Analysis of zz-sudoku-de-752645-base.sdk
Contents
Original Sudoku
level: medium
position: .3......7..67.....2.5.84..1.....3.49..4.7.2..19.8.....5..32.8.4.....86..7......5. initial
Autosolve
position: .3......7..673....275.843.16....3.49354.7.2..19.84..3.56.3278.4.....867.7..4...5. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # F1: 1,9 => SOL * DIS # D1: 6,9 => CTR => D1: 1,2,5 * DIS # F1: 6,9 => CTR => F1: 1,2,5 * DIS # D5: 1 => CTR => D5: 6,9 * DIS # H1: 6,9 => CTR => H1: 2,8 * DIS # C4: 2,8 => CTR => C4: 7 * DIS # C4: 8 => CTR => C4: 2,7 * DIS # D4: 1,5 => CTR => D4: 2 * DIS # G4: 7 => CTR => G4: 1,5 * DIS # E1: 1,5 => CTR => E1: 6,9 * PRF # G4: 5,7 => SOL * DIS # G4: 1 => CTR => G4: 5,7 * DIS # F6: 2 => CTR => F6: 5,6 * DIS # A1: 4,9 => CTR => A1: 8 * DIS # C9: 2,3 => CTR => C9: 8 * DIS # C9: 3 => CTR => C9: 2,8 * PRF # E9: 1,9 => SOL * DIS # C9: 2,3 => CTR => C9: 8 * CNT 18 HDP CHAINS / 40 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # F1: 1,9 => SOL * STA F1: 1,9 * CNT 1 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .3......7..67.....2.5.84..1.....3.49..4.7.2..19.8.....5..32.8.4.....86..7......5. | initial |
| .3......7..673....275.843.16....3.49354.7.2..19.84..3.56.3278.4.....867.7..4...5. | autosolve |
| 839561427416732985275984361687213549354679218192845736561327894943158672728496153 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (21) C1: 1,9 B2: 1,4 D3: 6,9 I2: 5,8 H3: 6,9 B4: 2,8 C6: 2,7 E4: 1,5 H5: 1,8 I5: 6,8 G6: 5,7 I6: 5,6 C7: 1,9 A8: 4,9 B8: 1,4 C8: 2,3 B9: 2,8 H7: 1,9 I8: 2,3 G9: 1,9 I9: 2,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,B2: 1.. / C1 = 1 => 0 pairs (X) / B2 = 1 => 0 pairs (_) G4,H5: 1.. / G4 = 1 => 0 pairs (X) / H5 = 1 => 0 pairs (_) C7,B8: 1.. / C7 = 1 => 0 pairs (*) / B8 = 1 => 0 pairs (X) H7,G9: 1.. / H7 = 1 => 0 pairs (X) / G9 = 1 => 0 pairs (_) B2,F2: 1.. / B2 = 1 => 0 pairs (*) / F2 = 1 => 0 pairs (X) C7,H7: 1.. / C7 = 1 => 0 pairs (*) / H7 = 1 => 0 pairs (X) B2,B8: 1.. / B2 = 1 => 0 pairs (*) / B8 = 1 => 0 pairs (X) C1,C7: 1.. / C1 = 1 => 0 pairs (X) / C7 = 1 => 0 pairs (_) G4,G9: 1.. / G4 = 1 => 0 pairs (X) / G9 = 1 => 0 pairs (_) H5,H7: 1.. / H5 = 1 => 0 pairs (*) / H7 = 1 => 0 pairs (X) H1,H2: 2.. / H1 = 2 => 0 pairs (*) / H2 = 2 => 0 pairs (X) D4,F6: 2.. / D4 = 2 => 16 pairs (_) / F6 = 2 => 0 pairs (X) I8,I9: 2.. / I8 = 2 => 19 pairs (_) / I9 = 2 => 0 pairs (X) F2,H2: 2.. / F2 = 2 => 0 pairs (*) / H2 = 2 => 0 pairs (X) C6,F6: 2.. / C6 = 2 => 16 pairs (_) / F6 = 2 => 0 pairs (X) C8,I8: 2.. / C8 = 2 => 0 pairs (X) / I8 = 2 => 19 pairs (_) B4,B9: 2.. / B4 = 2 => 0 pairs (X) / B9 = 2 => 17 pairs (_) D1,D4: 2.. / D1 = 2 => 0 pairs (X) / D4 = 2 => 16 pairs (_) C8,C9: 3.. / C8 = 3 => 19 pairs (_) / C9 = 3 => 0 pairs (X) I8,I9: 3.. / I8 = 3 => 0 pairs (X) / I9 = 3 => 19 pairs (_) C8,I8: 3.. / C8 = 3 => 19 pairs (_) / I8 = 3 => 0 pairs (X) C9,I9: 3.. / C9 = 3 => 0 pairs (X) / I9 = 3 => 19 pairs (_) G1,G2: 4.. / G1 = 4 => 23 pairs (_) / G2 = 4 => 0 pairs (X) A8,B8: 4.. / A8 = 4 => 0 pairs (X) / B8 = 4 => 0 pairs (_) A1,G1: 4.. / A1 = 4 => 0 pairs (X) / G1 = 4 => 23 pairs (_) B2,B8: 4.. / B2 = 4 => 0 pairs (X) / B8 = 4 => 0 pairs (_) D8,E8: 5.. / D8 = 5 => 23 pairs (_) / E8 = 5 => 0 pairs (*) I2,I6: 5.. / I2 = 5 => 0 pairs (*) / I6 = 5 => 0 pairs (X) H1,H3: 6.. / H1 = 6 => 0 pairs (X) / H3 = 6 => 22 pairs (_) I5,I6: 6.. / I5 = 6 => 0 pairs (X) / I6 = 6 => 0 pairs (_) E9,F9: 6.. / E9 = 6 => 22 pairs (_) / F9 = 6 => 0 pairs (*) D3,H3: 6.. / D3 = 6 => 0 pairs (X) / H3 = 6 => 22 pairs (_) F6,I6: 6.. / F6 = 6 => 0 pairs (X) / I6 = 6 => 0 pairs (_) E1,E9: 6.. / E1 = 6 => 0 pairs (*) / E9 = 6 => 0 pairs (X) C4,C6: 7.. / C4 = 7 => 16 pairs (_) / C6 = 7 => 0 pairs (X) G4,G6: 7.. / G4 = 7 => 0 pairs (X) / G6 = 7 => 16 pairs (_) C4,G4: 7.. / C4 = 7 => 16 pairs (_) / G4 = 7 => 0 pairs (X) C6,G6: 7.. / C6 = 7 => 0 pairs (X) / G6 = 7 => 16 pairs (_) A1,A2: 8.. / A1 = 8 => 23 pairs (_) / A2 = 8 => 0 pairs (X) B4,C4: 8.. / B4 = 8 => 17 pairs (_) / C4 = 8 => 0 pairs (X) H5,I5: 8.. / H5 = 8 => 0 pairs (X) / I5 = 8 => 0 pairs (_) B9,C9: 8.. / B9 = 8 => 0 pairs (X) / C9 = 8 => 17 pairs (_) A1,H1: 8.. / A1 = 8 => 23 pairs (_) / H1 = 8 => 0 pairs (X) B4,B9: 8.. / B4 = 8 => 17 pairs (_) / B9 = 8 => 0 pairs (X) C4,C9: 8.. / C4 = 8 => 0 pairs (X) / C9 = 8 => 17 pairs (_) I2,I5: 8.. / I2 = 8 => 0 pairs (X) / I5 = 8 => 0 pairs (_) D5,F5: 9.. / D5 = 9 => 0 pairs (X) / F5 = 9 => 23 pairs (_) C7,A8: 9.. / C7 = 9 => 0 pairs (X) / A8 = 9 => 0 pairs (_) H7,G9: 9.. / H7 = 9 => 0 pairs (*) / G9 = 9 => 0 pairs (X) D3,H3: 9.. / D3 = 9 => 22 pairs (_) / H3 = 9 => 0 pairs (X) C7,H7: 9.. / C7 = 9 => 0 pairs (X) / H7 = 9 => 0 pairs (_) C1,C7: 9.. / C1 = 9 => 0 pairs (*) / C7 = 9 => 0 pairs (X) * DURATION: 0:01:37.668617 START: 08:27:29.163065 END: 08:29:06.831682 2017-05-01 * CP COUNT: (52) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B2,B4,B8,B9,C1,C6,C7,C8,D3,E4,G6,G9,H3,H5,H7,I2,I5,I6,I8,I9) * .3......7..673....275.843.16....3.49354.7.2..19.84..3.56.3278.4.....867.7..4...5. * PAIR C1: 1,9 ROW 1 D1: 1,9,2,5,6 # reduction candidate for 1,9 D1: 1,9 # 22 pairs E1: 1,9,5,6 # reduction candidate for 1,9 E1: 1,9 # 25 pairs F1: 1,9,2,5,6 # reduction candidate for 1,9 F1: 1,9 => SOLVED * 839561427416732985275984361687213549354679218192845736561327894943158672728496153 F1: 2,5,6 # 21 pairs * PAIR D3: 6,9 BLK 2 D1: 6,9,1,2,5 # reduction candidate for 6,9 D1: 6,9 => CTR * .3......7..673....275.843.16872.3.4935417928619284673556.327814.13598672728461953 D1: 1,2,5 # 21 pairs E1: 6,9,1,5 # reduction candidate for 6,9 E1: 6,9 # 22 pairs F1: 6,9,1,2,5 # reduction candidate for 6,9 F1: 6,9 => CTR * .3......7.1673....275.843.16....3.49354.7.2..19.84..365613278949....867.7..4...5. F1: 1,2,5 # 21 pairs * PAIR D3: 6,9 COL D D5: 6,9,1 # reduction candidate for 6,9 D5: 1 => CTR * .3......7..673....275.843.16....3.4935417928619.846.3556.327814.1...867.7..46195. D5: 6,9 # 23 pairs * PAIR H3: 6,9 BLK 3 H1: 6,9,2,8 # reduction candidate for 6,9 H1: 6,9 => CTR * 83....4.7..673..28275.843.16....3.49354.7.28619.846.3556.327814.1...867.7..46195. H1: 2,8 # 23 pairs * PAIR B4: 2,8 BLK 4 C4: 2,8,7 # reduction candidate for 2,8 C4: 2,8 => CTR * .392..4.741673....275.843.16....3749354.7.21819784253656132789494...867.7..4..15. C4: 7 # 16 pairs * PAIR C6: 2,7 BLK 4 C4: 2,7,8 # reduction candidate for 2,7 C4: 8 => CTR * .392..4.741673....275.843.16.8..3749354.7.21819784253656132789494...867.78.4..15. C4: 2,7 # 17 pairs * PAIR E4: 1,5 BLK 5 D4: 1,5,2 # reduction candidate for 1,5 D4: 1,5 => CTR * .3.2.5.878.673..25275.843616....374935467921819784253656132789494...867.7..49..5. D4: 2 # 16 pairs * PAIR E4: 1,5 ROW 4 G4: 1,5,7 # reduction candidate for 1,5 G4: 7 => CTR * .392..4.741673....275.843.16....3749354.7.21819784253656132789494...867.7..4..15. G4: 1,5 # 16 pairs * PAIR E4: 1,5 COL E E1: 1,5,6,9 # reduction candidate for 1,5 E1: 1,5 => CTR * .3......7.1673....275.843.16....314935417928619.84673556.3278.4....9867.7..46195. E1: 6,9 # 22 pairs E8: 1,5,9 # reduction candidate for 1,5 E8: 1,5 # 24 pairs * PAIR G6: 5,7 BLK 6 G4: 5,7,1 # reduction candidate for 5,7 G4: 5,7 => SOLVED * 839561427416732985275984361687213549354679218192845736561327894943158672728496153 G4: 1 => CTR * .3......7..673....275.843.16.7..3149354.7.28619284673556.327814.13..8672728461953 * PAIR I6: 5,6 ROW 6 F6: 5,6,2 # reduction candidate for 5,6 F6: 2 => CTR * .3.2.5.878.673..25275.843616....374935467921819784253656132789494...867.7..49..5. F6: 5,6 # 16 pairs * PAIR A8: 4,9 COL A A1: 4,9,8 # reduction candidate for 4,9 A1: 4,9 => CTR * 439....878.673..25275.843616....3.49354.7.21819.84..3656132789494...867.7..4..15. A1: 8 # 23 pairs A2: 4,9,8 # reduction candidate for 4,9 A2: 4,9 # 23 pairs * PAIR C8: 2,3 BLK 7 C9: 2,3,8 # reduction candidate for 2,3 C9: 2,3 => CTR * .392..4.741673....275.843.16.8..3749354.7.21819784253656132789494...867.78.4..15. C9: 8 # 17 pairs * PAIR B9: 2,8 BLK 7 C9: 2,8,3 # reduction candidate for 2,8 C9: 3 => CTR * .392..4.741673....275.843.16.8..3749354.7.218197842536561327894942..86737834..152 C9: 2,8 # 19 pairs * PAIR G9: 1,9 ROW 9 E9: 1,9,6 # reduction candidate for 1,9 E9: 1,9 => SOLVED * 839561427416732985275984361687213549354679218192845736561327894943158672728496153 E9: 6 # 22 pairs F9: 1,9,6 # reduction candidate for 1,9 F9: 1,9 # 22 pairs * PAIR I9: 2,3 ROW 9 C9: 2,3,8 # reduction candidate for 2,3 C9: 2,3 => CTR * .392..4.741673....275.843.16.8..3749354.7.21819784253656132789494...867.78.4..15. C9: 8 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-752645-base-pr-000.dot * REASONING * PRF # F1: 1,9 => SOL * DIS # D1: 6,9 => CTR => D1: 1,2,5 * DIS # F1: 6,9 => CTR => F1: 1,2,5 * DIS # D5: 1 => CTR => D5: 6,9 * DIS # H1: 6,9 => CTR => H1: 2,8 * DIS # C4: 2,8 => CTR => C4: 7 * DIS # C4: 8 => CTR => C4: 2,7 * DIS # D4: 1,5 => CTR => D4: 2 * DIS # G4: 7 => CTR => G4: 1,5 * DIS # E1: 1,5 => CTR => E1: 6,9 * PRF # G4: 5,7 => SOL * DIS # G4: 1 => CTR => G4: 5,7 * DIS # F6: 2 => CTR => F6: 5,6 * DIS # A1: 4,9 => CTR => A1: 8 * DIS # C9: 2,3 => CTR => C9: 8 * DIS # C9: 3 => CTR => C9: 2,8 * PRF # E9: 1,9 => SOL * DIS # C9: 2,3 => CTR => C9: 8 * CNT 18 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B2,B4,B8,B9,C1,C6,C7,C8,D3,E4,G6,G9,H3,H5,H7,I2,I5,I6,I8,I9) * .3......7..673....275.843.16....3.49354.7.2..19.84..3.56.3278.4.....867.7..4...5. * PAIR C1: 1,9 ROW 1 D1: 1,9,2,5,6 # reduction candidate for 1,9 D1: 1,9 # 22 pairs E1: 1,9,5,6 # reduction candidate for 1,9 E1: 1,9 # 25 pairs F1: 1,9,2,5,6 # reduction candidate for 1,9 F1: 1,9 => SOLVED * 839561427416732985275984361687213549354679218192845736561327894943158672728496153 * DURATION: 0:00:04.603304 START: 08:29:46.267824 END: 08:29:50.871128 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-752645-base-pr-001.dot * REASONING * PRF # F1: 1,9 => SOL * STA F1: 1,9 * CNT 1 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokus.de/752645.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: .3......7..673....275.843.16....3.49354.7.2..19.84..3.56.3278.4.....867.7..4...5. C1: 1,9 D1: 1,2,5,6,9 # reduction candidate for 1,9 E1: 1,5,6,9 # reduction candidate for 1,9 F1: 1,2,5,6,9 # reduction candidate for 1,9 F1: 1,9 => SOLVED * 839561427416732985275984361687213549354679218192845736561327894943158672728496153 * SOLVED! -------------------------------------------------- |:step:| 00 -------------------------------------------------- highlight 3 C8: 2,3 I8: 2,3 C9: 2,3,8 I9: 2,3 => C9 = 8 # pair quad |:step:| 01 -------------------------------------------------- E9: 1,6,9 F9: 1,6,9 G9: 1,9 => E9 = 6 or F9 = 6 * DISABLE VALUE:: E9 != 6 * SOLVED! |:step:| reasoning -------------------------------------------------- highlight 6 D3 = 6 => coloring => D5: 1,9 F5: 1,6,9 F9: 1,9 => F5 = 6 => finish coloring => analysis => CTR * DISABLE VALUE:: D3 != 6 D3: 9 # naked single H3: 6.. # hidden single
Solution
position: 839561427416732985275984361687213549354679218192845736561327894943158672728496153 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 # D1: 1,9 => UNS * INC # E1: 1,9 => UNS * PRF # F1: 1,9 => SOL * INC # F1: 2,5,6 => UNS * DIS # D1: 6,9 => CTR => D1: 1,2,5 * INC # D1: 1,2,5 => UNS * INC # E1: 6,9 => UNS * DIS # F1: 6,9 => CTR => F1: 1,2,5 * INC # F1: 1,2,5 => UNS * INC # D5: 6,9 => UNS * DIS # D5: 1 => CTR => D5: 6,9 * DIS # H1: 6,9 => CTR => H1: 2,8 * INC # H1: 2,8 => UNS * DIS # C4: 2,8 => CTR => C4: 7 * INC # C4: 7 => UNS * INC # C4: 2,7 => UNS * DIS # C4: 8 => CTR => C4: 2,7 * DIS # D4: 1,5 => CTR => D4: 2 * INC # D4: 2 => UNS * INC # G4: 1,5 => UNS * DIS # G4: 7 => CTR => G4: 1,5 * DIS # E1: 1,5 => CTR => E1: 6,9 * INC # E1: 6,9 => UNS * INC # E8: 1,5 => UNS * PRF # G4: 5,7 => SOL * DIS # G4: 1 => CTR => G4: 5,7 * INC # F6: 5,6 => UNS * DIS # F6: 2 => CTR => F6: 5,6 * DIS # A1: 4,9 => CTR => A1: 8 * INC # A1: 8 => UNS * INC # A2: 4,9 => UNS * DIS # C9: 2,3 => CTR => C9: 8 * INC # C9: 8 => UNS * INC # C9: 2,8 => UNS * DIS # C9: 3 => CTR => C9: 2,8 * PRF # E9: 1,9 => SOL * INC # E9: 6 => UNS * INC # F9: 1,9 => UNS * DIS # C9: 2,3 => CTR => C9: 8 * INC # C9: 8 => UNS * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D1: 1,9 => UNS * INC # E1: 1,9 => UNS * PRF # F1: 1,9 => SOL * STA F1: 1,9 * CNT 3 HDP CHAINS / 3 HYP OPENED