Analysis of zz-sudoku-de-626776-base.sdk
Contents
Original Sudoku
level: medium
position: .2.....3...9...2..48.276.91.9.8.7.2.1.......3.7.6.4.5.65.489.12..8...7...3.....8. initial
Autosolve
position: .2.....3...9...2..483276591395817.2.1.....8738726341596574893129.8...7..23.7..98. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E1: 9 => CTR => E1: 4,5 * DIS # E5: 2 => CTR => E5: 5,9 * DIS # D1: 1 => CTR => D1: 5,9 * DIS # E5: 2,5 => CTR => E5: 9 * PRF # F8: 2,5 => SOL * PRF # I8: 4,6 => SOL * DIS # E8: 5,6 => CTR => E8: 2 * PRF # I9: 5,6 => SOL * DIS # I9: 4 => CTR => I9: 5,6 * DIS # F1: 1,5 => CTR => F1: 8 * PRF # I8: 4,6 => SOL * CNT 11 HDP CHAINS / 25 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E1: 9 => CTR => E1: 4,5 * PRF E1: 4,5 # I8: 4,6 => SOL * STA E1: 4,5 + I8: 4,6 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2.....3...9...2..48.276.91.9.8.7.2.1.......3.7.6.4.5.65.489.12..8...7...3.....8. | initial |
| .2.....3...9...2..483276591395817.2.1.....8738726341596574893129.8...7..23.7..98. | autosolve |
| 521948637769153248483276591395817426146592873872634159657489312918325764234761985 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) A1: 5,7 C1: 1,6 A2: 5,7 B2: 1,6 E2: 4,5 G1: 4,6 I1: 7,8 H2: 4,6 I2: 7,8 B5: 4,6 C5: 4,6 D5: 5,9 F5: 2,5 G4: 4,6 I4: 4,6 B8: 1,4 C9: 1,4 E9: 5,6 F9: 1,5 H8: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,B2: 1.. / C1 = 1 => 0 pairs (*) / B2 = 1 => 0 pairs (X) B8,C9: 1.. / B8 = 1 => 0 pairs (*) / C9 = 1 => 0 pairs (X) C9,F9: 1.. / C9 = 1 => 0 pairs (X) / F9 = 1 => 0 pairs (_) B2,B8: 1.. / B2 = 1 => 0 pairs (X) / B8 = 1 => 0 pairs (_) C1,C9: 1.. / C1 = 1 => 0 pairs (*) / C9 = 1 => 0 pairs (X) E5,F5: 2.. / E5 = 2 => 0 pairs (X) / F5 = 2 => 20 pairs (_) E8,F8: 2.. / E8 = 2 => 20 pairs (_) / F8 = 2 => 0 pairs (X) E5,E8: 2.. / E5 = 2 => 0 pairs (X) / E8 = 2 => 20 pairs (_) F5,F8: 2.. / F5 = 2 => 20 pairs (_) / F8 = 2 => 0 pairs (X) D2,F2: 3.. / D2 = 3 => 21 pairs (_) / F2 = 3 => 19 pairs (_) D8,F8: 3.. / D8 = 3 => 19 pairs (_) / F8 = 3 => 21 pairs (_) D2,D8: 3.. / D2 = 3 => 21 pairs (_) / D8 = 3 => 19 pairs (_) F2,F8: 3.. / F2 = 3 => 19 pairs (_) / F8 = 3 => 21 pairs (_) E1,E2: 4.. / E1 = 4 => 0 pairs (*) / E2 = 4 => 0 pairs (X) G1,H2: 4.. / G1 = 4 => 0 pairs (X) / H2 = 4 => 0 pairs (_) B5,C5: 4.. / B5 = 4 => 0 pairs (*) / C5 = 4 => 0 pairs (X) G4,I4: 4.. / G4 = 4 => 0 pairs (*) / I4 = 4 => 0 pairs (X) B8,C9: 4.. / B8 = 4 => 0 pairs (X) / C9 = 4 => 0 pairs (_) E1,G1: 4.. / E1 = 4 => 0 pairs (*) / G1 = 4 => 0 pairs (X) E2,H2: 4.. / E2 = 4 => 0 pairs (X) / H2 = 4 => 0 pairs (_) C9,I9: 4.. / C9 = 4 => 0 pairs (*) / I9 = 4 => 0 pairs (X) B5,B8: 4.. / B5 = 4 => 0 pairs (*) / B8 = 4 => 0 pairs (X) C5,C9: 4.. / C5 = 4 => 0 pairs (X) / C9 = 4 => 0 pairs (_) G1,G4: 4.. / G1 = 4 => 0 pairs (X) / G4 = 4 => 0 pairs (_) H2,H8: 4.. / H2 = 4 => 0 pairs (*) / H8 = 4 => 0 pairs (X) A1,A2: 5.. / A1 = 5 => 18 pairs (_) / A2 = 5 => 0 pairs (X) I8,I9: 5.. / I8 = 5 => 23 pairs (_) / I9 = 5 => 0 pairs (*) C1,B2: 6.. / C1 = 6 => 0 pairs (X) / B2 = 6 => 0 pairs (_) G1,H2: 6.. / G1 = 6 => 0 pairs (*) / H2 = 6 => 0 pairs (X) B5,C5: 6.. / B5 = 6 => 0 pairs (X) / C5 = 6 => 0 pairs (_) G4,I4: 6.. / G4 = 6 => 0 pairs (X) / I4 = 6 => 0 pairs (_) E8,E9: 6.. / E8 = 6 => 0 pairs (X) / E9 = 6 => 21 pairs (_) C1,G1: 6.. / C1 = 6 => 0 pairs (X) / G1 = 6 => 0 pairs (_) B2,H2: 6.. / B2 = 6 => 0 pairs (*) / H2 = 6 => 0 pairs (X) E9,I9: 6.. / E9 = 6 => 21 pairs (_) / I9 = 6 => 0 pairs (X) B2,B5: 6.. / B2 = 6 => 0 pairs (*) / B5 = 6 => 0 pairs (X) C1,C5: 6.. / C1 = 6 => 0 pairs (X) / C5 = 6 => 0 pairs (_) G1,G4: 6.. / G1 = 6 => 0 pairs (*) / G4 = 6 => 0 pairs (X) H2,H8: 6.. / H2 = 6 => 0 pairs (X) / H8 = 6 => 0 pairs (_) A1,A2: 7.. / A1 = 7 => 0 pairs (X) / A2 = 7 => 18 pairs (_) I1,I2: 7.. / I1 = 7 => 18 pairs (_) / I2 = 7 => 0 pairs (X) A1,I1: 7.. / A1 = 7 => 0 pairs (X) / I1 = 7 => 18 pairs (_) A2,I2: 7.. / A2 = 7 => 18 pairs (_) / I2 = 7 => 0 pairs (X) F1,F2: 8.. / F1 = 8 => 18 pairs (_) / F2 = 8 => 0 pairs (X) I1,I2: 8.. / I1 = 8 => 0 pairs (X) / I2 = 8 => 18 pairs (_) F1,I1: 8.. / F1 = 8 => 18 pairs (_) / I1 = 8 => 0 pairs (X) F2,I2: 8.. / F2 = 8 => 0 pairs (X) / I2 = 8 => 18 pairs (_) D1,E1: 9.. / D1 = 9 => 22 pairs (_) / E1 = 9 => 0 pairs (X) D5,E5: 9.. / D5 = 9 => 0 pairs (X) / E5 = 9 => 22 pairs (_) D1,D5: 9.. / D1 = 9 => 22 pairs (_) / D5 = 9 => 0 pairs (X) E1,E5: 9.. / E1 = 9 => 0 pairs (X) / E5 = 9 => 22 pairs (_) * DURATION: 0:01:24.893511 START: 07:25:02.274817 END: 07:26:27.168328 2017-05-01 * CP COUNT: (51) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,B2,B5,B8,C1,C5,C9,D5,E2,E9,F5,F9,G1,G4,H2,H8,I1,I2,I4) * .2.....3...9...2..483276591395817.2.1.....8738726341596574893129.8...7..23.7..98. * PAIR E2: 4,5 BLK 2 E1: 4,5,9 # reduction candidate for 4,5 E1: 9 => CTR * .2..9.43...9.4.26.4832765913958176241649..873872634159657489312948...7..23.7..98. E1: 4,5 # 22 pairs * PAIR D5: 5,9 BLK 5 E5: 5,9,2 # reduction candidate for 5,9 E5: 2 => CTR * .2..9.43...9.4.26.483276591395817624164925873872634159657489312948...7..23.7..98. E5: 5,9 # 20 pairs * PAIR D5: 5,9 COL D D1: 5,9,1 # reduction candidate for 5,9 D1: 1 => CTR * .2.19.43..19.4.26.483276591395817624164...8738726341596574893129.8...7..23.7..98. D1: 5,9 # 24 pairs * PAIR F5: 2,5 BLK 5 E5: 2,5,9 # reduction candidate for 2,5 E5: 2,5 => CTR * .2..9.43...9.4.26.4832765913958176241649..873872634159657489312948...7..23.7..98. E5: 9 # 22 pairs * PAIR F5: 2,5 COL F F8: 2,5,1,3 # reduction candidate for 2,5 F8: 2,5 => SOLVED * 521948637769153248483276591395817426146592873872634159657489312918325764234761985 F8: 1,3 # 21 pairs * PAIR I4: 4,6 COL I I8: 4,6,5 # reduction candidate for 4,6 I8: 4,6 => SOLVED * 521948637769153248483276591395817426146592873872634159657489312918325764234761985 I8: 5 # 23 pairs I9: 4,6,5 # reduction candidate for 4,6 I9: 4,6 # 23 pairs * PAIR E9: 5,6 BLK 8 E8: 5,6,2 # reduction candidate for 5,6 E8: 5,6 => CTR * .21.98.3...9...2..483276591395817.2.1...258738726341596574893129.8..27..23.7.198. E8: 2 # 20 pairs * PAIR E9: 5,6 ROW 9 I9: 5,6,4 # reduction candidate for 5,6 I9: 5,6 => SOLVED * 521948637769153248483276591395817426146592873872634159657489312918325764234761985 I9: 4 => CTR * .2.....3...9...24.4832765913958174261.4..2873872634159657489312948.2.765231765984 * PAIR F9: 1,5 BLK 8 D8: 1,5,3 # reduction candidate for 1,5 D8: 1,5 # 21 pairs F8: 1,5,2,3 # reduction candidate for 1,5 F8: 1,5 # 20 pairs * PAIR F9: 1,5 COL F F1: 1,5,8 # reduction candidate for 1,5 F1: 1,5 => CTR * 72.....385.9348267483276591395817624164..2873872634159657489312948..37..23.7..98. F1: 8 # 18 pairs F2: 1,5,3,8 # reduction candidate for 1,5 F2: 1,5 # 20 pairs * PAIR H8: 4,6 BLK 9 I8: 4,6,5 # reduction candidate for 4,6 I8: 4,6 => SOLVED * 521948637769153248483276591395817426146592873872634159657489312918325764234761985 I8: 5 # 23 pairs I9: 4,6,5 # reduction candidate for 4,6 I9: 4,6 # 23 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-626776-base-pr-000.dot * REASONING * DIS # E1: 9 => CTR => E1: 4,5 * DIS # E5: 2 => CTR => E5: 5,9 * DIS # D1: 1 => CTR => D1: 5,9 * DIS # E5: 2,5 => CTR => E5: 9 * PRF # F8: 2,5 => SOL * PRF # I8: 4,6 => SOL * DIS # E8: 5,6 => CTR => E8: 2 * PRF # I9: 5,6 => SOL * DIS # I9: 4 => CTR => I9: 5,6 * DIS # F1: 1,5 => CTR => F1: 8 * PRF # I8: 4,6 => SOL * CNT 11 HDP CHAINS / 25 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,B2,B5,B8,C1,C5,C9,D5,E2,E9,F5,F9,G1,G4,H2,H8,I1,I2,I4) * .2.....3...9...2..483276591395817.2.1.....8738726341596574893129.8...7..23.7..98. * PAIR E2: 4,5 BLK 2 E1: 4,5,9 # reduction candidate for 4,5 E1: 9 => CTR * .2..9.43...9.4.26.4832765913958176241649..873872634159657489312948...7..23.7..98. * PAIR I4: 4,6 COL I I8: 4,6,5 # reduction candidate for 4,6 I8: 4,6 => SOLVED * 521948637769153248483276591395817426146592873872634159657489312918325764234761985 * DURATION: 0:00:05.076194 START: 07:26:52.760719 END: 07:26:57.836913 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-626776-base-pr-001.dot * REASONING * DIS # E1: 9 => CTR => E1: 4,5 * PRF E1: 4,5 # I8: 4,6 => SOL * STA E1: 4,5 + I8: 4,6 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokus.de/626776.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: .2.....3...9...2..483276591395817.2.1.....8738726341596574893129.8...7..23.7..98. A1: 5,7 C1: 1,6 A2: 5,7 B2: 1,6 E2: 4,5 E1: 4,5,9 # reduction candidate for 4,5 E1: 9 => CTR * .2..9.43...9.4.26.4832765913958176241649..873872634159657489312948...7..23.7..98. G1: 4,6 I1: 7,8 H2: 4,6 I2: 7,8 B5: 4,6 C5: 4,6 G4: 4,6 I4: 4,6 I8: 4,5,6 # reduction candidate for 4,6 I8: 4,6 => SOLVED * 521948637769153248483276591395817426146592873872634159657489312918325764234761985 * SOLVED! -------------------------------------------------- * AUTO .. C3 = 3 # set value C6: 2 # naked single G3 = 5 # set value G5 = 8 # set value I6: 9 # naked single H5 = 7 # set value A6 = 8 # set value C6 = 2 # set value I6 = 9 # set value G6: 1 # naked single C7 = 7 # set value G7 = 3 # set value D9 = 7 # set value A4: 3.. # hidden single G9: 9.. # hidden single E6: 3.. # hidden single A8: 9.. # hidden single A4 = 3 # set value E6 = 3 # set value G6 = 1 # set value A8 = 9 # set value A9: 2 # naked single A9 = 2 # set value G9 = 9 # set value E4: 1.. # hidden single E4 = 1 # set value C4: 5.. # hidden single C4 = 5 # set value I1,I2: 7,8.. => I1,I2 != 4,6 # hidden pair * UNSOLVED! |:step:| 00 -------------------------------------------------- highlight 6 C1: 1,6 H2: 4,6 G4: 4,6 B5: 4,6 I8: 4,5,6 G1: 4,6 B2: 1,6 I4: 4,6 C5: 4,6 H8: 4,6 C1,H2,G4,B5,I8 = 6 => G1,B2,I4,C5,H8 != 6 C1 = 6 => C5 = 4 => H8 = 4 C5 = 4 => C9 != 4 => I9 = 4 H8,I9: 4 => CTR => C1 != 6 # forcing chain |:step:| 01 --------------------------------------------------
Solution
position: 521948637769153248483276591395817426146592873872634159657489312918325764234761985 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 # E1: 4,5 => UNS * DIS # E1: 9 => CTR => E1: 4,5 * INC # E5: 5,9 => UNS * DIS # E5: 2 => CTR => E5: 5,9 * INC # D1: 5,9 => UNS * DIS # D1: 1 => CTR => D1: 5,9 * DIS # E5: 2,5 => CTR => E5: 9 * INC # E5: 9 => UNS * PRF # F8: 2,5 => SOL * INC # F8: 1,3 => UNS * PRF # I8: 4,6 => SOL * INC # I8: 5 => UNS * INC # I9: 4,6 => UNS * DIS # E8: 5,6 => CTR => E8: 2 * INC # E8: 2 => UNS * PRF # I9: 5,6 => SOL * DIS # I9: 4 => CTR => I9: 5,6 * INC # D8: 1,5 => UNS * INC # F8: 1,5 => UNS * DIS # F1: 1,5 => CTR => F1: 8 * INC # F1: 8 => UNS * INC # F2: 1,5 => UNS * PRF # I8: 4,6 => SOL * INC # I8: 5 => UNS * INC # I9: 4,6 => UNS * CNT 25 HDP CHAINS / 25 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E1: 4,5 => UNS * DIS # E1: 9 => CTR => E1: 4,5 * PRF E1: 4,5 # I8: 4,6 => SOL * STA E1: 4,5 + I8: 4,6 * CNT 3 HDP CHAINS / 3 HYP OPENED