Analysis of zz-sudoku-de-651186-base.sdk
Contents
Original Sudoku
level: medium
position: .8......9...328..71....764..1...3.....7...8.....5...2..267....43..496...4......5. initial
Autosolve
position: 785...239...32851713295764821...3..55.7...8.3..35...21.267.5..435.496..247.....56 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B2: 4 => SOL * DIS # A6: 6,9 => CTR => A6: 8 * PRF # A6: 8 => SOL * DIS # B2: 6 => CTR => B2: 4,9 * PRF # C4: 4,9 => SOL * DIS # C4: 8 => CTR => C4: 4,9 * DIS # E1: 4 => CTR => E1: 1,6 * DIS # D5: 1,6 => CTR => D5: 2 * DIS # E1: 1,4 => CTR => E1: 6 * PRF # E4: 6,8 => SOL * DIS # E6: 6,8 => CTR => E6: 4,7 * PRF # E6: 4,7 => SOL * DIS # F5: 4,9 => CTR => F5: 1,2 * DIS # B6: 4,9 => CTR => B6: 6 * PRF # G6: 4,9 => SOL * DIS # G6: 7 => CTR => G6: 4,9 * PRF # H4: 6,9 => SOL * DIS # H4: 7 => CTR => H4: 6,9 * DIS # A6: 6 => CTR => A6: 8,9 * DIS # G9: 3 => CTR => G9: 1,9 * DIS # E9: 8 => CTR => E9: 1,3 * DIS # D9: 1,2 => CTR => D9: 8 * DIS # F5: 4,9 => CTR => F5: 1,2 * DIS # G9: 1,3 => CTR => G9: 9 * PRF # G9: 9 => SOL * CNT 25 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B2: 4 => SOL * STA B2: 4 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .8......9...328..71....764..1...3.....7...8.....5...2..267....43..496...4......5. | initial |
| 785...239...32851713295764821...3..55.7...8.3..35...21.267.5..435.496..247.....56 | autosolve |
| 785164239649328517132957648214683795597241863863579421926715384358496172471832956 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) A2: 6,9 C2: 4,9 D1: 1,6 F1: 1,4 D4: 6,8 F6: 4,9 H5: 6,9 A7: 8,9 C8: 1,8 C9: 1,9 E7: 1,3 F9: 1,2 G7: 1,3 H7: 8,9 G8: 1,7 H8: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C8,C9: 1.. / C8 = 1 => 0 pairs (X) / C9 = 1 => 0 pairs (_) E7,G7: 1.. / E7 = 1 => 17 pairs (_) / G7 = 1 => 0 pairs (X) C8,G8: 1.. / C8 = 1 => 0 pairs (X) / G8 = 1 => 0 pairs (_) D5,F5: 2.. / D5 = 2 => 16 pairs (_) / F5 = 2 => 0 pairs (X) D9,F9: 2.. / D9 = 2 => 0 pairs (X) / F9 = 2 => 16 pairs (_) D5,D9: 2.. / D5 = 2 => 16 pairs (_) / D9 = 2 => 0 pairs (X) F5,F9: 2.. / F5 = 2 => 0 pairs (X) / F9 = 2 => 16 pairs (_) E7,E9: 3.. / E7 = 3 => 0 pairs (X) / E9 = 3 => 17 pairs (_) G7,G9: 3.. / G7 = 3 => 17 pairs (_) / G9 = 3 => 0 pairs (X) E7,G7: 3.. / E7 = 3 => 0 pairs (X) / G7 = 3 => 17 pairs (_) E9,G9: 3.. / E9 = 3 => 17 pairs (_) / G9 = 3 => 0 pairs (X) B2,C2: 4.. / B2 = 4 => 0 pairs (*) / C2 = 4 => 0 pairs (X) E1,F1: 4.. / E1 = 4 => 0 pairs (X) / F1 = 4 => 19 pairs (_) G4,G6: 4.. / G4 = 4 => 18 pairs (_) / G6 = 4 => 0 pairs (*) C2,C4: 4.. / C2 = 4 => 17 pairs (_) / C4 = 4 => 0 pairs (*) A2,B2: 6.. / A2 = 6 => 17 pairs (_) / B2 = 6 => 0 pairs (X) D1,E1: 6.. / D1 = 6 => 0 pairs (X) / E1 = 6 => 21 pairs (_) H4,H5: 6.. / H4 = 6 => 0 pairs (X) / H5 = 6 => 20 pairs (_) A2,A6: 6.. / A2 = 6 => 17 pairs (_) / A6 = 6 => 0 pairs (X) E4,E6: 7.. / E4 = 7 => 0 pairs (X) / E6 = 7 => 0 pairs (_) G8,H8: 7.. / G8 = 7 => 0 pairs (X) / H8 = 7 => 0 pairs (_) E6,G6: 7.. / E6 = 7 => 0 pairs (*) / G6 = 7 => 0 pairs (X) H4,H8: 7.. / H4 = 7 => 0 pairs (X) / H8 = 7 => 0 pairs (_) C4,A6: 8.. / C4 = 8 => 0 pairs (X) / A6 = 8 => 0 pairs (_) A7,C8: 8.. / A7 = 8 => 0 pairs (X) / C8 = 8 => 0 pairs (_) D9,E9: 8.. / D9 = 8 => 19 pairs (_) / E9 = 8 => 0 pairs (X) H7,H8: 8.. / H7 = 8 => 0 pairs (*) / H8 = 8 => 0 pairs (X) A6,E6: 8.. / A6 = 8 => 0 pairs (*) / E6 = 8 => 0 pairs (X) A7,H7: 8.. / A7 = 8 => 0 pairs (X) / H7 = 8 => 0 pairs (_) C8,H8: 8.. / C8 = 8 => 0 pairs (*) / H8 = 8 => 0 pairs (X) A6,A7: 8.. / A6 = 8 => 0 pairs (*) / A7 = 8 => 0 pairs (X) C4,C8: 8.. / C4 = 8 => 0 pairs (X) / C8 = 8 => 0 pairs (_) D4,D9: 8.. / D4 = 8 => 0 pairs (X) / D9 = 8 => 19 pairs (_) F5,F6: 9.. / F5 = 9 => 0 pairs (X) / F6 = 9 => 18 pairs (_) A7,C9: 9.. / A7 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) H7,G9: 9.. / H7 = 9 => 0 pairs (X) / G9 = 9 => 0 pairs (_) A7,H7: 9.. / A7 = 9 => 0 pairs (*) / H7 = 9 => 0 pairs (X) C9,G9: 9.. / C9 = 9 => 0 pairs (X) / G9 = 9 => 0 pairs (_) * DURATION: 0:01:05.696076 START: 07:36:02.919310 END: 07:37:08.615386 2017-05-01 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,C2,C8,C9,D1,D4,E7,F1,F6,F9,G7,G8,H5,H7,H8) * 785...239...32851713295764821...3..55.7...8.3..35...21.267.5..435.496..247.....56 * PAIR A2: 6,9 BLK 1 B2: 6,9,4 # reduction candidate for 6,9 B2: 4 => SOLVED * 785164239649328517132957648214683795597241863863579421926715384358496172471832956 B2: 6,9 # 17 pairs * PAIR A2: 6,9 COL A A6: 6,9,8 # reduction candidate for 6,9 A6: 6,9 => CTR * 785...239...3285171329576482186.3..55.7...863..358.7218267.5.9435.496..247.....56 A6: 8 => SOLVED * 785164239649328517132957648214683795597241863863579421926715384358496172471832956 * PAIR C2: 4,9 BLK 1 B2: 4,9,6 # reduction candidate for 4,9 B2: 6 => CTR * 785...239.6432851713295764821...3..55.7...8.36.358.7218267.5.9435.496..247.....56 B2: 4,9 # 17 pairs * PAIR C2: 4,9 COL C C4: 4,9,8 # reduction candidate for 4,9 C4: 4,9 => SOLVED * 785164239649328517132957648214683795597241863863579421926715384358496172471832956 C4: 8 => CTR * 785...239..43285171329576482186.3..55.7...863..358.7218267.5.9435.496..247.....56 * PAIR D1: 1,6 BLK 2 E1: 1,6,4 # reduction candidate for 1,6 E1: 4 => CTR * 785641239...32851713295764821.8.3..55.7...8.38.35...219267.5.843584961724712...56 E1: 1,6 # 19 pairs * PAIR D1: 1,6 COL D D5: 1,6,2 # reduction candidate for 1,6 D5: 1,6 => CTR * 785..4239...32851713295764821.8.39.5597.428638635794219267.5..435.496..247.281356 D5: 2 # 16 pairs * PAIR F1: 1,4 BLK 2 E1: 1,4,6 # reduction candidate for 1,4 E1: 1,4 => CTR * 7856..239...32851713295764821.8.3..55.7...8.38.35...219267.5.843584961724712...56 E1: 6 # 21 pairs * PAIR F1: 1,4 COL F F5: 1,4,2,9 # reduction candidate for 1,4 F5: 1,4 # 19 pairs F5: 2,9 # 17 pairs * PAIR D4: 6,8 BLK 5 E4: 6,8,4,7 # reduction candidate for 6,8 E4: 6,8 => SOLVED * 785164239649328517132957648214683795597241863863579421926715384358496172471832956 E4: 4,7 # 17 pairs E6: 6,8,4,7 # reduction candidate for 6,8 E6: 6,8 => CTR * 785...239...32851713295764821..734.55.72..8.3..35..721926715384358496172471832956 E6: 4,7 => SOLVED * 785164239649328517132957648214683795597241863863579421926715384358496172471832956 * PAIR F6: 4,9 BLK 5 F5: 4,9,1,2 # reduction candidate for 4,9 F5: 4,9 => CTR * 785..1239..43285171329576482186.3..55.721.8.3..35...21.267351.4351496782479.82356 F5: 1,2 # 19 pairs * PAIR F6: 4,9 ROW 6 B6: 4,9,6 # reduction candidate for 4,9 B6: 4,9 => CTR * 785...239..43285171329576482198734.55.7...8.3..35..721.267.5..435.496172471..2956 B6: 6 # 18 pairs G6: 4,9,7 # reduction candidate for 4,9 G6: 4,9 => SOLVED * 785164239649328517132957648214683795597241863863579421926715384358496172471832956 G6: 7 => CTR * 785...239..4328517132957648219.734655.72..8938.35.9721926715..435.496172471..2956 * PAIR H5: 6,9 BLK 6 H4: 6,9,7 # reduction candidate for 6,9 H4: 6,9 => SOLVED * 785164239649328517132957648214683795597241863863579421926715384358496172471832956 H4: 7 => CTR * 785...239..4328517132957648218643975547.19863..357..21.267.5.9435.496782479....56 * PAIR H5: 6,9 ROW 5 B5: 6,9,4 # reduction candidate for 6,9 B5: 6,9 # 21 pairs B5: 4 # 19 pairs * PAIR A7: 8,9 COL A A6: 8,9,6 # reduction candidate for 8,9 A6: 6 => CTR * 785...239...3285171329576482186.3..55.7...8636.358.7218267.5.9435.496..247.....56 A6: 8,9 # 17 pairs * PAIR C9: 1,9 ROW 9 G9: 1,9,3 # reduction candidate for 1,9 G9: 3 => CTR * 785...239..43285171329576482186.39755.7...863..35...21.267.5.9435.496.82479...356 G9: 1,9 # 17 pairs * PAIR E7: 1,3 BLK 8 E9: 1,3,8 # reduction candidate for 1,3 E9: 8 => CTR * 785...239..43285171329576482186.3.755.7...863..357..21826735194351496782479.8.356 E9: 1,3 # 19 pairs * PAIR F9: 1,2 BLK 8 D9: 1,2,8 # reduction candidate for 1,2 D9: 1,2 => CTR * 785...239...32851713295764821.8.3..55.7...8.38.35...219267.5.843584961724712...56 D9: 8 # 19 pairs * PAIR F9: 1,2 COL F F5: 1,2,4,9 # reduction candidate for 1,2 F5: 4,9 => CTR * 785..1239..43285171329576482186.3..55.721.8.3..35...21.267351.4351496782479.82356 F5: 1,2 # 19 pairs * PAIR G7: 1,3 BLK 9 G9: 1,3,9 # reduction candidate for 1,3 G9: 1,3 => CTR * 785...239..43285171329576482186.39755.7...863..35...21.267.5.9435.496.82479....56 G9: 9 => SOLVED * 785164239649328517132957648214683795597241863863579421926715384358496172471832956 * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-651186-base-pr-000.dot * REASONING * PRF # B2: 4 => SOL * DIS # A6: 6,9 => CTR => A6: 8 * PRF # A6: 8 => SOL * DIS # B2: 6 => CTR => B2: 4,9 * PRF # C4: 4,9 => SOL * DIS # C4: 8 => CTR => C4: 4,9 * DIS # E1: 4 => CTR => E1: 1,6 * DIS # D5: 1,6 => CTR => D5: 2 * DIS # E1: 1,4 => CTR => E1: 6 * PRF # E4: 6,8 => SOL * DIS # E6: 6,8 => CTR => E6: 4,7 * PRF # E6: 4,7 => SOL * DIS # F5: 4,9 => CTR => F5: 1,2 * DIS # B6: 4,9 => CTR => B6: 6 * PRF # G6: 4,9 => SOL * DIS # G6: 7 => CTR => G6: 4,9 * PRF # H4: 6,9 => SOL * DIS # H4: 7 => CTR => H4: 6,9 * DIS # A6: 6 => CTR => A6: 8,9 * DIS # G9: 3 => CTR => G9: 1,9 * DIS # E9: 8 => CTR => E9: 1,3 * DIS # D9: 1,2 => CTR => D9: 8 * DIS # F5: 4,9 => CTR => F5: 1,2 * DIS # G9: 1,3 => CTR => G9: 9 * PRF # G9: 9 => SOL * CNT 25 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,C2,C8,C9,D1,D4,E7,F1,F6,F9,G7,G8,H5,H7,H8) * 785...239...32851713295764821...3..55.7...8.3..35...21.267.5..435.496..247.....56 * PAIR A2: 6,9 BLK 1 B2: 6,9,4 # reduction candidate for 6,9 B2: 4 => SOLVED * 785164239649328517132957648214683795597241863863579421926715384358496172471832956 * DURATION: 0:00:02.983297 START: 07:37:50.056652 END: 07:37:53.039949 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-651186-base-pr-001.dot * REASONING * PRF # B2: 4 => SOL * STA B2: 4 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokus.de/651186.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: 785...239...32851713295764821...3..55.7...8.3..35...21.267.5..435.496..247.....56 A2: 6,9 B2: 4,6,9 # reduction candidate for 6,9 B2: 4 => SOLVED * 785164239649328517132957648214683795597241863863579421926715384358496172471832956 * SOLVED! -------------------------------------------------- * AUTO .. A1 = 7 # set value H2 = 1 # set value H1: 3 # naked single G2: 5 # naked single D3 = 9 # set value E3 = 5 # set value B3: 3 # naked single I3 = 8 # set value I9 = 6 # set value I4: 5 # naked single G1: 2.. # hidden single F7: 5.. # hidden single C3: 2.. # hidden single I8: 2.. # hidden single G1 = 2 # set value H1 = 3 # set value G2 = 5 # set value B3 = 3 # set value C3: 2 # naked single C3 = 2 # set value I4 = 5 # set value F7 = 5 # set value I8 = 2 # set value C1: 5.. # hidden single C6: 3.. # hidden single I5: 3.. # hidden single A5: 5.. # hidden single C1 = 5 # set value A5 = 5 # set value I5 = 3 # set value I6: 1 # naked single C6 = 3 # set value I6 = 1 # set value A4: 2.. # hidden single B8: 5.. # hidden single A4 = 2 # set value B8 = 5 # set value B9: 7.. # hidden single B9 = 7 # set value E7,G7: 1,3.. => E7,G7 != 8,9 # hidden pair Q8: 8.. = D9,E9: 8.. => C9 != 8 |:step:| 00 -------------------------------------------------- pair quad E7: 1,3 G7: 1,3 E9: 1,3,8 G9: 1,3,9 * FORCE VALUE:: G9 = 9 G9 = 9 # set value H7: 8 # naked single C9: 1 # naked single A7: 9.. # hidden single G7: 3.. # hidden single E9: 3.. # hidden single |:step:| 01 -------------------------------------------------- highlight 7 observe that E4,E6 and G4,G6 are symmetrical G4,G6,H4,H5 => G4,G5 = 4,9 or G=4 or G5 = 4 G9 != 9 leads to a contradiction very fast. -------------------------------------------------- * DISABLE VALUE:: G9 != 9 * DISABLE VALUE:: G8 != 1 G8: 7 # naked single * DISABLE VALUE:: G6 != 7 * DISABLE VALUE:: G4 != 7 * DISABLE VALUE:: H4 != 9 * DISABLE VALUE:: H4 != 6 H4: 7 # naked single * DISABLE VALUE:: E6 != 8 * DISABLE VALUE:: E6 != 4 * DISABLE VALUE:: E6 != 6 E6: 7 # naked single * DISABLE VALUE:: A6 != 9 * DISABLE VALUE:: A6 != 6 A6: 8 # naked single * DISABLE VALUE:: A7 != 8 A7: 9 # naked single * DISABLE VALUE:: C9 != 9 C9: 1 # naked single * DISABLE VALUE:: C8 != 1 C8: 8 # naked single * DISABLE VALUE:: H8 != 8 H8: 7 # naked single * ANALYZE .. G8,H8 = 7 => CTR G8,H8 = 7 => CTR |:step:| 02 --------------------------------------------------
Solution
position: 785164239649328517132957648214683795597241863863579421926715384358496172471832956 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 # B2: 6,9 => UNS * PRF # B2: 4 => SOL * DIS # A6: 6,9 => CTR => A6: 8 * PRF # A6: 8 => SOL * INC # B2: 4,9 => UNS * DIS # B2: 6 => CTR => B2: 4,9 * PRF # C4: 4,9 => SOL * DIS # C4: 8 => CTR => C4: 4,9 * INC # E1: 1,6 => UNS * DIS # E1: 4 => CTR => E1: 1,6 * DIS # D5: 1,6 => CTR => D5: 2 * INC # D5: 2 => UNS * DIS # E1: 1,4 => CTR => E1: 6 * INC # E1: 6 => UNS * INC # F5: 1,4 => UNS * INC # F5: 2,9 => UNS * PRF # E4: 6,8 => SOL * INC # E4: 4,7 => UNS * DIS # E6: 6,8 => CTR => E6: 4,7 * PRF # E6: 4,7 => SOL * DIS # F5: 4,9 => CTR => F5: 1,2 * INC # F5: 1,2 => UNS * DIS # B6: 4,9 => CTR => B6: 6 * INC # B6: 6 => UNS * PRF # G6: 4,9 => SOL * DIS # G6: 7 => CTR => G6: 4,9 * PRF # H4: 6,9 => SOL * DIS # H4: 7 => CTR => H4: 6,9 * INC # B5: 6,9 => UNS * INC # B5: 4 => UNS * INC # A6: 8,9 => UNS * DIS # A6: 6 => CTR => A6: 8,9 * INC # G9: 1,9 => UNS * DIS # G9: 3 => CTR => G9: 1,9 * INC # E9: 1,3 => UNS * DIS # E9: 8 => CTR => E9: 1,3 * DIS # D9: 1,2 => CTR => D9: 8 * INC # D9: 8 => UNS * INC # F5: 1,2 => UNS * DIS # F5: 4,9 => CTR => F5: 1,2 * DIS # G9: 1,3 => CTR => G9: 9 * PRF # G9: 9 => SOL * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 6,9 => UNS * PRF # B2: 4 => SOL * STA B2: 4 * CNT 2 HDP CHAINS / 2 HYP OPENED