOL * DIS # A9: 8,9 => CTR => A9: 5 * PRF # A9: 5 => SOL * DIS # C2: 8,9 => CTR => C2: 7 * PRF # D6: 2,6 => SOL * DIS # D6: 4 => CTR => D6: 2,6 * PRF # A9: 5,8 => SOL * DIS # A9: 9 => CTR => A9: 5,8 * CNT 15 HDP CHAINS / 19 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 8,9 => CTR => C2: 7 * DIS C2: 7 # A9: 8,9 => CTR => A9: 5 * PRF C2: 7 + A9: 5 => SOL * STA C2: 7 + A9: 5 * CNT 3 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 3.47...9....36.1..2....5...4......271.5...3.478......9...5....3..3.89....4...36.2 | initial |
| 3.471829....36214.2....573.43..518271.58.736478..3.519...5..9.3..3.894.1.4.1736.2 | autosolve |
| 364718295957362148218495736436951827195827364782634519821546973673289451549173682 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (25) B1: 5,6 A2: 8,9 B3: 1,6 C3: 1,8 D3: 4,9 E3: 4,9 I1: 5,6 I2: 5,8 I3: 6,8 C4: 6,9 B5: 2,9 C6: 2,6 D4: 6,9 E5: 2,9 F6: 4,6 A7: 6,8 A8: 5,6 B8: 2,7 C9: 8,9 E7: 2,4 F7: 4,6 D8: 2,6 H7: 7,8 H8: 5,7 H9: 5,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B3,C3: 1.. / B3 = 1 => 0 pairs (*) / C3 = 1 => 0 pairs (X) B7,C7: 1.. / B7 = 1 => 21 pairs (_) / C7 = 1 => 0 pairs (*) B3,B7: 1.. / B3 = 1 => 0 pairs (*) / B7 = 1 => 0 pairs (X) C3,C7: 1.. / C3 = 1 => 21 pairs (_) / C7 = 1 => 0 pairs (*) B5,C6: 2.. / B5 = 2 => 0 pairs (X) / C6 = 2 => 0 pairs (_) E5,D6: 2.. / E5 = 2 => 0 pairs (*) / D6 = 2 => 0 pairs (X) E7,D8: 2.. / E7 = 2 => 0 pairs (X) / D8 = 2 => 0 pairs (_) B5,E5: 2.. / B5 = 2 => 0 pairs (X) / E5 = 2 => 0 pairs (_) C6,D6: 2.. / C6 = 2 => 0 pairs (*) / D6 = 2 => 0 pairs (X) B8,D8: 2.. / B8 = 2 => 0 pairs (X) / D8 = 2 => 0 pairs (_) C6,C7: 2.. / C6 = 2 => 0 pairs (*) / C7 = 2 => 0 pairs (X) D6,D8: 2.. / D6 = 2 => 0 pairs (X) / D8 = 2 => 0 pairs (_) E5,E7: 2.. / E5 = 2 => 0 pairs (*) / E7 = 2 => 0 pairs (X) D3,E3: 4.. / D3 = 4 => 0 pairs (*) / E3 = 4 => 0 pairs (X) D6,F6: 4.. / D6 = 4 => 0 pairs (X) / F6 = 4 => 0 pairs (_) E7,F7: 4.. / E7 = 4 => 0 pairs (*) / F7 = 4 => 0 pairs (X) D3,D6: 4.. / D3 = 4 => 0 pairs (*) / D6 = 4 => 0 pairs (X) E3,E7: 4.. / E3 = 4 => 0 pairs (X) / E7 = 4 => 0 pairs (_) F6,F7: 4.. / F6 = 4 => 0 pairs (*) / F7 = 4 => 0 pairs (X) B1,B2: 5.. / B1 = 5 => 21 pairs (_) / B2 = 5 => 0 pairs (*) I1,I2: 5.. / I1 = 5 => 0 pairs (*) / I2 = 5 => 0 pairs (X) A8,A9: 5.. / A8 = 5 => 0 pairs (X) / A9 = 5 => 0 pairs (_) H8,H9: 5.. / H8 = 5 => 0 pairs (*) / H9 = 5 => 0 pairs (X) B1,I1: 5.. / B1 = 5 => 21 pairs (_) / I1 = 5 => 0 pairs (*) B2,I2: 5.. / B2 = 5 => 0 pairs (*) / I2 = 5 => 0 pairs (X) A8,H8: 5.. / A8 = 5 => 0 pairs (X) / H8 = 5 => 0 pairs (_) A9,H9: 5.. / A9 = 5 => 0 pairs (*) / H9 = 5 => 0 pairs (X) B1,B3: 6.. / B1 = 6 => 0 pairs (*) / B3 = 6 => 0 pairs (X) I1,I3: 6.. / I1 = 6 => 21 pairs (_) / I3 = 6 => 0 pairs (*) C4,C6: 6.. / C4 = 6 => 0 pairs (*) / C6 = 6 => 0 pairs (X) A7,A8: 6.. / A7 = 6 => 0 pairs (X) / A8 = 6 => 0 pairs (_) F7,D8: 6.. / F7 = 6 => 0 pairs (*) / D8 = 6 => 0 pairs (X) B1,I1: 6.. / B1 = 6 => 0 pairs (*) / I1 = 6 => 0 pairs (X) B3,I3: 6.. / B3 = 6 => 21 pairs (_) / I3 = 6 => 0 pairs (*) C4,D4: 6.. / C4 = 6 => 0 pairs (*) / D4 = 6 => 0 pairs (X) A7,F7: 6.. / A7 = 6 => 0 pairs (X) / F7 = 6 => 0 pairs (_) A8,D8: 6.. / A8 = 6 => 0 pairs (*) / D8 = 6 => 0 pairs (X) F6,F7: 6.. / F6 = 6 => 0 pairs (X) / F7 = 6 => 0 pairs (_) B2,C2: 7.. / B2 = 7 => 0 pairs (X) / C2 = 7 => 27 pairs (_) H7,H8: 7.. / H7 = 7 => 0 pairs (*) / H8 = 7 => 0 pairs (X) B8,H8: 7.. / B8 = 7 => 0 pairs (*) / H8 = 7 => 0 pairs (X) C2,C7: 7.. / C2 = 7 => 27 pairs (_) / C7 = 7 => 0 pairs (X) I2,I3: 8.. / I2 = 8 => 0 pairs (*) / I3 = 8 => 0 pairs (X) H7,H9: 8.. / H7 = 8 => 0 pairs (X) / H9 = 8 => 0 pairs (_) C3,I3: 8.. / C3 = 8 => 0 pairs (*) / I3 = 8 => 0 pairs (X) A7,H7: 8.. / A7 = 8 => 0 pairs (*) / H7 = 8 => 0 pairs (X) D3,E3: 9.. / D3 = 9 => 0 pairs (X) / E3 = 9 => 0 pairs (_) C4,B5: 9.. / C4 = 9 => 0 pairs (X) / B5 = 9 => 0 pairs (_) D4,E5: 9.. / D4 = 9 => 0 pairs (*) / E5 = 9 => 0 pairs (X) A9,C9: 9.. / A9 = 9 => 0 pairs (X) / C9 = 9 => 0 pairs (_) C4,D4: 9.. / C4 = 9 => 0 pairs (X) / D4 = 9 => 0 pairs (_) B5,E5: 9.. / B5 = 9 => 0 pairs (*) / E5 = 9 => 0 pairs (X) A2,A9: 9.. / A2 = 9 => 0 pairs (*) / A9 = 9 => 0 pairs (X) B2,B5: 9.. / B2 = 9 => 0 pairs (X) / B5 = 9 => 0 pairs (_) D3,D4: 9.. / D3 = 9 => 0 pairs (X) / D4 = 9 => 0 pairs (_) E3,E5: 9.. / E3 = 9 => 0 pairs (*) / E5 = 9 => 0 pairs (X) * DURATION: 0:01:38.688606 START: 08:15:03.348109 END: 08:16:42.036715 2017-05-01 * CP COUNT: (56) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,A8,B1,B3,B5,B8,C3,C4,C6,C9,D3,D4,D8,E3,E5,E7,F6,F7,H7,H8,H9,I1,I2,I3) * 3.471829....36214.2....573.43..518271.58.736478..3.519...5..9.3..3.894.1.4.1736.2 * PAIR A2: 8,9 BLK 1 C2: 8,9,7 # reduction candidate for 8,9 C2: 8,9 => CTR * 3.471829..7.3621452....573843..51827195827364782.3.519.2.5..9.3..3.894.1.4.1736.2 C2: 7 # 27 pairs * PAIR A2: 8,9 COL A A9: 8,9,5 # reduction candidate for 8,9 A9: 8,9 => CTR * 3.471829....36214.2....573.43695182719582736478243.519...5..9.35.3689471.4.173652 A9: 5 => SOLVED * 364718295957362148218495736436951827195827364782634519821546973673289451549173682 * PAIR C6: 2,6 ROW 6 D6: 2,6,4 # reduction candidate for 2,6 D6: 2,6 => SOLVED * 364718295957362148218495736436951827195827364782634519821546973673289451549173682 D6: 4 => CTR * 3.471829....36214.2....573.43..518271.582736478243651962154.9.3..3.894.1.4.1736.2 * PAIR F6: 4,6 BLK 5 D6: 4,6,2 # reduction candidate for 4,6 D6: 4,6 => SOLVED * 364718295957362148218495736436951827195827364782634519821546973673289451549173682 D6: 2 => CTR * 3.471829....36214.2..49573.43.95182719582736478..3.519...5..9.3..3.894.1.4.1736.2 * PAIR B8: 2,7 BLK 7 B7: 2,7,1 # reduction candidate for 2,7 B7: 2,7 => SOLVED * 364718295957362148218495736436951827195827364782634519821546973673289451549173682 B7: 1 # 21 pairs C7: 2,7,1 # reduction candidate for 2,7 C7: 2,7 # 21 pairs * PAIR C9: 8,9 BLK 7 A9: 8,9,5 # reduction candidate for 8,9 A9: 8,9 => CTR * 3.471829....36214.2....573.43695182719582736478243.519...5..9.35.3689471.4.173652 A9: 5 => SOLVED * 364718295957362148218495736436951827195827364782634519821546973673289451549173682 * PAIR C9: 8,9 COL C C2: 8,9,7 # reduction candidate for 8,9 C2: 8,9 => CTR * 3.471829..7.3621452....573843..51827195827364782.3.519.2.5..9.3..3.894.1.4.1736.2 C2: 7 # 27 pairs * PAIR D8: 2,6 COL D D6: 2,6,4 # reduction candidate for 2,6 D6: 2,6 => SOLVED * 364718295957362148218495736436951827195827364782634519821546973673289451549173682 D6: 4 => CTR * 3.471829....36214.2....573.43..518271.582736478243651962154.9.3..3.894.1.4.1736.2 * PAIR H9: 5,8 ROW 9 A9: 5,8,9 # reduction candidate for 5,8 A9: 5,8 => SOLVED * 364718295957362148218495736436951827195827364782634519821546973673289451549173682 A9: 9 => CTR * 3.471829.8..3621452.1..573843695182719582736478243.519...5..9.35.3689471948173652 * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-719598-base-pr-000.dot * REASONING * DIS # C2: 8,9 => CTR => C2: 7 * DIS # A9: 8,9 => CTR => A9: 5 * PRF # A9: 5 => SOL * PRF # D6: 2,6 => SOL * DIS # D6: 4 => CTR => D6: 2,6 * PRF # D6: 4,6 => SOL * DIS # D6: 2 => CTR => D6: 4,6 * PRF # B7: 2,7 => SOL * DIS # A9: 8,9 => CTR => A9: 5 * PRF # A9: 5 => SOL * DIS # C2: 8,9 => CTR => C2: 7 * PRF # D6: 2,6 => SOL * DIS # D6: 4 => CTR => D6: 2,6 * PRF # A9: 5,8 => SOL * DIS # A9: 9 => CTR => A9: 5,8 * CNT 15 HDP CHAINS / 19 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,A8,B1,B3,B5,B8,C3,C4,C6,C9,D3,D4,D8,E3,E5,E7,F6,F7,H7,H8,H9,I1,I2,I3) * 3.471829....36214.2....573.43..518271.58.736478..3.519...5..9.3..3.894.1.4.1736.2 * PAIR A2: 8,9 BLK 1 C2: 8,9,7 # reduction candidate for 8,9 C2: 8,9 => CTR * 3.471829..7.3621452....573843..51827195827364782.3.519.2.5..9.3..3.894.1.4.1736.2 * PAIR A2: 8,9 COL A A9: 8,9,5 # reduction candidate for 8,9 A9: 8,9 => CTR * 3.471829...736214.2....573.43695182719582736478243.519...5..9.35.3689471.4.173652 A9: 5 => SOLVED * 364718295957362148218495736436951827195827364782634519821546973673289451549173682 * DURATION: 0:00:05.116408 START: 08:17:04.491660 END: 08:17:09.608068 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-719598-base-pr-001.dot * REASONING * DIS # C2: 8,9 => CTR => C2: 7 * DIS C2: 7 # A9: 8,9 => CTR => A9: 5 * PRF C2: 7 + A9: 5 => SOL * STA C2: 7 + A9: 5 * CNT 3 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokus.de/719598.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: 3.471829....36214.2....573.43..518271.58.736478..3.519...5..9.3..3.894.1.4.1736.2 B1: 5,6 A2: 8,9 C2: 7,8,9 # reduction candidate for 8,9 C2: 8,9 => CTR * 3.471829..7.3621452....573843..51827195827364782.3.519.2.5..9.3..3.894.1.4.1736.2 A9: 5,8,9 # reduction candidate for 8,9 A9: 8,9 => CTR * 3.471829...736214.2....573.43695182719582736478243.519...5..9.35.3689471.4.173652 A9: 5 => SOLVED * 364718295957362148218495736436951827195827364782634519821546973673289451549173682 * SOLVED! -------------------------------------------------- |:step:| 00 -------------------------------------------------- * FORCE VALUE:: D6 = 2 D6 = 2 # set value E5: 9 # naked single D8: 6 # naked single C6: 6 # naked single B5: 2.. # hidden single F6: 4.. # hidden single E7: 2.. # hidden single B8: 2.. # hidden single C7: 2.. # hidden single D3: 4.. # hidden single * AUTO .. D3 = 4 # set value E3: 9 # naked single E3 = 9 # set value E5 = 0 => CTR * CTR! * DISABLE VALUE:: D6 != 2 E5: 2.. # hidden single C6: 2.. # hidden single D8: 2.. # hidden single * SOLVED! |:step:| 01 --------------------------------------------------
Solution
position: 364718295957362148218495736436951827195827364782634519821546973673289451549173682 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 # C2: 8,9 => CTR => C2: 7 * INC # C2: 7 => UNS * DIS # A9: 8,9 => CTR => A9: 5 * PRF # A9: 5 => SOL * PRF # D6: 2,6 => SOL * DIS # D6: 4 => CTR => D6: 2,6 * PRF # D6: 4,6 => SOL * DIS # D6: 2 => CTR => D6: 4,6 * PRF # B7: 2,7 => SOL * INC # B7: 1 => UNS * INC # C7: 2,7 => UNS * DIS # A9: 8,9 => CTR => A9: 5 * PRF # A9: 5 => SOL * DIS # C2: 8,9 => CTR => C2: 7 * INC # C2: 7 => UNS * PRF # D6: 2,6 => SOL * DIS # D6: 4 => CTR => D6: 2,6 * PRF # A9: 5,8 => SOL * DIS # A9: 9 => CTR => A9: 5,8 * CNT 19 HDP CHAINS / 19 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C2: 8,9 => CTR => C2: 7 * DIS C2: 7 # A9: 8,9 => CTR => A9: 5 * PRF C2: 7 + A9: 5 => SOL * STA C2: 7 + A9: 5 * CNT 3 HDP CHAINS / 2 HYP OPENED