Analysis of zz-www.sudokuwiki.org-0041-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=41
level: medium
position: 1...6...9.8...5.....2....6...3..61.2....12...5..9..3...1....8.....8...7.7...4...3 initial
Autosolve
position: 1...6...9.8...5.....2....6..73..61.2...312...5219..3.6.1....8.....8...7.7.8.4...3 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F6: 7,8 => CTR => F6: 4 * DIS # E3: 7,8 => CTR => E3: 3,9 * DIS # F6: 7 => CTR => F6: 4,8 * DIS # H1: 4,8 => CTR => H1: 2,3,5 * DIS # F8: 3 => CTR => F8: 1,9 * DIS # H9: 2,5 => CTR => H9: 1,9 * DIS # F3: 1,9 => CTR => F3: 3,4,7,8 * DIS # H7: 4,5 => CTR => H7: 2,9 * DIS # G8: 4,5 => CTR => G8: 2,6,9 * DIS # I3: 4,5 => CTR => I3: 1,7,8 * DIS # I5: 4,5 => CTR => I5: 7,8 * CNT 11 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F6: 7,8 => CTR => F6: 4 * DIS F6: 4 # F8: 3 => CTR => F8: 1,9 * DIS F6: 4 + F8: 1,9 # H9: 2,5 => CTR => H9: 1,9 * DIS F6: 4 + F8: 1,9 + H9: 1,9 # H7: 4,5 => CTR => H7: 2,9 * DIS F6: 4 + F8: 1,9 + H9: 1,9 + H7: 2,9 # G8: 4,5 => CTR => G8: 2,6,9 * PRF F6: 4 + F8: 1,9 + H9: 1,9 + H7: 2,9 + G8: 2,6,9 # I8: 4,5 => SOL * STA F6: 4 + F8: 1,9 + H9: 1,9 + H7: 2,9 + G8: 2,6,9 + I8: 4,5 * CNT 6 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1...6...9.8...5.....2....6...3..61.2....12...5..9..3...1....8.....8...7.7...4...3 | initial |
| 1...6...9.8...5.....2....6..73..61.2...312...5219..3.6.1....8.....8...7.7.8.4...3 | autosolve |
| 135468729687295431492137568973586142864312957521974386216753894349821675758649213 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) D4: 4,5 E4: 5,8 E6: 7,8 H6: 4,8 F9: 1,9 I7: 4,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I8,H9: 1.. / I8 = 1 => 0 pairs (X) / H9 = 1 => 12 pairs (_) F8,I8: 1.. / F8 = 1 => 12 pairs (_) / I8 = 1 => 0 pairs (X) H2,H9: 1.. / H2 = 1 => 0 pairs (X) / H9 = 1 => 12 pairs (_) A7,A8: 2.. / A7 = 2 => 12 pairs (_) / A8 = 2 => 6 pairs (_) H1,H2: 3.. / H1 = 3 => 0 pairs (X) / H2 = 3 => 12 pairs (_) D4,F6: 4.. / D4 = 4 => 0 pairs (X) / F6 = 4 => 5 pairs (_) F6,H6: 4.. / F6 = 4 => 5 pairs (_) / H6 = 4 => 0 pairs (X) D4,E4: 5.. / D4 = 5 => 5 pairs (_) / E4 = 5 => 0 pairs (X) A2,C2: 6.. / A2 = 6 => 6 pairs (_) / C2 = 6 => 9 pairs (_) D7,D9: 6.. / D7 = 6 => 6 pairs (_) / D9 = 6 => 0 pairs (*) G8,G9: 6.. / G8 = 6 => 6 pairs (_) / G9 = 6 => 7 pairs (_) C1,C2: 7.. / C1 = 7 => 8 pairs (_) / C2 = 7 => 0 pairs (*) E6,F6: 7.. / E6 = 7 => 6 pairs (_) / F6 = 7 => 0 pairs (X) G5,I5: 7.. / G5 = 7 => 13 pairs (_) / I5 = 7 => 8 pairs (_) H1,I3: 8.. / H1 = 8 => 0 pairs (X) / I3 = 8 => 7 pairs (_) A4,A5: 8.. / A4 = 8 => 0 pairs (X) / A5 = 8 => 8 pairs (_) F1,H1: 8.. / F1 = 8 => 7 pairs (_) / H1 = 8 => 0 pairs (X) I3,I5: 8.. / I3 = 8 => 7 pairs (_) / I5 = 8 => 0 pairs (X) A4,H4: 9.. / A4 = 9 => 13 pairs (_) / H4 = 9 => 9 pairs (_) * DURATION: 0:00:29.384581 START: 04:13:53.629589 END: 04:14:23.014170 2017-05-01 * CP COUNT: (19) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D4,E4,E6,F9,H6,I7) * 1...6...9.8...5.....2....6..73..61.2...312...5219..3.6.1....8.....8...7.7.8.4...3 * PAIR E6: 7,8 BLK 5 F6: 7,8,4 # reduction candidate for 7,8 F6: 7,8 => CTR * 14726853968973521435219476897345618286431295752198734621.67389..3.829.71798541623 F6: 4 # 5 pairs * PAIR E6: 7,8 COL E E3: 7,8,3,9 # reduction candidate for 7,8 E3: 7,8 => CTR * 1...6..89.8...5.3...2.8..6.873456192...312.58521978346.1...782.2..8...7.7.8.4..13 E3: 3,9 # 8 pairs * PAIR H6: 4,8 BLK 6 H4: 4,8,9 # reduction candidate for 4,8 H4: 4,8 # 13 pairs H5: 4,8,5,9 # reduction candidate for 4,8 H5: 4,8 # 17 pairs I5: 4,8,5,7 # reduction candidate for 4,8 I5: 4,8 # 17 pairs * PAIR H6: 4,8 ROW 6 F6: 4,8,7 # reduction candidate for 4,8 F6: 7 => CTR * 14726853968973521435219476897345618286431295752198734621.67389..3.829.71798541623 F6: 4,8 # 6 pairs * PAIR H6: 4,8 COL H H1: 4,8,2,3,5 # reduction candidate for 4,8 H1: 4,8 => CTR * 1.5768249.8..25.3...2.9.56..73586192896312.5.521974386.1.6.782.26.83197.758249613 H1: 2,3,5 # 7 pairs * PAIR F9: 1,9 BLK 8 F8: 1,9,3 # reduction candidate for 1,9 F8: 3 => CTR * 157.68.39.8..35.1.432...568.735861428..312...52197438631..2.8..2.5893.717.8.4..23 F8: 1,9 # 8 pairs * PAIR F9: 1,9 ROW 9 H9: 1,9,2,5 # reduction candidate for 1,9 H9: 2,5 => CTR * 147268539.89735214352194768973456182...3129.7521987346214673895..5829471798541623 H9: 1,9 # 8 pairs * PAIR F9: 1,9 COL F F3: 1,9,3,4,7,8 # reduction candidate for 1,9 F3: 1,9 => CTR * 1...68.39689.35.1.432.915689735861428..312...52197438631.62789529.853471758.49.23 F3: 3,4,7,8 # 6 pairs * PAIR I7: 4,5 BLK 9 H7: 4,5,2,9 # reduction candidate for 4,5 H7: 4,5 => CTR * 1.7.68.39.8...5.17..21...68.734.61.2..43127.55219..3.6.1....854..58...717.8541.23 H7: 2,9 # 7 pairs G8: 4,5,2,6,9 # reduction candidate for 4,5 G8: 4,5 => CTR * 1.7.68.39.89.35.14..21947689734561828.6312957521987346.1.6..8.5..582.471798541623 G8: 2,6,9 # 6 pairs I8: 4,5,1 # reduction candidate for 4,5 I8: 4,5 # 12 pairs * PAIR I7: 4,5 ROW 7 C7: 4,5,6,9 # reduction candidate for 4,5 C7: 4,5 # 8 pairs C7: 6,9 # 7 pairs * PAIR I7: 4,5 COL I I3: 4,5,1,7,8 # reduction candidate for 4,5 I3: 4,5 => CTR * 1...6..89.8...5.31..2....6..73..61.2...312...5219..3.6.1....8.....8...7.7.8.4...3 I3: 1,7,8 # 6 pairs I5: 4,5,7,8 # reduction candidate for 4,5 I5: 4,5 => CTR * 1.7.68.39.8...5.17..2....68.73..61.2...3127..5219..3.6.1....8.....8...717.8.4...3 I5: 7,8 # 7 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0041-base-pr-000.dot * REASONING * DIS # F6: 7,8 => CTR => F6: 4 * DIS # E3: 7,8 => CTR => E3: 3,9 * DIS # F6: 7 => CTR => F6: 4,8 * DIS # H1: 4,8 => CTR => H1: 2,3,5 * DIS # F8: 3 => CTR => F8: 1,9 * DIS # H9: 2,5 => CTR => H9: 1,9 * DIS # F3: 1,9 => CTR => F3: 3,4,7,8 * DIS # H7: 4,5 => CTR => H7: 2,9 * DIS # G8: 4,5 => CTR => G8: 2,6,9 * DIS # I3: 4,5 => CTR => I3: 1,7,8 * DIS # I5: 4,5 => CTR => I5: 7,8 * CNT 11 HDP CHAINS / 28 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D4,E4,E6,F9,H6,I7) * 1...6...9.8...5.....2....6..73..61.2...312...5219..3.6.1....8.....8...7.7.8.4...3 * PAIR E6: 7,8 BLK 5 F6: 7,8,4 # reduction candidate for 7,8 F6: 7,8 => CTR * 14726853968973521435219476897345618286431295752198734621.67389..3.829.71798541623 * PAIR F9: 1,9 BLK 8 F8: 1,9,3 # reduction candidate for 1,9 F8: 3 => CTR * 1...68.39689.35.1.432.9.5689735861428..312...52197438631..2.8..2..853.71758.4..23 * PAIR F9: 1,9 ROW 9 H9: 1,9,2,5 # reduction candidate for 1,9 H9: 2,5 => CTR * 1.7.68.39.8...5.1...21.7.68.735861.28..312...521974386.1.7.38.....8.9671758641923 * PAIR RESTART * PAIR I7: 4,5 BLK 9 H7: 4,5,2,9 # reduction candidate for 4,5 H7: 4,5 => CTR * 1...68..9.8...5.....21...68.735861.28..312...521974386.1....8.....8...7.7.8.4...3 G8: 4,5,2,6,9 # reduction candidate for 4,5 G8: 4,5 => CTR * 1...68..9.8...5.....21...689735861428..312957521974386.1.6.782.2..8...7.75824.693 I8: 4,5,1 # reduction candidate for 4,5 I8: 4,5 => SOLVED * 135468729687295431492137568973586142864312957521974386216753894349821675758649213 * DURATION: 0:00:10.268567 START: 04:14:43.600723 END: 04:14:53.869290 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0041-base-pr-001.dot * REASONING * DIS # F6: 7,8 => CTR => F6: 4 * DIS F6: 4 # F8: 3 => CTR => F8: 1,9 * DIS F6: 4 + F8: 1,9 # H9: 2,5 => CTR => H9: 1,9 * DIS F6: 4 + F8: 1,9 + H9: 1,9 # H7: 4,5 => CTR => H7: 2,9 * DIS F6: 4 + F8: 1,9 + H9: 1,9 + H7: 2,9 # G8: 4,5 => CTR => G8: 2,6,9 * PRF F6: 4 + F8: 1,9 + H9: 1,9 + H7: 2,9 + G8: 2,6,9 # I8: 4,5 => SOL * STA F6: 4 + F8: 1,9 + H9: 1,9 + H7: 2,9 + G8: 2,6,9 + I8: 4,5 * CNT 6 HDP CHAINS / 8 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=41
Solution
position: 135468729687295431492137568973586142864312957521974386216753894349821675758649213 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:
* DIS # F6: 7,8 => CTR => F6: 4 * INC # F6: 4 => UNS * DIS # E3: 7,8 => CTR => E3: 3,9 * INC # E3: 3,9 => UNS * INC # H4: 4,8 => UNS * INC # H5: 4,8 => UNS * INC # I5: 4,8 => UNS * INC # F6: 4,8 => UNS * DIS # F6: 7 => CTR => F6: 4,8 * DIS # H1: 4,8 => CTR => H1: 2,3,5 * INC # H1: 2,3,5 => UNS * INC # F8: 1,9 => UNS * DIS # F8: 3 => CTR => F8: 1,9 * INC # H9: 1,9 => UNS * DIS # H9: 2,5 => CTR => H9: 1,9 * DIS # F3: 1,9 => CTR => F3: 3,4,7,8 * INC # F3: 3,4,7,8 => UNS * DIS # H7: 4,5 => CTR => H7: 2,9 * INC # H7: 2,9 => UNS * DIS # G8: 4,5 => CTR => G8: 2,6,9 * INC # G8: 2,6,9 => UNS * INC # I8: 4,5 => UNS * INC # C7: 4,5 => UNS * INC # C7: 6,9 => UNS * DIS # I3: 4,5 => CTR => I3: 1,7,8 * INC # I3: 1,7,8 => UNS * DIS # I5: 4,5 => CTR => I5: 7,8 * INC # I5: 7,8 => UNS * CNT 28 HDP CHAINS / 28 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # F6: 7,8 => CTR => F6: 4 * INC F6: 4 # F8: 1,9 => UNS * DIS F6: 4 # F8: 3 => CTR => F8: 1,9 * INC F6: 4 + F8: 1,9 # H9: 1,9 => UNS * DIS F6: 4 + F8: 1,9 # H9: 2,5 => CTR => H9: 1,9 * DIS F6: 4 + F8: 1,9 + H9: 1,9 # H7: 4,5 => CTR => H7: 2,9 * DIS F6: 4 + F8: 1,9 + H9: 1,9 + H7: 2,9 # G8: 4,5 => CTR => G8: 2,6,9 * PRF F6: 4 + F8: 1,9 + H9: 1,9 + H7: 2,9 + G8: 2,6,9 # I8: 4,5 => SOL * STA F6: 4 + F8: 1,9 + H9: 1,9 + H7: 2,9 + G8: 2,6,9 + I8: 4,5 * CNT 8 HDP CHAINS / 8 HYP OPENED