Analysis of zz-menneske-no-06913216-base.sdk
Contents
Original Sudoku
level: medium
position: 7.8....4.....7.3...46..5.....21.....3..8....1.....67........29..8..9..5..1......8 initial
Autosolve
position: 738....4..2..7.3...46..5.....21.....3..8....1.....67........29..8..9.15..1......8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G1: 6,9 => CTR => G1: 5 * DIS # I1: 6,9 => CTR => I1: 2,5 * DIS # D2: 6,9 => CTR => D2: 4 * DIS # I4: 6,9 => CTR => I4: 3,4,5 * DIS # G4: 4,5,6 => CTR => G4: 8,9 * DIS # A9: 4,6 => CTR => A9: 2,5,9 * DIS # D9: 4,6 => CTR => D9: 2,3,5,7 * DIS # G4: 4,6 => CTR => G4: 5,8,9 * CNT 8 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:
* DIS # G1: 6,9 => CTR => G1: 5 * DIS G1: 5 # I1: 6,9 => CTR => I1: 2 * PRF G1: 5 + I1: 2 => SOL * STA G1: 5 + I1: 2 * CNT 3 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7.8....4.....7.3...46..5.....21.....3..8....1.....67........29..8..9..5..1......8 | initial |
| 738....4..2..7.3...46..5.....21.....3..8....1.....67........29..8..9.15..1......8 | autosolve |
| 738619542125478369946235817672143985394857621851926734467581293283794156519362478 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) A3: 1,9 I2: 6,9 G3: 8,9 B6: 5,9 H5: 2,6 E7: 1,8 F7: 1,8 G9: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,F1: 1.. / E1 = 1 => 0 pairs (*) / F1 = 1 => 0 pairs (X) H2,H3: 1.. / H2 = 1 => 0 pairs (X) / H3 = 1 => 0 pairs (_) A6,C6: 1.. / A6 = 1 => 0 pairs (X) / C6 = 1 => 9 pairs (_) E7,F7: 1.. / E7 = 1 => 0 pairs (X) / F7 = 1 => 0 pairs (_) A3,H3: 1.. / A3 = 1 => 0 pairs (X) / H3 = 1 => 0 pairs (_) C2,C6: 1.. / C2 = 1 => 0 pairs (X) / C6 = 1 => 9 pairs (_) E1,E7: 1.. / E1 = 1 => 0 pairs (*) / E7 = 1 => 0 pairs (X) F1,F7: 1.. / F1 = 1 => 0 pairs (X) / F7 = 1 => 0 pairs (_) A8,A9: 2.. / A8 = 2 => 9 pairs (_) / A9 = 2 => 11 pairs (_) D3,E3: 3.. / D3 = 3 => 9 pairs (_) / E3 = 3 => 0 pairs (*) D2,F2: 4.. / D2 = 4 => 10 pairs (_) / F2 = 4 => 0 pairs (X) A2,C2: 5.. / A2 = 5 => 10 pairs (_) / C2 = 5 => 10 pairs (_) G1,I1: 5.. / G1 = 5 => 8 pairs (_) / I1 = 5 => 0 pairs (X) E1,E9: 6.. / E1 = 6 => 0 pairs (X) / E9 = 6 => 0 pairs (_) H3,I3: 7.. / H3 = 7 => 0 pairs (X) / I3 = 7 => 8 pairs (_) F4,F5: 7.. / F4 = 7 => 8 pairs (_) / F5 = 7 => 10 pairs (_) B4,F4: 7.. / B4 = 7 => 10 pairs (_) / F4 = 7 => 8 pairs (_) H3,H9: 7.. / H3 = 7 => 0 pairs (X) / H9 = 7 => 8 pairs (_) F2,E3: 8.. / F2 = 8 => 0 pairs (*) / E3 = 8 => 0 pairs (X) A4,A6: 8.. / A4 = 8 => 0 pairs (X) / A6 = 8 => 10 pairs (_) E7,F7: 8.. / E7 = 8 => 0 pairs (*) / F7 = 8 => 0 pairs (X) F2,H2: 8.. / F2 = 8 => 0 pairs (*) / H2 = 8 => 0 pairs (X) A6,H6: 8.. / A6 = 8 => 10 pairs (_) / H6 = 8 => 0 pairs (X) E3,E7: 8.. / E3 = 8 => 0 pairs (X) / E7 = 8 => 0 pairs (_) F2,F7: 8.. / F2 = 8 => 0 pairs (*) / F7 = 8 => 0 pairs (X) G3,G4: 8.. / G3 = 8 => 0 pairs (*) / G4 = 8 => 0 pairs (X) A9,C9: 9.. / A9 = 9 => 0 pairs (X) / C9 = 9 => 9 pairs (_) C2,C9: 9.. / C2 = 9 => 0 pairs (X) / C9 = 9 => 9 pairs (_) * DURATION: 0:00:41.563603 START: 07:07:01.867568 END: 07:07:43.431171 2017-05-01 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B6,E7,F7,G3,G9,H5,I2) * 738....4..2..7.3...46..5.....21.....3..8....1.....67........29..8..9.15..1......8 * PAIR A3: 1,9 BLK 1 A2: 1,9,5 # reduction candidate for 1,9 A2: 1,9 # 10 pairs C2: 1,9,5 # reduction candidate for 1,9 C2: 1,9 # 10 pairs * PAIR I2: 6,9 BLK 3 G1: 6,9,5 # reduction candidate for 6,9 G1: 6,9 => CTR * 738.12945.2.4783161469358....21.....3..8....1..1..67......8129..8..9.15..1..6.4.8 G1: 5 # 8 pairs I1: 6,9,2,5 # reduction candidate for 6,9 I1: 6,9 => CTR * 738.12549.2.4783161469358....21.....3..8....1.91..67......8129..8..9.15..1..6.4.8 I1: 2,5 # 9 pairs * PAIR I2: 6,9 ROW 2 D2: 6,9,4 # reduction candidate for 6,9 D2: 6,9 => CTR * 738....4..2..7438..46.8591...21.....3..8....1.....67........29..8..9.15..1......8 D2: 4 # 10 pairs * PAIR I2: 6,9 COL I I4: 6,9,3,4,5 # reduction candidate for 6,9 I4: 6,9 => CTR * 738.61.4..2..7.386.46.8591...21.....3..8....1.....67......1829..8..9.15..1......8 I4: 3,4,5 # 8 pairs * PAIR G3: 8,9 COL G G4: 8,9,4,5,6 # reduction candidate for 8,9 G4: 4,5,6 => CTR * 738619542.2.478369946235817.921.....3..8..921...9267......8129..8..9415..19.6.478 G4: 8,9 # 10 pairs * PAIR B6: 5,9 BLK 4 B4: 5,9,6,7 # reduction candidate for 5,9 B4: 5,9 # 13 pairs B5: 5,9,6,7 # reduction candidate for 5,9 B5: 5,9 # 14 pairs * PAIR B6: 5,9 ROW 6 D6: 5,9,2,3,4 # reduction candidate for 5,9 D6: 5,9 # 10 pairs I6: 5,9,2,3,4 # reduction candidate for 5,9 I6: 5,9 # 14 pairs * PAIR G9: 4,6 BLK 9 I7: 4,6,3,7 # reduction candidate for 4,6 I7: 4,6 # 11 pairs I8: 4,6,3,7 # reduction candidate for 4,6 I8: 4,6 # 11 pairs * PAIR G9: 4,6 ROW 9 A9: 4,6,2,5,9 # reduction candidate for 4,6 A9: 4,6 => CTR * 738.61.4..2..7.386.46.8591...21.....3..8....1.....67......1829.28..9.15..19.....8 A9: 2,5,9 # 8 pairs D9: 4,6,2,3,5,7 # reduction candidate for 4,6 D9: 4,6 => CTR * 738.61.4..2..7.386.46.8591...21.....3..8....1.....67......1829..8..9.15..1......8 D9: 2,3,5,7 # 8 pairs E9: 4,6,2,3,5 # reduction candidate for 4,6 E9: 4,6 # 11 pairs * PAIR G9: 4,6 COL G G4: 4,6,5,8,9 # reduction candidate for 4,6 G4: 4,6 => CTR * 738619542.2.478369946235817.921..6..36.8..921...9267......8129..8..9415..19.6.478 G4: 5,8,9 # 8 pairs G5: 4,6,5,9 # reduction candidate for 4,6 G5: 4,6 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-menneske-no-06913216-base-pr-000.dot * REASONING * DIS # G1: 6,9 => CTR => G1: 5 * DIS # I1: 6,9 => CTR => I1: 2,5 * DIS # D2: 6,9 => CTR => D2: 4 * DIS # I4: 6,9 => CTR => I4: 3,4,5 * DIS # G4: 4,5,6 => CTR => G4: 8,9 * DIS # A9: 4,6 => CTR => A9: 2,5,9 * DIS # D9: 4,6 => CTR => D9: 2,3,5,7 * DIS # G4: 4,6 => CTR => G4: 5,8,9 * CNT 8 HDP CHAINS / 26 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B6,E7,F7,G3,G9,H5,I2) * 738....4..2..7.3...46..5.....21.....3..8....1.....67........29..8..9.15..1......8 * PAIR A3: 1,9 BLK 1 A2: 1,9,5 # reduction candidate for 1,9 A2: 1,9 # 10 pairs C2: 1,9,5 # reduction candidate for 1,9 C2: 1,9 # 10 pairs * PAIR I2: 6,9 BLK 3 G1: 6,9,5 # reduction candidate for 6,9 G1: 6,9 => CTR * 738.12945.2.4783161469358....21.....3..8....1..1..67......8129..8..9.15..1..6.4.8 I1: 6,9,2 # reduction candidate for 6,9 I1: 6,9 => CTR * 738.12549.2.4783161469358....21.....3..8....1.91..67......8129..8..9.15..1..6.4.8 I1: 2 => SOLVED * 738619542125478369946235817672143985394857621851926734467581293283794156519362478 * DURATION: 0:00:04.273441 START: 07:08:01.728170 END: 07:08:06.001611 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-menneske-no-06913216-base-pr-001.dot * REASONING * DIS # G1: 6,9 => CTR => G1: 5 * DIS G1: 5 # I1: 6,9 => CTR => I1: 2 * PRF G1: 5 + I1: 2 => SOL * STA G1: 5 + I1: 2 * CNT 3 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.menneske.no/sudoku/utskrift.html?number=6913216 umulig * PAIR REDUCTION .. * ROUND 1: 738....4..2..7.3...46..5.....21.....3..8....1.....67........29..8..9.15..1......8 A3: 1,9 A2: 1,5,9 # reduction candidate for 1,9 C2: 1,5,9 # reduction candidate for 1,9 A2: 1,5,9 # reduction candidate for 1,9 I2: 6,9 G1: 5,6,9 # reduction candidate for 6,9 G1: 6,9 => CTR * 738.12945.2.4783161469358....21.....3..8....1..1..67......8129..8..9.15..1..6.4.8 I1: 2,6,9 # reduction candidate for 6,9 I1: 6,9 => CTR * 738.12549.2.4783161469358....21.....3..8....1.91..67......8129..8..9.15..1..6.4.8 I1: 2 => SOLVED * 738619542125478369946235817672143985394857621851926734467581293283794156519362478 * SOLVED! |:step:| 00 -------------------------------------------------- G4: 8,9 I1: 2,5 G5: 4,6 |:step:| 01 --------------------------------------------------
Solution
position: 738619542125478369946235817672143985394857621851926734467581293283794156519362478 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 # A2: 1,9 => UNS * INC # C2: 1,9 => UNS * DIS # G1: 6,9 => CTR => G1: 5 * INC # G1: 5 => UNS * DIS # I1: 6,9 => CTR => I1: 2,5 * INC # I1: 2,5 => UNS * DIS # D2: 6,9 => CTR => D2: 4 * INC # D2: 4 => UNS * DIS # I4: 6,9 => CTR => I4: 3,4,5 * INC # I4: 3,4,5 => UNS * INC # G4: 8,9 => UNS * DIS # G4: 4,5,6 => CTR => G4: 8,9 * INC # B4: 5,9 => UNS * INC # B5: 5,9 => UNS * INC # D6: 5,9 => UNS * INC # I6: 5,9 => UNS * INC # I7: 4,6 => UNS * INC # I8: 4,6 => UNS * DIS # A9: 4,6 => CTR => A9: 2,5,9 * INC # A9: 2,5,9 => UNS * DIS # D9: 4,6 => CTR => D9: 2,3,5,7 * INC # D9: 2,3,5,7 => UNS * INC # E9: 4,6 => UNS * DIS # G4: 4,6 => CTR => G4: 5,8,9 * INC # G4: 5,8,9 => UNS * INC # G5: 4,6 => UNS * CNT 26 HDP CHAINS / 26 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 1,9 => UNS * INC # C2: 1,9 => UNS * DIS # G1: 6,9 => CTR => G1: 5 * DIS G1: 5 # I1: 6,9 => CTR => I1: 2 * PRF G1: 5 + I1: 2 => SOL * STA G1: 5 + I1: 2 * CNT 5 HDP CHAINS / 4 HYP OPENED