Analysis of zz-sudoku-de-796090-base.sdk
Contents
Original Sudoku
level: medium
position: .9.178.5.7.......8..5...4...4.3.9.1...........3.6.1.2...4...8..6.......7.7.952.4. initial
Autosolve
position: 496178.5.7..4.5.68.852..47..4.3.9.1..6.5.7.8..3.6.1.2...47..8..6..8.4..7.7.952.4. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C2: 1,2 => SOL * DIS # B7: 1,2 => CTR => B7: 5 * PRF # C2: 2 => SOL * PRF # E3: 9 => SOL * DIS # C4: 2,8 => CTR => C4: 7 * DIS # G4: 7 => CTR => G4: 5,6 * PRF # I5: 4 => SOL * DIS # E7: 1 => CTR => E7: 3,6 * DIS # B7: 1 => CTR => B7: 2,5 * DIS # B8: 1 => CTR => B8: 2,5 * CNT 10 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C2: 1,2 => SOL * STA C2: 1,2 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .9.178.5.7.......8..5...4...4.3.9.1...........3.6.1.2...4...8..6.......7.7.952.4. | initial |
| 496178.5.7..4.5.68.852..47..4.3.9.1..6.5.7.8..3.6.1.2...47..8..6..8.4..7.7.952.4. | autosolve |
| 496178253712435968385296471247389615961527384538641729154763892629814537873952146 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (23) B2: 1,2 A3: 1,3 E2: 3,9 F3: 3,6 G1: 2,3 I1: 2,3 G2: 1,9 I3: 1,9 E4: 2,8 E5: 2,4 E6: 4,8 I4: 5,6 G5: 3,9 A9: 3,8 C9: 3,8 F7: 3,6 E8: 1,3 H7: 3,9 I7: 2,5 G8: 2,5 H8: 3,9 G9: 1,6 I9: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G2,I3: 1.. / G2 = 1 => 27 pairs (_) / I3 = 1 => 0 pairs (*) A5,C5: 1.. / A5 = 1 => 0 pairs (X) / C5 = 1 => 26 pairs (_) E7,E8: 1.. / E7 = 1 => 0 pairs (X) / E8 = 1 => 25 pairs (_) G9,I9: 1.. / G9 = 1 => 0 pairs (*) / I9 = 1 => 0 pairs (X) A3,I3: 1.. / A3 = 1 => 27 pairs (_) / I3 = 1 => 0 pairs (*) G2,G9: 1.. / G2 = 1 => 27 pairs (_) / G9 = 1 => 0 pairs (*) I3,I9: 1.. / I3 = 1 => 0 pairs (*) / I9 = 1 => 0 pairs (X) B2,C2: 2.. / B2 = 2 => 27 pairs (_) / C2 = 2 => 0 pairs (*) G1,I1: 2.. / G1 = 2 => 25 pairs (_) / I1 = 2 => 0 pairs (X) E4,E5: 2.. / E4 = 2 => 28 pairs (_) / E5 = 2 => 0 pairs (*) I7,G8: 2.. / I7 = 2 => 25 pairs (_) / G8 = 2 => 0 pairs (X) G1,G8: 2.. / G1 = 2 => 25 pairs (_) / G8 = 2 => 0 pairs (X) I1,I7: 2.. / I1 = 2 => 0 pairs (X) / I7 = 2 => 25 pairs (_) C2,A3: 3.. / C2 = 3 => 27 pairs (_) / A3 = 3 => 0 pairs (*) G1,I1: 3.. / G1 = 3 => 0 pairs (X) / I1 = 3 => 25 pairs (_) G5,I5: 3.. / G5 = 3 => 25 pairs (_) / I5 = 3 => 0 pairs (X) A9,C9: 3.. / A9 = 3 => 27 pairs (_) / C9 = 3 => 0 pairs (*) H7,H8: 3.. / H7 = 3 => 0 pairs (X) / H8 = 3 => 25 pairs (_) C2,E2: 3.. / C2 = 3 => 27 pairs (_) / E2 = 3 => 0 pairs (*) E8,H8: 3.. / E8 = 3 => 0 pairs (X) / H8 = 3 => 25 pairs (_) A3,A9: 3.. / A3 = 3 => 0 pairs (*) / A9 = 3 => 0 pairs (X) C2,C9: 3.. / C2 = 3 => 27 pairs (_) / C9 = 3 => 0 pairs (*) F3,F7: 3.. / F3 = 3 => 25 pairs (_) / F7 = 3 => 23 pairs (_) G1,G5: 3.. / G1 = 3 => 0 pairs (X) / G5 = 3 => 25 pairs (_) I1,I5: 3.. / I1 = 3 => 25 pairs (_) / I5 = 3 => 0 pairs (X) E5,E6: 4.. / E5 = 4 => 28 pairs (_) / E6 = 4 => 0 pairs (*) I5,I6: 4.. / I5 = 4 => 0 pairs (*) / I6 = 4 => 0 pairs (X) E5,I5: 4.. / E5 = 4 => 28 pairs (_) / I5 = 4 => 0 pairs (*) E6,I6: 4.. / E6 = 4 => 0 pairs (*) / I6 = 4 => 0 pairs (X) A4,A6: 5.. / A4 = 5 => 0 pairs (X) / A6 = 5 => 27 pairs (_) B7,B8: 5.. / B7 = 5 => 25 pairs (_) / B8 = 5 => 0 pairs (X) I7,G8: 5.. / I7 = 5 => 0 pairs (X) / G8 = 5 => 25 pairs (_) B7,I7: 5.. / B7 = 5 => 25 pairs (_) / I7 = 5 => 0 pairs (X) B8,G8: 5.. / B8 = 5 => 0 pairs (X) / G8 = 5 => 25 pairs (_) E3,F3: 6.. / E3 = 6 => 25 pairs (_) / F3 = 6 => 23 pairs (_) G4,I4: 6.. / G4 = 6 => 0 pairs (*) / I4 = 6 => 0 pairs (X) E7,F7: 6.. / E7 = 6 => 23 pairs (_) / F7 = 6 => 25 pairs (_) G9,I9: 6.. / G9 = 6 => 27 pairs (_) / I9 = 6 => 0 pairs (*) E3,E7: 6.. / E3 = 6 => 25 pairs (_) / E7 = 6 => 23 pairs (_) F3,F7: 6.. / F3 = 6 => 23 pairs (_) / F7 = 6 => 25 pairs (_) G4,G9: 6.. / G4 = 6 => 0 pairs (*) / G9 = 6 => 0 pairs (X) I4,I9: 6.. / I4 = 6 => 27 pairs (_) / I9 = 6 => 0 pairs (*) C4,C6: 7.. / C4 = 7 => 27 pairs (_) / C6 = 7 => 0 pairs (X) G4,G6: 7.. / G4 = 7 => 0 pairs (X) / G6 = 7 => 27 pairs (_) C4,G4: 7.. / C4 = 7 => 27 pairs (_) / G4 = 7 => 0 pairs (X) C6,G6: 7.. / C6 = 7 => 0 pairs (X) / G6 = 7 => 27 pairs (_) E4,E6: 8.. / E4 = 8 => 0 pairs (*) / E6 = 8 => 0 pairs (X) A9,C9: 8.. / A9 = 8 => 0 pairs (*) / C9 = 8 => 0 pairs (X) E2,E3: 9.. / E2 = 9 => 27 pairs (_) / E3 = 9 => 0 pairs (*) G2,I3: 9.. / G2 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) A7,C8: 9.. / A7 = 9 => 0 pairs (X) / C8 = 9 => 25 pairs (_) H7,H8: 9.. / H7 = 9 => 25 pairs (_) / H8 = 9 => 0 pairs (X) E2,G2: 9.. / E2 = 9 => 27 pairs (_) / G2 = 9 => 0 pairs (*) E3,I3: 9.. / E3 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) A7,H7: 9.. / A7 = 9 => 0 pairs (X) / H7 = 9 => 25 pairs (_) C8,H8: 9.. / C8 = 9 => 25 pairs (_) / H8 = 9 => 0 pairs (X) * DURATION: 0:01:50.527976 START: 08:54:59.901120 END: 08:56:50.429096 2017-05-01 * CP COUNT: (56) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A9,B2,C9,E2,E4,E5,E6,E8,F3,F7,G1,G2,G5,G8,G9,H7,H8,I1,I3,I4,I7,I9) * 496178.5.7..4.5.68.852..47..4.3.9.1..6.5.7.8..3.6.1.2...47..8..6..8.4..7.7.952.4. * PAIR B2: 1,2 BLK 1 C2: 1,2,3 # reduction candidate for 1,2 C2: 1,2 => SOLVED * 496178253712435968385296471247389615961527384538641729154763892629814537873952146 C2: 3 # 27 pairs * PAIR B2: 1,2 COL B B7: 1,2,5 # reduction candidate for 1,2 B7: 1,2 => CTR * 4961783527..4951681852..479.4.3.9.162615.7983.3.6.1.24..47..8.565.8.42.7.7.952641 B7: 5 # 25 pairs B8: 1,2,5 # reduction candidate for 1,2 B8: 1,2 # 25 pairs * PAIR A3: 1,3 BLK 1 C2: 1,3,2 # reduction candidate for 1,3 C2: 2 => SOLVED * 496178253712435968385296471247389615961527384538641729154763892629814537873952146 C2: 1,3 # 27 pairs * PAIR E2: 3,9 BLK 2 E3: 3,9,6 # reduction candidate for 3,9 E3: 6 # 25 pairs E3: 3,9 # 23 pairs * PAIR F3: 3,6 BLK 2 E3: 3,6,9 # reduction candidate for 3,6 E3: 9 => SOLVED * 496178253712435968385296471247389615961527384538641729154763892629814537873952146 E3: 3,6 # 27 pairs * PAIR E4: 2,8 ROW 4 A4: 2,8,5 # reduction candidate for 2,8 A4: 2,8 # 27 pairs C4: 2,8,7 # reduction candidate for 2,8 C4: 2,8 => CTR * 496178.5.7234951681852..4795423897169615273848376419252.47..8..6.98.4.37378952641 C4: 7 # 27 pairs * PAIR I4: 5,6 BLK 6 G4: 5,6,7 # reduction candidate for 5,6 G4: 7 => CTR * 496178.5.7234951681852..4795423897169615273848376419252.47..8..6.98.4.37378952641 G4: 5,6 # 27 pairs * PAIR G5: 3,9 BLK 6 I5: 3,9,4 # reduction candidate for 3,9 I5: 4 => SOLVED * 496178253712435968385296471247389615961527384538641729154763892629814537873952146 I5: 3,9 # 28 pairs * PAIR F7: 3,6 BLK 8 E7: 3,6,1 # reduction candidate for 3,6 E7: 1 => CTR * 496178.5.7.3495168185263479.4.3.9.16.615.7.8..396.172.9.471683.612834597378952.41 E7: 3,6 # 25 pairs * PAIR E8: 1,3 BLK 8 E7: 1,3,6 # reduction candidate for 1,3 E7: 1,3 # 25 pairs E7: 6 # 23 pairs * PAIR I7: 2,5 ROW 7 B7: 2,5,1 # reduction candidate for 2,5 B7: 1 => CTR * 49617835272.4951681852..47..4.3.9.16.6.5.7983.3.6.1.242147..895659814237.7.952641 B7: 2,5 # 27 pairs * PAIR G8: 2,5 ROW 8 B8: 2,5,1 # reduction candidate for 2,5 B8: 1 => CTR * 496178253723495168185263479.4.3.9.1..615.7384.3964172595471683261283459737895264. B8: 2,5 # 25 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-796090-base-pr-000.dot * REASONING * PRF # C2: 1,2 => SOL * DIS # B7: 1,2 => CTR => B7: 5 * PRF # C2: 2 => SOL * PRF # E3: 9 => SOL * DIS # C4: 2,8 => CTR => C4: 7 * DIS # G4: 7 => CTR => G4: 5,6 * PRF # I5: 4 => SOL * DIS # E7: 1 => CTR => E7: 3,6 * DIS # B7: 1 => CTR => B7: 2,5 * DIS # B8: 1 => CTR => B8: 2,5 * CNT 10 HDP CHAINS / 26 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A9,B2,C9,E2,E4,E5,E6,E8,F3,F7,G1,G2,G5,G8,G9,H7,H8,I1,I3,I4,I7,I9) * 496178.5.7..4.5.68.852..47..4.3.9.1..6.5.7.8..3.6.1.2...47..8..6..8.4..7.7.952.4. * PAIR B2: 1,2 BLK 1 C2: 1,2,3 # reduction candidate for 1,2 C2: 1,2 => SOLVED * 496178253712435968385296471247389615961527384538641729154763892629814537873952146 * DURATION: 0:00:02.361679 START: 08:57:19.947444 END: 08:57:22.309123 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-796090-base-pr-001.dot * REASONING * PRF # C2: 1,2 => SOL * STA C2: 1,2 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokus.de/796090.html sehr schwierig * STABLE PAIRS (25p + 56s = 81c) # zz-sudoku-de-796090-base.sdk position: 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 * STABLE PAIRS (25p + 56s = 81c) # zz-sudoku-de-796090-base.sdk position: 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 -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: 496178.5.7..4.5.68.852..47..4.3.9.1..6.5.7.8..3.6.1.2...47..8..6..8.4..7.7.952.4. B2: 1,2 C2: 1,2,3 # reduction candidate for 1,2 C2: 1,2 => SOLVED * 496178253712435968385296471247389615961527384538641729154763892629814537873952146 * SOLVED! |:step:| 00 -------------------------------------------------- pair quad E3: 3,6,9 F3: 3,6 E7: 1,3,6 F7: 3,6 => E3 = 9 or E7 = 1 E7 = 1 => CTR |:step:| 01 --------------------------------------------------
Solution
position: 496178253712435968385296471247389615961527384538641729154763892629814537873952146 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:
* PRF # C2: 1,2 => SOL * INC # C2: 3 => UNS * DIS # B7: 1,2 => CTR => B7: 5 * INC # B7: 5 => UNS * INC # B8: 1,2 => UNS * INC # C2: 1,3 => UNS * PRF # C2: 2 => SOL * INC # E3: 3,9 => UNS * INC # E3: 6 => UNS * INC # E3: 3,6 => UNS * PRF # E3: 9 => SOL * INC # A4: 2,8 => UNS * DIS # C4: 2,8 => CTR => C4: 7 * INC # C4: 7 => UNS * INC # G4: 5,6 => UNS * DIS # G4: 7 => CTR => G4: 5,6 * INC # I5: 3,9 => UNS * PRF # I5: 4 => SOL * INC # E7: 3,6 => UNS * DIS # E7: 1 => CTR => E7: 3,6 * INC # E7: 1,3 => UNS * INC # E7: 6 => UNS * INC # B7: 2,5 => UNS * DIS # B7: 1 => CTR => B7: 2,5 * INC # B8: 2,5 => UNS * DIS # B8: 1 => CTR => B8: 2,5 * CNT 26 HDP CHAINS / 26 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C2: 1,2 => SOL * STA C2: 1,2 * CNT 1 HDP CHAINS / 1 HYP OPENED