Analysis of zz-knacker-132282-base.sdk
Contents
Original Sudoku
level: medium
position: 1.........5....89..36..4...6..7.3..87.......92.561.37..4..7..1..682....73.......5 initial
Autosolve
position: 129..7...457...89.836..475.6.47.3.287.3....692.561.374.42.7..1..682.1..7371...285 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D5: 5,8 => CTR => D5: 4 * PRF # D5: 4 => SOL * PRF # D7: 5,8 => SOL * DIS # D7: 3 => CTR => D7: 5,8 * DIS # E5: 5,8 => CTR => E5: 2,4 * PRF # E2: 2,6 => SOL * DIS # E2: 3 => CTR => E2: 2,6 * PRF # D7: 5,8 => SOL * DIS # D7: 3 => CTR => D7: 5,8 * PRF # F5: 5,8 => SOL * DIS # F5: 2 => CTR => F5: 5,8 * DIS # D7: 3,5 => CTR => D7: 8 * PRF # D7: 8 => SOL * PRF # E9: 4,9 => SOL * DIS # E9: 6 => CTR => E9: 4,9 * DIS # E9: 6,9 => CTR => E9: 4 * PRF # E9: 4 => SOL * CNT 17 HDP CHAINS / 18 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D5: 5,8 => CTR => D5: 4 * PRF D5: 4 => SOL * STA D5: 4 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.........5....89..36..4...6..7.3..87.......92.561.37..4..7..1..682....73.......5 | initial |
| 129..7...457...89.836..475.6.47.3.287.3....692.561.374.42.7..1..682.1..7371...285 | autosolve |
| 129587436457362891836194752694753128713428569285619374942875613568231947371946285 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (28) D1: 5,8 E1: 5,8 D2: 1,3 F2: 2,6 D3: 1,9 E3: 2,9 G1: 4,6 H1: 3,4 I1: 3,6 I2: 1,2 I3: 1,2 B4: 1,9 B5: 1,8 B6: 8,9 E4: 5,9 F6: 8,9 G4: 1,5 G5: 1,5 A7: 5,9 A8: 5,9 F7: 5,8 E8: 3,5 D9: 4,9 F9: 6,9 G7: 6,9 I7: 3,6 G8: 4,9 H8: 3,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,D3: 1.. / D2 = 1 => 0 pairs (X) / D3 = 1 => 0 pairs (_) I2,I3: 1.. / I2 = 1 => 0 pairs (*) / I3 = 1 => 0 pairs (X) B4,B5: 1.. / B4 = 1 => 0 pairs (X) / B5 = 1 => 0 pairs (_) G4,G5: 1.. / G4 = 1 => 0 pairs (*) / G5 = 1 => 0 pairs (X) D2,I2: 1.. / D2 = 1 => 0 pairs (X) / I2 = 1 => 0 pairs (_) D3,I3: 1.. / D3 = 1 => 0 pairs (*) / I3 = 1 => 0 pairs (X) B4,G4: 1.. / B4 = 1 => 0 pairs (X) / G4 = 1 => 0 pairs (_) B5,G5: 1.. / B5 = 1 => 0 pairs (*) / G5 = 1 => 0 pairs (X) I2,I3: 2.. / I2 = 2 => 0 pairs (X) / I3 = 2 => 0 pairs (_) E5,F5: 2.. / E5 = 2 => 0 pairs (*) / F5 = 2 => 0 pairs (X) E3,I3: 2.. / E3 = 2 => 0 pairs (X) / I3 = 2 => 0 pairs (_) F2,F5: 2.. / F2 = 2 => 0 pairs (*) / F5 = 2 => 0 pairs (X) D2,E2: 3.. / D2 = 3 => 0 pairs (*) / E2 = 3 => 0 pairs (X) H1,I1: 3.. / H1 = 3 => 0 pairs (*) / I1 = 3 => 0 pairs (X) D7,E8: 3.. / D7 = 3 => 0 pairs (X) / E8 = 3 => 0 pairs (_) I7,H8: 3.. / I7 = 3 => 0 pairs (*) / H8 = 3 => 0 pairs (X) D7,I7: 3.. / D7 = 3 => 0 pairs (X) / I7 = 3 => 0 pairs (_) E8,H8: 3.. / E8 = 3 => 0 pairs (*) / H8 = 3 => 0 pairs (X) D2,D7: 3.. / D2 = 3 => 0 pairs (*) / D7 = 3 => 0 pairs (X) E2,E8: 3.. / E2 = 3 => 0 pairs (X) / E8 = 3 => 0 pairs (_) H1,H8: 3.. / H1 = 3 => 0 pairs (*) / H8 = 3 => 0 pairs (X) I1,I7: 3.. / I1 = 3 => 0 pairs (X) / I7 = 3 => 0 pairs (_) G1,H1: 4.. / G1 = 4 => 0 pairs (*) / H1 = 4 => 0 pairs (X) D5,E5: 4.. / D5 = 4 => 0 pairs (*) / E5 = 4 => 0 pairs (X) D9,E9: 4.. / D9 = 4 => 0 pairs (X) / E9 = 4 => 0 pairs (_) G8,H8: 4.. / G8 = 4 => 0 pairs (X) / H8 = 4 => 0 pairs (_) D5,D9: 4.. / D5 = 4 => 0 pairs (*) / D9 = 4 => 0 pairs (X) E5,E9: 4.. / E5 = 4 => 0 pairs (X) / E9 = 4 => 0 pairs (_) G1,G8: 4.. / G1 = 4 => 0 pairs (*) / G8 = 4 => 0 pairs (X) H1,H8: 4.. / H1 = 4 => 0 pairs (X) / H8 = 4 => 0 pairs (_) D1,E1: 5.. / D1 = 5 => 28 pairs (_) / E1 = 5 => 0 pairs (X) G4,G5: 5.. / G4 = 5 => 0 pairs (X) / G5 = 5 => 0 pairs (_) A7,A8: 5.. / A7 = 5 => 0 pairs (X) / A8 = 5 => 0 pairs (_) E4,G4: 5.. / E4 = 5 => 0 pairs (*) / G4 = 5 => 0 pairs (X) A8,E8: 5.. / A8 = 5 => 0 pairs (*) / E8 = 5 => 0 pairs (X) F5,F7: 5.. / F5 = 5 => 0 pairs (X) / F7 = 5 => 0 pairs (_) E2,F2: 6.. / E2 = 6 => 0 pairs (*) / F2 = 6 => 0 pairs (X) G1,I1: 6.. / G1 = 6 => 0 pairs (X) / I1 = 6 => 0 pairs (_) E9,F9: 6.. / E9 = 6 => 0 pairs (X) / F9 = 6 => 0 pairs (_) G7,I7: 6.. / G7 = 6 => 0 pairs (*) / I7 = 6 => 0 pairs (X) E2,E9: 6.. / E2 = 6 => 0 pairs (*) / E9 = 6 => 0 pairs (X) F2,F9: 6.. / F2 = 6 => 0 pairs (X) / F9 = 6 => 0 pairs (_) G1,G7: 6.. / G1 = 6 => 0 pairs (X) / G7 = 6 => 0 pairs (_) I1,I7: 6.. / I1 = 6 => 0 pairs (*) / I7 = 6 => 0 pairs (X) D1,E1: 8.. / D1 = 8 => 0 pairs (X) / E1 = 8 => 28 pairs (_) B5,B6: 8.. / B5 = 8 => 0 pairs (X) / B6 = 8 => 0 pairs (_) D7,F7: 8.. / D7 = 8 => 0 pairs (*) / F7 = 8 => 0 pairs (X) B6,F6: 8.. / B6 = 8 => 0 pairs (*) / F6 = 8 => 0 pairs (X) E1,E5: 8.. / E1 = 8 => 28 pairs (_) / E5 = 8 => 0 pairs (X) D3,E3: 9.. / D3 = 9 => 0 pairs (X) / E3 = 9 => 0 pairs (_) B4,B6: 9.. / B4 = 9 => 0 pairs (*) / B6 = 9 => 0 pairs (X) E4,F6: 9.. / E4 = 9 => 0 pairs (X) / F6 = 9 => 0 pairs (_) A7,A8: 9.. / A7 = 9 => 0 pairs (*) / A8 = 9 => 0 pairs (X) G7,G8: 9.. / G7 = 9 => 0 pairs (X) / G8 = 9 => 0 pairs (_) B4,E4: 9.. / B4 = 9 => 0 pairs (*) / E4 = 9 => 0 pairs (X) B6,F6: 9.. / B6 = 9 => 0 pairs (X) / F6 = 9 => 0 pairs (_) A7,G7: 9.. / A7 = 9 => 0 pairs (*) / G7 = 9 => 0 pairs (X) A8,G8: 9.. / A8 = 9 => 0 pairs (X) / G8 = 9 => 0 pairs (_) D3,D9: 9.. / D3 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) F6,F9: 9.. / F6 = 9 => 0 pairs (*) / F9 = 9 => 0 pairs (X) * DURATION: 0:01:45.416986 START: 06:26:38.050651 END: 06:28:23.467637 2017-05-01 * CP COUNT: (60) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A8,B4,B5,B6,D1,D2,D3,D9,E1,E3,E4,E8,F2,F6,F7,F9,G1,G4,G5,G7,G8,H1,H8,I1,I2,I3,I7) * 129..7...457...89.836..475.6.47.3.287.3....692.561.374.42.7..1..682.1..7371...285 * PAIR D1: 5,8 COL D D5: 5,8,4 # reduction candidate for 5,8 D5: 5,8 => CTR * 129.874364573.689.836..475.6.47.3.287.3.42.692.561.374.42.75.1.5682319473714..285 D5: 4 => SOLVED * 129587436457362891836194752694753128713428569285619374942875613568231947371946285 D7: 5,8,3 # reduction candidate for 5,8 D7: 5,8 => SOLVED * 129587436457362891836194752694753128713428569285619374942875613568231947371946285 D7: 3 => CTR * 129..7...457...89.836..475.6.47.3.287.3....692.561.374.42378.16.68251.37371...285 * PAIR E1: 5,8 COL E E5: 5,8,2,4 # reduction candidate for 5,8 E5: 5,8 => CTR * 129..7...457...89.836..475.6.47.3.287.34.2.692.561.374.42.75.1.568231947371946285 E5: 2,4 # 29 pairs * PAIR F2: 2,6 BLK 2 E2: 2,6,3 # reduction candidate for 2,6 E2: 2,6 => SOLVED * 129587436457362891836194752694753128713428569285619374942875613568231947371946285 E2: 3 => CTR * 129..7...457.36892836.247516.47.3.287.3..2.692.561.374.4237..1..682.1..7371...285 * PAIR F7: 5,8 BLK 8 D7: 5,8,3 # reduction candidate for 5,8 D7: 5,8 => SOLVED * 129587436457362891836194752694753128713428569285619374942875613568231947371946285 D7: 3 => CTR * 129..7...457...89.836..475.6.47.3.287.3....692.561.374.42378.16.68251.37371...285 * PAIR F7: 5,8 COL F F5: 5,8,2 # reduction candidate for 5,8 F5: 5,8 => SOLVED * 129587436457362891836194752694753128713428569285619374942875613568231947371946285 F5: 2 => CTR * 129..74364573.6891836194752694753.287.3..2.692.561.374.42.75.1.568231947371...285 * PAIR E8: 3,5 BLK 8 D7: 3,5,8 # reduction candidate for 3,5 D7: 3,5 => CTR * 129..7...457...89.836..475.6.47.3.287.3..516928561.374.42.78.1..682.1..7371...285 D7: 8 => SOLVED * 129587436457362891836194752694753128713428569285619374942875613568231947371946285 * PAIR D9: 4,9 BLK 8 E9: 4,9,6 # reduction candidate for 4,9 E9: 4,9 => SOLVED * 129587436457362891836194752694753128713428569285619374942875613568231947371946285 E9: 6 => CTR * 129.8743645732.89.836..475.6.47.3.287.3.42.692.561.374.42.75.1.568231947371469285 * PAIR F9: 6,9 BLK 8 E9: 6,9,4 # reduction candidate for 6,9 E9: 6,9 => CTR * 129.874364573.689.836..475.6.47.3.287.3.42.692.561.374.42.75.1.5682319473714..285 E9: 4 => SOLVED * 129587436457362891836194752694753128713428569285619374942875613568231947371946285 * INCONCLUSIVE * SAVE PR GRAPH zz-knacker-132282-base-pr-000.dot * REASONING * DIS # D5: 5,8 => CTR => D5: 4 * PRF # D5: 4 => SOL * PRF # D7: 5,8 => SOL * DIS # D7: 3 => CTR => D7: 5,8 * DIS # E5: 5,8 => CTR => E5: 2,4 * PRF # E2: 2,6 => SOL * DIS # E2: 3 => CTR => E2: 2,6 * PRF # D7: 5,8 => SOL * DIS # D7: 3 => CTR => D7: 5,8 * PRF # F5: 5,8 => SOL * DIS # F5: 2 => CTR => F5: 5,8 * DIS # D7: 3,5 => CTR => D7: 8 * PRF # D7: 8 => SOL * PRF # E9: 4,9 => SOL * DIS # E9: 6 => CTR => E9: 4,9 * DIS # E9: 6,9 => CTR => E9: 4 * PRF # E9: 4 => SOL * CNT 17 HDP CHAINS / 18 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A8,B4,B5,B6,D1,D2,D3,D9,E1,E3,E4,E8,F2,F6,F7,F9,G1,G4,G5,G7,G8,H1,H8,I1,I2,I3,I7) * 129..7...457...89.836..475.6.47.3.287.3....692.561.374.42.7..1..682.1..7371...285 * PAIR D1: 5,8 COL D D5: 5,8,4 # reduction candidate for 5,8 D5: 5,8 => CTR * 129.874364573.689.836..475.6.47.3.287.3.42.692.561.374.42.75.1.5682319473714..285 D5: 4 => SOLVED * 129587436457362891836194752694753128713428569285619374942875613568231947371946285 * DURATION: 0:00:01.801013 START: 06:28:45.403803 END: 06:28:47.204816 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-knacker-132282-base-pr-001.dot * REASONING * DIS # D5: 5,8 => CTR => D5: 4 * PRF D5: 4 => SOL * STA D5: 4 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudoku-knacker.de/132282.htm sehr schwierig level: medium * PAIR REDUCTION .. * ROUND 1: 129..7...457...89.836..475.6.47.3.287.3....692.561.374.42.7..1..682.1..7371...285 D1: 5,8 D5: 4,5,8 # reduction candidate for 5,8 D5: 5,8 => CTR * 129.874364573.689.836..475.6.47.3.287.3.42.692.561.374.42.75.1.5682319473714..285 D5: 4 => SOLVED * 129587436457362891836194752694753128713428569285619374942875613568231947371946285 * SOLVED! -------------------------------------------------- * AUTO .. Q9: 4.. = G8,H8: 4.. => E8 != 4 Q9: 6.. = G7,I7: 6.. => F7 != 6 Q7,Q9: 9.. => D7,F7,E8 != 9 Q6: 2.. = H4,H5: 2.. => H3 != 2 D1,E1: 5,8.. => D1,E1 != 3,6 # hidden pair I2,I3: 1,2.. => I2 != 3,6 # hidden pair * UNSOLVED! |:step:| 00 -------------------------------------------------- E1,E4,F6: 5,8,9 => E5 != 8 # xy-wing D5,F6,D9: 4,8,9 => F9 != 9 # xy-wing |:step:| 00 -------------------------------------------------- guess by pair quad 5,8: D1,E1,D5,E5: 5,8.. D5 != 4 => CTR => D5 = 4 * SOLVED! |:step:| 00 -------------------------------------------------- guess via swordfish -> forced chain highlight 5 * DISABLE VALUE:: F7 != 5 F7: 8 # naked single => D7,A7,A8,E8,E1: 5.. => E4,D5,E5 != 5 # swordfish => F5 = 5 => G5 != 5 => G5 = 1 => G4 = 5 G5 = 1 => B5 = 8 => B6 = 9 F7 = 8 => F6 = 9 => B6,F6 = 9 => CTR => F7 = 5 * FORCE VALUE:: F7 = 5 F7 = 5 # set value E8: 3 # naked single A7: 9 # naked single A8: 5.. # hidden single D7: 8.. # hidden single |:step:| 01 -------------------------------------------------- * AUTO .. A7 = 9 # set value A8: 5 # naked single G7: 6 # naked single D7 = 8 # set value D1: 5 # naked single G7 = 6 # set value I7: 3 # naked single G1: 4 # naked single I7 = 3 # set value H8: 4 # naked single I1: 6 # naked single A8 = 5 # set value E8 = 3 # set value H8 = 4 # set value G8: 9 # naked single H1: 3 # naked single D2: 3.. # hidden single E1: 8.. # hidden single D1 = 5 # set value E1: 8 # naked single D5: 4 # naked single E1 = 8 # set value G1 = 4 # set value H1 = 3 # set value I1 = 6 # set value D2 = 3 # set value D5 = 4 # set value D9: 9 # naked single G8 = 9 # set value D9 = 9 # set value F9: 6 # naked single D3: 1 # naked single F9 = 6 # set value E9: 4 # naked single F2: 2 # naked single E2: 6.. # hidden single E3: 9.. # hidden single I2: 1.. # hidden single F6: 9.. # hidden single E2 = 6 # set value F2 = 2 # set value E3: 9 # naked single F5: 8 # naked single I2: 1 # naked single I2 = 1 # set value I3: 2 # naked single D3 = 1 # set value E3 = 9 # set value E4: 5 # naked single I3 = 2 # set value E4 = 5 # set value E5: 2 # naked single G4: 1 # naked single G4 = 1 # set value G5: 5 # naked single B4: 9 # naked single E5 = 2 # set value F5 = 8 # set value F6: 9 # naked single B5: 1 # naked single G5 = 5 # set value F6 = 9 # set value B6: 8 # naked single E9 = 4 # set value B4 = 9 # set value B5 = 1 # set value B6 = 8 # set value * SOLVED! -------------------------------------------------- wild |:guess:| -------------------------------------------------- D7 = 3 => CTR => D7 != 3 => A7..C7,D8..F9,G7..I7 != 5,8
Solution
position: 129587436457362891836194752694753128713428569285619374942875613568231947371946285 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 # D5: 5,8 => CTR => D5: 4 * PRF # D5: 4 => SOL * PRF # D7: 5,8 => SOL * DIS # D7: 3 => CTR => D7: 5,8 * DIS # E5: 5,8 => CTR => E5: 2,4 * INC # E5: 2,4 => UNS * PRF # E2: 2,6 => SOL * DIS # E2: 3 => CTR => E2: 2,6 * PRF # D7: 5,8 => SOL * DIS # D7: 3 => CTR => D7: 5,8 * PRF # F5: 5,8 => SOL * DIS # F5: 2 => CTR => F5: 5,8 * DIS # D7: 3,5 => CTR => D7: 8 * PRF # D7: 8 => SOL * PRF # E9: 4,9 => SOL * DIS # E9: 6 => CTR => E9: 4,9 * DIS # E9: 6,9 => CTR => E9: 4 * PRF # E9: 4 => SOL * CNT 18 HDP CHAINS / 18 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D5: 5,8 => CTR => D5: 4 * PRF D5: 4 => SOL * STA D5: 4 * CNT 2 HDP CHAINS / 1 HYP OPENED