Analysis of zz-sudoku-de-759127-base.sdk
Contents
Original Sudoku
level: medium
position: 8.2..5.3.....78..41...9.8....5....7...15.62...2....5....4.8...76..95.....1.3..4.6 initial
Autosolve
position: 8.2.6573.....78..41...938.5..58.2.7.7.15.62...2.7.95..2.4681..76..954..2.1.3274.6 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 4 => CTR => B3: 6,7 * PRF # H2: 6,9 => SOL * DIS # H2: 1,9 => CTR => H2: 2,6 * DIS # H2: 1,9 => CTR => H2: 2,6 * DIS # A4: 9 => CTR => A4: 3,4 * DIS # E6: 3,4 => CTR => E6: 1 * DIS # E6: 3,4 => CTR => E6: 1 * DIS # B7: 5,9 => CTR => B7: 3 * DIS # H9: 5,9 => CTR => H9: 8 * DIS # A2: 3 => CTR => A2: 5,9 * DIS # H9: 5 => CTR => H9: 8,9 * DIS # B7: 5 => CTR => B7: 3,9 * DIS # H9: 5,9 => CTR => H9: 8 * DIS # B7: 5,9 => CTR => B7: 3 * CNT 14 HDP CHAINS / 32 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 4 => CTR => B3: 6,7 * DIS B3: 6,7 # A4: 9 => CTR => A4: 3,4 * DIS B3: 6,7 + A4: 3,4 # E6: 3,4 => CTR => E6: 1 * PRF B3: 6,7 + A4: 3,4 + E6: 1 # C8: 7,8 => SOL * STA B3: 6,7 + A4: 3,4 + E6: 1 + C8: 7,8 * CNT 4 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 8.2..5.3.....78..41...9.8....5....7...15.62...2....5....4.8...76..95.....1.3..4.6 | initial |
| 8.2.6573.....78..41...938.5..58.2.7.7.15.62...2.7.95..2.4681..76..954..2.1.3274.6 | autosolve |
| 842165739953278164167493825495832671781546293326719548234681957678954312519327486 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) B1: 4,9 C3: 6,7 D1: 1,4 D2: 1,2 D3: 2,4 I1: 1,9 H3: 2,6 A6: 3,4 E5: 3,4 H5: 4,9 A9: 5,9 C9: 8,9 G7: 3,9 H7: 5,9 G8: 1,3 H8: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,D2: 1.. / D1 = 1 => 18 pairs (_) / D2 = 1 => 0 pairs (X) E4,E6: 1.. / E4 = 1 => 0 pairs (X) / E6 = 1 => 19 pairs (_) G8,H8: 1.. / G8 = 1 => 0 pairs (X) / H8 = 1 => 19 pairs (_) D1,I1: 1.. / D1 = 1 => 18 pairs (_) / I1 = 1 => 0 pairs (X) D2,D3: 2.. / D2 = 2 => 18 pairs (_) / D3 = 2 => 0 pairs (X) H2,H3: 2.. / H2 = 2 => 0 pairs (X) / H3 = 2 => 18 pairs (_) D2,H2: 2.. / D2 = 2 => 18 pairs (_) / H2 = 2 => 0 pairs (X) D3,H3: 2.. / D3 = 2 => 0 pairs (X) / H3 = 2 => 18 pairs (_) G7,G8: 3.. / G7 = 3 => 0 pairs (X) / G8 = 3 => 19 pairs (_) B7,G7: 3.. / B7 = 3 => 19 pairs (_) / G7 = 3 => 0 pairs (X) B1,B3: 4.. / B1 = 4 => 18 pairs (_) / B3 = 4 => 0 pairs (X) D1,D3: 4.. / D1 = 4 => 0 pairs (X) / D3 = 4 => 18 pairs (_) A4,A6: 4.. / A4 = 4 => 28 pairs (_) / A6 = 4 => 0 pairs (X) H5,H6: 4.. / H5 = 4 => 19 pairs (_) / H6 = 4 => 0 pairs (*) B1,D1: 4.. / B1 = 4 => 18 pairs (_) / D1 = 4 => 0 pairs (X) B3,D3: 4.. / B3 = 4 => 0 pairs (X) / D3 = 4 => 18 pairs (_) A4,E4: 4.. / A4 = 4 => 28 pairs (_) / E4 = 4 => 0 pairs (X) E5,H5: 4.. / E5 = 4 => 0 pairs (*) / H5 = 4 => 0 pairs (X) A2,B2: 5.. / A2 = 5 => 0 pairs (X) / B2 = 5 => 17 pairs (_) B7,A9: 5.. / B7 = 5 => 0 pairs (X) / A9 = 5 => 17 pairs (_) H7,H9: 5.. / H7 = 5 => 17 pairs (_) / H9 = 5 => 0 pairs (X) B7,H7: 5.. / B7 = 5 => 0 pairs (X) / H7 = 5 => 17 pairs (_) A9,H9: 5.. / A9 = 5 => 17 pairs (_) / H9 = 5 => 0 pairs (X) A2,A9: 5.. / A2 = 5 => 0 pairs (X) / A9 = 5 => 17 pairs (_) B2,B7: 5.. / B2 = 5 => 17 pairs (_) / B7 = 5 => 0 pairs (X) B4,C6: 6.. / B4 = 6 => 0 pairs (X) / C6 = 6 => 24 pairs (_) G4,H6: 6.. / G4 = 6 => 24 pairs (_) / H6 = 6 => 0 pairs (X) B4,G4: 6.. / B4 = 6 => 0 pairs (X) / G4 = 6 => 24 pairs (_) C6,H6: 6.. / C6 = 6 => 24 pairs (_) / H6 = 6 => 0 pairs (X) G2,G4: 6.. / G2 = 6 => 0 pairs (X) / G4 = 6 => 24 pairs (_) B3,C3: 7.. / B3 = 7 => 0 pairs (X) / C3 = 7 => 21 pairs (_) B8,C8: 7.. / B8 = 7 => 21 pairs (_) / C8 = 7 => 0 pairs (X) B3,B8: 7.. / B3 = 7 => 0 pairs (X) / B8 = 7 => 21 pairs (_) C3,C8: 7.. / C3 = 7 => 21 pairs (_) / C8 = 7 => 0 pairs (X) B5,C6: 8.. / B5 = 8 => 21 pairs (_) / C6 = 8 => 0 pairs (X) I5,I6: 8.. / I5 = 8 => 0 pairs (X) / I6 = 8 => 21 pairs (_) H8,H9: 8.. / H8 = 8 => 0 pairs (X) / H9 = 8 => 19 pairs (_) B5,I5: 8.. / B5 = 8 => 21 pairs (_) / I5 = 8 => 0 pairs (X) C6,I6: 8.. / C6 = 8 => 0 pairs (X) / I6 = 8 => 21 pairs (_) C9,H9: 8.. / C9 = 8 => 0 pairs (X) / H9 = 8 => 19 pairs (_) B5,B8: 8.. / B5 = 8 => 21 pairs (_) / B8 = 8 => 0 pairs (X) B1,I1: 9.. / B1 = 9 => 0 pairs (X) / I1 = 9 => 18 pairs (_) C2,C9: 9.. / C2 = 9 => 0 pairs (X) / C9 = 9 => 19 pairs (_) * DURATION: 0:01:08.225413 START: 08:33:28.553240 END: 08:34:36.778653 2017-05-01 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A9,B1,C3,C9,D1,D2,D3,E5,G7,G8,H3,H5,H7,H8,I1) * 8.2.6573.....78..41...938.5..58.2.7.7.15.62...2.7.95..2.4681..76..954..2.1.3274.6 * PAIR C3: 6,7 BLK 1 B3: 6,7,4 # reduction candidate for 6,7 B3: 4 => CTR * 892465731.631789.4147293865..58.267.7.15.62...267.95.82.4681..767.954..2.1.3274.6 B3: 6,7 # 18 pairs * PAIR D2: 1,2 ROW 2 H2: 1,2,6,9 # reduction candidate for 1,2 H2: 6,9 => SOLVED * 842165739953278164167493825495832671781546293326719548234681957678954312519327486 H2: 1,2 # 18 pairs * PAIR I1: 1,9 BLK 3 G2: 1,9,6 # reduction candidate for 1,9 G2: 1,9 # 24 pairs H2: 1,9,2,6 # reduction candidate for 1,9 H2: 1,9 => CTR * 842165739...2786141.6493825.658.2.7.7.15.624..2.7.956.2.4681..76.7954182.183274.6 H2: 2,6 # 24 pairs * PAIR I1: 1,9 COL I I4: 1,9,3 # reduction candidate for 1,9 I4: 3 # 21 pairs I4: 1,9 # 19 pairs * PAIR H3: 2,6 BLK 3 H2: 2,6,1,9 # reduction candidate for 2,6 H2: 1,9 => CTR * 842165739...2786141.6493825.658.2.7.7.15.624..2.7.956.2.4681..76.7954182.183274.6 H2: 2,6 # 24 pairs * PAIR A6: 3,4 BLK 4 A4: 3,4,9 # reduction candidate for 3,4 A4: 9 => CTR * 8924657313561789241...938.59.5842.7.7.153624942.7195682.4681..76..954..251.3274.6 A4: 3,4 # 27 pairs * PAIR A6: 3,4 ROW 6 E6: 3,4,1 # reduction candidate for 3,4 E6: 3,4 => CTR * 842165739...278..41..4938254.58129737915362483287495612.468139768.954..2.1.3274.6 E6: 1 # 19 pairs * PAIR E5: 3,4 BLK 5 E4: 3,4,1 # reduction candidate for 3,4 E4: 3,4 # 19 pairs E6: 3,4,1 # reduction candidate for 3,4 E6: 3,4 => CTR * 842165739...278..41..4938254.58129737915362483287495612.468139768.954..2.1.3274.6 E6: 1 # 19 pairs * PAIR A9: 5,9 BLK 7 B7: 5,9,3 # reduction candidate for 5,9 B7: 5,9 => CTR * 8.2.6573...9.786.41...93825.658.297.7.15.62...2.7.95..2.46813.76..954182.183274.6 B7: 3 # 19 pairs * PAIR A9: 5,9 ROW 9 H9: 5,9,8 # reduction candidate for 5,9 H9: 5,9 => CTR * 842165739..92786141..493825.658.29717815.6243.2.7.95.82.4681..76..954182.183274.6 H9: 8 # 19 pairs * PAIR A9: 5,9 COL A A2: 5,9,3 # reduction candidate for 5,9 A2: 3 => CTR * 8924657313561789241...938.59.5842.7.7.153624942.7195682.4681.576..954..251.3274.6 A2: 5,9 # 27 pairs * PAIR C9: 8,9 ROW 9 H9: 8,9,5 # reduction candidate for 8,9 H9: 5 => CTR * 8421657395392786141..493825..58.2.7.7815.62...2.7.95.82546813976..954182918327456 H9: 8,9 # 17 pairs * PAIR G7: 3,9 ROW 7 B7: 3,9,5 # reduction candidate for 3,9 B7: 5 => CTR * 8.2.6573.5.9.786.41...93825.658.297.7.15.62...2.7.95..2546813976..954182918327456 B7: 3,9 # 17 pairs * PAIR H7: 5,9 BLK 9 H9: 5,9,8 # reduction candidate for 5,9 H9: 5,9 => CTR * 842165739..92786141..493825.658.29717815.6243.2.7.95.82.4681..76..954182.183274.6 H9: 8 # 19 pairs * PAIR H7: 5,9 ROW 7 B7: 5,9,3 # reduction candidate for 5,9 B7: 5,9 => CTR * 8.2.6573...9.786.41...93825.658.297.7.15.62...2.7.95..2.46813.76..954182.183274.6 B7: 3 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-759127-base-pr-000.dot * REASONING * DIS # B3: 4 => CTR => B3: 6,7 * PRF # H2: 6,9 => SOL * DIS # H2: 1,9 => CTR => H2: 2,6 * DIS # H2: 1,9 => CTR => H2: 2,6 * DIS # A4: 9 => CTR => A4: 3,4 * DIS # E6: 3,4 => CTR => E6: 1 * DIS # E6: 3,4 => CTR => E6: 1 * DIS # B7: 5,9 => CTR => B7: 3 * DIS # H9: 5,9 => CTR => H9: 8 * DIS # A2: 3 => CTR => A2: 5,9 * DIS # H9: 5 => CTR => H9: 8,9 * DIS # B7: 5 => CTR => B7: 3,9 * DIS # H9: 5,9 => CTR => H9: 8 * DIS # B7: 5,9 => CTR => B7: 3 * CNT 14 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A9,B1,C3,C9,D1,D2,D3,E5,G7,G8,H3,H5,H7,H8,I1) * 8.2.6573.....78..41...938.5..58.2.7.7.15.62...2.7.95..2.4681..76..954..2.1.3274.6 * PAIR C3: 6,7 BLK 1 B3: 6,7,4 # reduction candidate for 6,7 B3: 4 => CTR * 892465731.631789.4147293865..58.267.7.15.62...267.95.82.4681..767.954..2.1.3274.6 * PAIR A6: 3,4 BLK 4 A4: 3,4,9 # reduction candidate for 3,4 A4: 9 => CTR * 842165739...278..41..4938259.584267.7.15.62...2.7.95..2.4681..76..954..2.1.3274.6 * PAIR A6: 3,4 ROW 6 E6: 3,4,1 # reduction candidate for 3,4 E6: 3,4 => CTR * 842165739...278..41..493825..5812.737.15362483287495612.4681.976879543.2.1.3274.6 * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,A4,A6,A9,B2,B3,B4,B5,B7,B8,C2,C3,C6,C9,E4,E5,G2,G4,G7,G8,H2,H5,H6,H7,H8,H9,I5,I6) * 842165739...278..41..493825..58.2.717.15.62...2.7195..2.4681..76..954..2.1.3274.6 * PAIR B8: 7,8 BLK 7 C8: 7,8,3 # reduction candidate for 7,8 C8: 7,8 => SOLVED * 842165739953278164167493825495832671781546293326719548234681957678954312519327486 * DURATION: 0:00:09.537985 START: 08:35:04.903470 END: 08:35:14.441455 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-759127-base-pr-001.dot * REASONING * DIS # B3: 4 => CTR => B3: 6,7 * DIS B3: 6,7 # A4: 9 => CTR => A4: 3,4 * DIS B3: 6,7 + A4: 3,4 # E6: 3,4 => CTR => E6: 1 * PRF B3: 6,7 + A4: 3,4 + E6: 1 # C8: 7,8 => SOL * STA B3: 6,7 + A4: 3,4 + E6: 1 + C8: 7,8 * CNT 4 HDP CHAINS / 6 HYP OPENED
Header Info
http://www.sudokus.de/759127.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: 8.2.6573.....78..41...938.5..58.2.7.7.15.62...2.7.95..2.4681..76..954..2.1.3274.6 B1: 4,9 C3: 6,7 B3: 4,6,7 # reduction candidate for 6,7 B3: 4 => CTR * 892465731.631789.4147293865..58.267.7.15.62...267.95.82.4681..767.954..2.1.3274.6 A6: 3,4 A4: 3,4,9 # reduction candidate for 3,4 A4: 9 => CTR * 842165739...278..41..4938259.584267.7.15.62...2.7.95..2.4681..76..954..2.1.3274.6 E6: 1,3,4 # reduction candidate for 3,4 E6: 3,4 => CTR * 842165739...278..41..493825..5812.737.15362483287495612.4681.976879543.2.1.3274.6 E5: 3,4 H5: 4,9 A9: 5,9 C9: 8,9 G7: 3,9 H7: 5,9 G8: 1,3 H8: 1,8 * ROUND 2: 842165739...278..41..493825..58.2.717.15.62...2.7195..2.4681..76..954..2.1.3274.6 A2: 5,9 B2: 3,5 C2: 3,9 B3: 6,7 C3: 6,7 G2: 1,6 H2: 1,6 A4: 3,4 B4: 6,9 B5: 8,9 A6: 3,4 C6: 6,8 E4: 3,4 E5: 3,4 G4: 6,9 H5: 4,9 I5: 3,8 H6: 4,6 I6: 3,8 B7: 3,5 B8: 7,8 C8: 3,7,8 # reduction candidate for 7,8 C8: 7,8 => SOLVED * 842165739953278164167493825495832671781546293326719548234681957678954312519327486 * SOLVED! -------------------------------------------------- |:step:| 00 -------------------------------------------------- * FORCE VALUE:: E4 = 3 E4 = 3 # set value E5: 4 # naked single E6: 1.. # hidden single A4: 4.. # hidden single |:step:| 01 --------------------------------------------------
Solution
position: 842165739953278164167493825495832671781546293326719548234681957678954312519327486 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 # B3: 6,7 => UNS * DIS # B3: 4 => CTR => B3: 6,7 * INC # H2: 1,2 => UNS * PRF # H2: 6,9 => SOL * INC # G2: 1,9 => UNS * DIS # H2: 1,9 => CTR => H2: 2,6 * INC # H2: 2,6 => UNS * INC # I4: 1,9 => UNS * INC # I4: 3 => UNS * INC # H2: 2,6 => UNS * DIS # H2: 1,9 => CTR => H2: 2,6 * INC # A4: 3,4 => UNS * DIS # A4: 9 => CTR => A4: 3,4 * DIS # E6: 3,4 => CTR => E6: 1 * INC # E6: 1 => UNS * INC # E4: 3,4 => UNS * DIS # E6: 3,4 => CTR => E6: 1 * INC # E6: 1 => UNS * DIS # B7: 5,9 => CTR => B7: 3 * INC # B7: 3 => UNS * DIS # H9: 5,9 => CTR => H9: 8 * INC # H9: 8 => UNS * INC # A2: 5,9 => UNS * DIS # A2: 3 => CTR => A2: 5,9 * INC # H9: 8,9 => UNS * DIS # H9: 5 => CTR => H9: 8,9 * INC # B7: 3,9 => UNS * DIS # B7: 5 => CTR => B7: 3,9 * DIS # H9: 5,9 => CTR => H9: 8 * INC # H9: 8 => UNS * DIS # B7: 5,9 => CTR => B7: 3 * INC # B7: 3 => UNS * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B3: 6,7 => UNS * DIS # B3: 4 => CTR => B3: 6,7 * INC B3: 6,7 # A4: 3,4 => UNS * DIS B3: 6,7 # A4: 9 => CTR => A4: 3,4 * DIS B3: 6,7 + A4: 3,4 # E6: 3,4 => CTR => E6: 1 * PRF B3: 6,7 + A4: 3,4 + E6: 1 # C8: 7,8 => SOL * STA B3: 6,7 + A4: 3,4 + E6: 1 + C8: 7,8 * CNT 6 HDP CHAINS / 6 HYP OPENED