Analysis of zz-sudoku-de-773218-base.sdk
Contents
Original Sudoku
level: medium
position: ..6...4......7.5.88..96..1....2....3..17.68..5....4....5..31..66.9.2......2...1.. initial
Autosolve
position: ..61..439193472568845963.1....21...3.317.68..5..3.4..1.5.831..66195273843826491.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B6: 6 => CTR => B6: 2,7 * DIS # G6: 2,7 => CTR => G6: 6,9 * DIS # B6: 6,7 => CTR => B6: 2 * DIS # G4: 9 => CTR => G4: 6,7 * DIS # C4: 4 => CTR => C4: 7,8 * PRF # H5: 5,9 => SOL * PRF # H5: 2,5 => SOL * DIS # A4: 4,7 => CTR => A4: 9 * DIS # C4: 4,7 => CTR => C4: 8 * PRF # C4: 8 => SOL * DIS # G6: 2,9 => CTR => G6: 6,7 * DIS # H5: 2,9 => CTR => H5: 4,5 * PRF # H4: 4,9 => SOL * CNT 13 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 # B6: 6 => CTR => B6: 2,7 * DIS B6: 2,7 # C4: 4 => CTR => C4: 7,8 * PRF B6: 2,7 + C4: 7,8 # H5: 2,5 => SOL * STA B6: 2,7 + C4: 7,8 + H5: 2,5 * CNT 3 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..6...4......7.5.88..96..1....2....3..17.68..5....4....5..31..66.9.2......2...1.. | initial |
| ..61..439193472568845963.1....21...3.317.68..5..3.4..1.5.831..66195273843826491.. | autosolve |
| 276158439193472568845963217968215743431796852527384691754831926619527384382649175 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) A1: 2,7 B1: 2,7 E1: 5,8 F1: 5,8 G3: 2,7 I3: 2,7 B4: 6,7 C6: 7,8 F4: 5,8 E5: 5,9 E6: 8,9 I5: 2,5 A7: 4,7 C7: 4,7 G7: 2,9 H7: 2,9 H9: 5,7 I9: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,B1: 2.. / A1 = 2 => 19 pairs (_) / B1 = 2 => 0 pairs (X) G3,I3: 2.. / G3 = 2 => 0 pairs (*) / I3 = 2 => 0 pairs (X) A5,B6: 2.. / A5 = 2 => 0 pairs (X) / B6 = 2 => 19 pairs (_) G7,H7: 2.. / G7 = 2 => 0 pairs (X) / H7 = 2 => 22 pairs (_) A1,A5: 2.. / A1 = 2 => 19 pairs (_) / A5 = 2 => 0 pairs (X) B1,B6: 2.. / B1 = 2 => 0 pairs (X) / B6 = 2 => 19 pairs (_) I3,I5: 2.. / I3 = 2 => 0 pairs (X) / I5 = 2 => 0 pairs (_) H4,H5: 4.. / H4 = 4 => 0 pairs (*) / H5 = 4 => 0 pairs (X) A7,C7: 4.. / A7 = 4 => 0 pairs (X) / C7 = 4 => 19 pairs (_) A5,H5: 4.. / A5 = 4 => 0 pairs (*) / H5 = 4 => 0 pairs (X) C4,C7: 4.. / C4 = 4 => 0 pairs (X) / C7 = 4 => 19 pairs (_) E1,F1: 5.. / E1 = 5 => 0 pairs (*) / F1 = 5 => 0 pairs (X) F4,E5: 5.. / F4 = 5 => 0 pairs (*) / E5 = 5 => 0 pairs (X) H9,I9: 5.. / H9 = 5 => 0 pairs (X) / I9 = 5 => 0 pairs (_) F4,H4: 5.. / F4 = 5 => 0 pairs (*) / H4 = 5 => 0 pairs (X) E1,E5: 5.. / E1 = 5 => 0 pairs (*) / E5 = 5 => 0 pairs (X) F1,F4: 5.. / F1 = 5 => 0 pairs (X) / F4 = 5 => 0 pairs (_) I5,I9: 5.. / I5 = 5 => 0 pairs (X) / I9 = 5 => 0 pairs (_) B4,B6: 6.. / B4 = 6 => 19 pairs (_) / B6 = 6 => 0 pairs (X) G4,G6: 6.. / G4 = 6 => 0 pairs (X) / G6 = 6 => 19 pairs (_) B4,G4: 6.. / B4 = 6 => 19 pairs (_) / G4 = 6 => 0 pairs (X) B6,G6: 6.. / B6 = 6 => 0 pairs (X) / G6 = 6 => 19 pairs (_) A1,B1: 7.. / A1 = 7 => 0 pairs (X) / B1 = 7 => 19 pairs (_) G3,I3: 7.. / G3 = 7 => 0 pairs (X) / I3 = 7 => 0 pairs (_) A7,C7: 7.. / A7 = 7 => 19 pairs (_) / C7 = 7 => 0 pairs (X) H9,I9: 7.. / H9 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) I3,I9: 7.. / I3 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) E1,F1: 8.. / E1 = 8 => 0 pairs (X) / F1 = 8 => 0 pairs (_) C4,C6: 8.. / C4 = 8 => 0 pairs (*) / C6 = 8 => 0 pairs (X) F4,E6: 8.. / F4 = 8 => 0 pairs (X) / E6 = 8 => 0 pairs (_) C4,F4: 8.. / C4 = 8 => 0 pairs (*) / F4 = 8 => 0 pairs (X) C6,E6: 8.. / C6 = 8 => 0 pairs (X) / E6 = 8 => 0 pairs (_) E1,E6: 8.. / E1 = 8 => 0 pairs (X) / E6 = 8 => 0 pairs (_) F1,F4: 8.. / F1 = 8 => 0 pairs (*) / F4 = 8 => 0 pairs (X) A4,A5: 9.. / A4 = 9 => 22 pairs (_) / A5 = 9 => 0 pairs (X) E5,E6: 9.. / E5 = 9 => 0 pairs (*) / E6 = 9 => 0 pairs (X) G7,H7: 9.. / G7 = 9 => 22 pairs (_) / H7 = 9 => 0 pairs (X) * DURATION: 0:01:00.226734 START: 08:45:01.468630 END: 08:46:01.695364 2017-05-01 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A7,B1,B4,C6,C7,E1,E5,E6,F1,F4,G3,G7,H7,H9,I3,I5,I9) * ..61..439193472568845963.1....21...3.317.68..5..3.4..1.5.831..66195273843826491.. * PAIR B1: 2,7 COL B B6: 2,7,6 # reduction candidate for 2,7 B6: 6 => CTR * .261..439193472568845963.1..7.21.6.32317.6845568394..1.5.831..66195273843826491.. B6: 2,7 # 19 pairs * PAIR G3: 2,7 COL G G6: 2,7,6,9 # reduction candidate for 2,7 G6: 2,7 => CTR * .261..439193472568845963.1..7.21.6.32317.6845568394..1.5.8319266195273843826491.. G6: 6,9 # 19 pairs * PAIR B4: 6,7 BLK 4 B6: 6,7,2 # reduction candidate for 6,7 B6: 6,7 => CTR * 7261584391934725688459637129..21...32317.68455..3.4..1.5.831..6619527384382649157 B6: 2 # 19 pairs * PAIR B4: 6,7 ROW 4 G4: 6,7,9 # reduction candidate for 6,7 G4: 9 => CTR * ..61..439193472568845963.1..6.21.9.393175684252.394671.5.831..66195273843826491.. G4: 6,7 # 21 pairs * PAIR C6: 7,8 BLK 4 C4: 7,8,4 # reduction candidate for 7,8 C4: 4 => CTR * ..61..439193472568845963.1...4218.53.31756842528394671.5.831..66195273843826491.. C4: 7,8 # 19 pairs * PAIR E5: 5,9 ROW 5 H5: 5,9,2,4 # reduction candidate for 5,9 H5: 5,9 => SOLVED * 276158439193472568845963217968215743431796852527384691754831926619527384382649175 H5: 2,4 # 19 pairs * PAIR I5: 2,5 BLK 6 H5: 2,5,4,9 # reduction candidate for 2,5 H5: 2,5 => SOLVED * 276158439193472568845963217968215743431796852527384691754831926619527384382649175 H5: 4,9 # 19 pairs * PAIR A7: 4,7 COL A A4: 4,7,9 # reduction candidate for 4,7 A4: 4,7 => CTR * ..61..439193472568845963.1....21...393175684252.394671.5.831.266195273843826491.. A4: 9 # 22 pairs * PAIR C7: 4,7 COL C C4: 4,7,8 # reduction candidate for 4,7 C4: 4,7 => CTR * ..61..439193472568845963.1....218.53.31756842528394671.5.831..66195273843826491.. C4: 8 => SOLVED * 276158439193472568845963217968215743431796852527384691754831926619527384382649175 * PAIR G7: 2,9 COL G G6: 2,9,6,7 # reduction candidate for 2,9 G6: 2,9 => CTR * .261..439193472568845963712.7.21.6.32317.6845568394..1.5.831..66195273843826491.. G6: 6,7 # 19 pairs * PAIR H7: 2,9 COL H H5: 2,9,4,5 # reduction candidate for 2,9 H5: 2,9 => CTR * 2761584391934725688459637129..21..434317.68.552.3.46.1754831..6619527384382649157 H5: 4,5 # 19 pairs H6: 2,9,7 # reduction candidate for 2,9 H6: 2,9 # 20 pairs * PAIR H9: 5,7 COL H H4: 5,7,4,9 # reduction candidate for 5,7 H4: 4,9 => SOLVED * 276158439193472568845963217968215743431796852527384691754831926619527384382649175 H4: 5,7 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-773218-base-pr-000.dot * REASONING * DIS # B6: 6 => CTR => B6: 2,7 * DIS # G6: 2,7 => CTR => G6: 6,9 * DIS # B6: 6,7 => CTR => B6: 2 * DIS # G4: 9 => CTR => G4: 6,7 * DIS # C4: 4 => CTR => C4: 7,8 * PRF # H5: 5,9 => SOL * PRF # H5: 2,5 => SOL * DIS # A4: 4,7 => CTR => A4: 9 * DIS # C4: 4,7 => CTR => C4: 8 * PRF # C4: 8 => SOL * DIS # G6: 2,9 => CTR => G6: 6,7 * DIS # H5: 2,9 => CTR => H5: 4,5 * PRF # H4: 4,9 => SOL * CNT 13 HDP CHAINS / 25 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A7,B1,B4,C6,C7,E1,E5,E6,F1,F4,G3,G7,H7,H9,I3,I5,I9) * ..61..439193472568845963.1....21...3.317.68..5..3.4..1.5.831..66195273843826491.. * PAIR B1: 2,7 COL B B6: 2,7,6 # reduction candidate for 2,7 B6: 6 => CTR * .261..439193472568845963.1..7.21.6.32317.6845568394..1.5.831..66195273843826491.. * PAIR RESTART * PAIR C6: 7,8 BLK 4 C4: 7,8,4 # reduction candidate for 7,8 C4: 4 => CTR * ..61..439193472568845963.1..64218.53.31756842528394671.5.831..66195273843826491.. * PAIR I5: 2,5 BLK 6 H5: 2,5,4 # reduction candidate for 2,5 H5: 2,5 => SOLVED * 276158439193472568845963217968215743431796852527384691754831926619527384382649175 * DURATION: 0:00:06.209135 START: 08:46:26.067980 END: 08:46:32.277115 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-773218-base-pr-001.dot * REASONING * DIS # B6: 6 => CTR => B6: 2,7 * DIS B6: 2,7 # C4: 4 => CTR => C4: 7,8 * PRF B6: 2,7 + C4: 7,8 # H5: 2,5 => SOL * STA B6: 2,7 + C4: 7,8 + H5: 2,5 * CNT 3 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokus.de/773218.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: ..61..439193472568845963.1....21...3.317.68..5..3.4..1.5.831..66195273843826491.. A1: 2,7 B1: 2,7 B6: 2,6,7 # reduction candidate for 2,7 B6: 6 => CTR * .261..439193472568845963.1..7.21.6.32317.6845568394..1.5.831..66195273843826491.. E1: 5,8 F1: 5,8 G3: 2,7 I3: 2,7 C6: 7,8 C4: 4,7,8 # reduction candidate for 7,8 C4: 4 => CTR * ..61..439193472568845963.1..64218.53.31756842528394671.5.831..66195273843826491.. F4: 5,8 E5: 5,9 E6: 8,9 I5: 2,5 H5: 2,4,5 # reduction candidate for 2,5 H5: 2,5 => SOLVED * 276158439193472568845963217968215743431796852527384691754831926619527384382649175 * SOLVED! -------------------------------------------------- |:step:| 00 -------------------------------------------------- optional pair quad 2,9 G6: 2,6,7,9 H6: 2,7,9 G7: 2,9 H7: 2,9 pair quad 4,7 A4: 4,7,9 C4: 4,7,8 A7: 4,7 C7: 4,7 |:step:| 01 --------------------------------------------------
Solution
position: 276158439193472568845963217968215743431796852527384691754831926619527384382649175 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 # B6: 2,7 => UNS * DIS # B6: 6 => CTR => B6: 2,7 * DIS # G6: 2,7 => CTR => G6: 6,9 * INC # G6: 6,9 => UNS * DIS # B6: 6,7 => CTR => B6: 2 * INC # B6: 2 => UNS * INC # G4: 6,7 => UNS * DIS # G4: 9 => CTR => G4: 6,7 * INC # C4: 7,8 => UNS * DIS # C4: 4 => CTR => C4: 7,8 * PRF # H5: 5,9 => SOL * INC # H5: 2,4 => UNS * PRF # H5: 2,5 => SOL * INC # H5: 4,9 => UNS * DIS # A4: 4,7 => CTR => A4: 9 * INC # A4: 9 => UNS * DIS # C4: 4,7 => CTR => C4: 8 * PRF # C4: 8 => SOL * DIS # G6: 2,9 => CTR => G6: 6,7 * INC # G6: 6,7 => UNS * DIS # H5: 2,9 => CTR => H5: 4,5 * INC # H5: 4,5 => UNS * INC # H6: 2,9 => UNS * INC # H4: 5,7 => UNS * PRF # H4: 4,9 => SOL * CNT 25 HDP CHAINS / 25 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B6: 2,7 => UNS * DIS # B6: 6 => CTR => B6: 2,7 * INC B6: 2,7 # C4: 7,8 => UNS * DIS B6: 2,7 # C4: 4 => CTR => C4: 7,8 * PRF B6: 2,7 + C4: 7,8 # H5: 2,5 => SOL * STA B6: 2,7 + C4: 7,8 + H5: 2,5 * CNT 5 HDP CHAINS / 5 HYP OPENED