Analysis of zz-menneske-no-06911767-base.sdk
Contents
Sudoku from http://www.menneske.no/sudoku/utskrift.html?number=6911767
level: medium
position: ....4......4..1.9....7..68..8.5......9.....4..6...9.3..1...3..7......9..6...82... initial
Autosolve
position: ..6.48...8.4..1.9....7.5684.8.5....9.9.....4..6...9.3..1...3..7......9..6...82... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 2,3 => CTR => A1: 5,7,9 * DIS # B1: 2,3 => CTR => B1: 5,7 * DIS # B2: 2,3 => CTR => B2: 5,7 * PRF # A3: 2,3 => SOL * DIS # C3: 2,3 => CTR => C3: 1,9 * DIS # E3: 2,3 => CTR => E3: 9 * PRF # E3: 9 => SOL * DIS # B8: 2,3 => CTR => B8: 4,5 * DIS # F4: 6,7 => CTR => F4: 4 * DIS # E5: 6,7 => CTR => E5: 1,2,3 * DIS # F8: 4 => CTR => F8: 6,7 * DIS # H8: 1,5 => CTR => H8: 2,6 * DIS # I8: 1,5 => CTR => I8: 2,3,6,8 * DIS # G9: 1,5 => CTR => G9: 3,4 * PRF # I9: 1,5 => SOL * DIS # H1: 1,5 => CTR => H1: 2,7 * CNT 16 HDP CHAINS / 31 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 2,3 => CTR => A1: 5,7,9 * DIS A1: 5,7,9 # B1: 2,3 => CTR => B1: 5,7 * DIS A1: 5,7,9 + B1: 5,7 # B2: 2,3 => CTR => B2: 5,7 * PRF A1: 5,7,9 + B1: 5,7 + B2: 5,7 => SOL * STA A1: 5,7,9 + B1: 5,7 + B2: 5,7 * CNT 4 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....4......4..1.9....7..68..8.5......9.....4..6...9.3..1...3..7......9..6...82... | initial |
| ..6.48...8.4..1.9....7.5684.8.5....9.9.....4..6...9.3..1...3..7......9..6...82... | autosolve |
| 956348172874621395321795684783564219192837546465219738219453867548176923637982451 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (3) B3: 2,3 F5: 6,7 H9: 1,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A3,C3: 1.. / A3 = 1 => 3 pairs (_) / C3 = 1 => 4 pairs (_) A4,A6: 4.. / A4 = 4 => 0 pairs (X) / A6 = 4 => 4 pairs (_) F4,D6: 4.. / F4 = 4 => 4 pairs (_) / D6 = 4 => 0 pairs (X) B8,B9: 4.. / B8 = 4 => 5 pairs (_) / B9 = 4 => 0 pairs (X) G7,G9: 4.. / G7 = 4 => 0 pairs (X) / G9 = 4 => 7 pairs (_) A4,F4: 4.. / A4 = 4 => 0 pairs (X) / F4 = 4 => 4 pairs (_) A6,D6: 4.. / A6 = 4 => 4 pairs (_) / D6 = 4 => 0 pairs (X) D7,G7: 4.. / D7 = 4 => 7 pairs (_) / G7 = 4 => 0 pairs (X) F4,F8: 4.. / F4 = 4 => 4 pairs (_) / F8 = 4 => 0 pairs (X) E7,E8: 5.. / E7 = 5 => 0 pairs (*) / E8 = 5 => 0 pairs (X) D2,E2: 6.. / D2 = 6 => 0 pairs (*) / E2 = 6 => 0 pairs (X) H4,I5: 6.. / H4 = 6 => 0 pairs (X) / I5 = 6 => 0 pairs (_) I5,I8: 6.. / I5 = 6 => 0 pairs (*) / I8 = 6 => 0 pairs (X) B9,C9: 7.. / B9 = 7 => 0 pairs (X) / C9 = 7 => 0 pairs (_) E8,F8: 7.. / E8 = 7 => 0 pairs (*) / F8 = 7 => 0 pairs (X) B2,G2: 7.. / B2 = 7 => 0 pairs (*) / G2 = 7 => 0 pairs (X) H1,H4: 7.. / H1 = 7 => 0 pairs (*) / H4 = 7 => 0 pairs (X) D5,D6: 8.. / D5 = 8 => 5 pairs (_) / D6 = 8 => 6 pairs (_) C7,C8: 8.. / C7 = 8 => 0 pairs (X) / C8 = 8 => 7 pairs (_) G7,I8: 8.. / G7 = 8 => 7 pairs (_) / I8 = 8 => 0 pairs (X) C7,G7: 8.. / C7 = 8 => 0 pairs (X) / G7 = 8 => 7 pairs (_) C8,I8: 8.. / C8 = 8 => 7 pairs (_) / I8 = 8 => 0 pairs (X) D1,E3: 9.. / D1 = 9 => 0 pairs (X) / E3 = 9 => 0 pairs (_) A1,D1: 9.. / A1 = 9 => 0 pairs (*) / D1 = 9 => 0 pairs (X) C9,D9: 9.. / C9 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) E3,E7: 9.. / E3 = 9 => 0 pairs (*) / E7 = 9 => 0 pairs (X) * DURATION: 0:00:36.023175 START: 06:51:08.501561 END: 06:51:44.524736 2017-05-01 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,F5,H9) * ..6.48...8.4..1.9....7.5684.8.5....9.9.....4..6...9.3..1...3..7......9..6...82... * PAIR B3: 2,3 BLK 1 A1: 2,3,5,7,9 # reduction candidate for 2,3 A1: 2,3 => CTR * ..6948...8.4..1.9.9.17.5684.8.5.4..9.9...6.4.46...9.3..1..93..7....579.6679.82... A1: 5,7,9 # 3 pairs B1: 2,3,5,7 # reduction candidate for 2,3 B1: 2,3 => CTR * 7.6948...854.6179.9.17.5684.8.5.4..9.9...6.4.46...9.3..1..93..7.4..579.6679.82... B1: 5,7 # 4 pairs B2: 2,3,5,7 # reduction candidate for 2,3 B2: 2,3 => CTR * 9.6.48...8.4..1795...795684.8.5...79.9...7.46.6...9.3..1..53..7....7.9..6...82... B2: 5,7 # 4 pairs A3: 2,3,1,9 # reduction candidate for 2,3 A3: 2,3 => SOLVED * 956348172874621395321795684783564219192837546465219738219453867548176923637982451 A3: 1,9 # 4 pairs C3: 2,3,1,9 # reduction candidate for 2,3 C3: 2,3 => CTR * 9.6.48...8.46.1.9.123795684.8.564..9.9.837.4646...9738.19453867548..69.36379824.. C3: 1,9 # 4 pairs * PAIR B3: 2,3 ROW 3 E3: 2,3,9 # reduction candidate for 2,3 E3: 2,3 => CTR * 7.6948...8.4.6179.9.17.5684.8.5.4..9.9...6.4.46...9.3..1..93..7....579.6679.82... E3: 9 => SOLVED * 956348172874621395321795684783564219192837546465219738219453867548176923637982451 * PAIR B3: 2,3 COL B B8: 2,3,4,5 # reduction candidate for 2,3 B8: 2,3 => CTR * 9.6.48...8.4..1.9....795684.8.5....9.9.....4..6...9.3..19..3..7......9..647982... B8: 4,5 # 4 pairs * PAIR F5: 6,7 BLK 5 E4: 6,7,1,2,3 # reduction candidate for 6,7 E4: 6,7 # 6 pairs F4: 6,7,4 # reduction candidate for 6,7 F4: 6,7 => CTR * 9.6.48...8.4..1.9....79568448.5....9.9.8...46.6.4.983..1...34.7.....49.8647982... F4: 4 # 4 pairs E5: 6,7,1,2,3 # reduction candidate for 6,7 E5: 6,7 => CTR * 956.48.7.874..1.9....7.568478.5.4.69.9...6.4.46...973..1...38.7..8..79.66.79824.3 E5: 1,2,3 # 3 pairs * PAIR F5: 6,7 COL F F8: 6,7,4 # reduction candidate for 6,7 F8: 4 => CTR * 9.6.48...8.4..1.9....79568448.5....9.9.....4..6.4.9.3..196.3..7....749..647982... F8: 6,7 # 4 pairs * PAIR H9: 1,5 BLK 9 H8: 1,5,2,6 # reduction candidate for 1,5 H8: 1,5 => CTR * ..6948...8.4..1.9....7.5684.8.5.4..9.9.....4646...9.3..1.493.67.4..5.9..6...824.3 H8: 2,6 # 4 pairs I8: 1,5,2,3,6,8 # reduction candidate for 1,5 I8: 1,5 => CTR * ..6.48...8.46.1.9....7.5684.8.564..9.9.837.4646..19.38.1.4538673481769256..982413 I8: 2,3,6,8 # 3 pairs G9: 1,5,3,4 # reduction candidate for 1,5 G9: 1,5 => CTR * 9.6.48...8.4..1.9....795684.8.5....9.9...7.46.6...9.3.218953467....7.928679482..3 G9: 3,4 # 4 pairs I9: 1,5,3 # reduction candidate for 1,5 I9: 1,5 => SOLVED * 956348172874621395321795684783564219192837546465219738219453867548176923637982451 I9: 3 # 4 pairs * PAIR H9: 1,5 COL H H1: 1,5,2,7 # reduction candidate for 1,5 H1: 1,5 => CTR * 9.6.48...8.4..1.9....795684.8.5...79.9...7.4676.4.9.3.21..53467....74928647982... H1: 2,7 # 5 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-menneske-no-06911767-base-pr-000.dot * REASONING * DIS # A1: 2,3 => CTR => A1: 5,7,9 * DIS # B1: 2,3 => CTR => B1: 5,7 * DIS # B2: 2,3 => CTR => B2: 5,7 * PRF # A3: 2,3 => SOL * DIS # C3: 2,3 => CTR => C3: 1,9 * DIS # E3: 2,3 => CTR => E3: 9 * PRF # E3: 9 => SOL * DIS # B8: 2,3 => CTR => B8: 4,5 * DIS # F4: 6,7 => CTR => F4: 4 * DIS # E5: 6,7 => CTR => E5: 1,2,3 * DIS # F8: 4 => CTR => F8: 6,7 * DIS # H8: 1,5 => CTR => H8: 2,6 * DIS # I8: 1,5 => CTR => I8: 2,3,6,8 * DIS # G9: 1,5 => CTR => G9: 3,4 * PRF # I9: 1,5 => SOL * DIS # H1: 1,5 => CTR => H1: 2,7 * CNT 16 HDP CHAINS / 31 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,F5,H9) * ..6.48...8.4..1.9....7.5684.8.5....9.9.....4..6...9.3..1...3..7......9..6...82... * PAIR B3: 2,3 BLK 1 A1: 2,3,5,7,9 # reduction candidate for 2,3 A1: 2,3 => CTR * ..6948...8.4..1.9.9.17.5684.8.5.4..9.9...6.4.46...9.3..1..93..7....579.6679.82... B1: 2,3,5,7 # reduction candidate for 2,3 B1: 2,3 => CTR * 7.6948...854.6179.9.17.5684.8.5.4..9.9...6.4.46...9.3..1..93..7.4..579.6679.82... B2: 2,3,5,7 # reduction candidate for 2,3 B2: 2,3 => CTR * 9.6.48...8.4..1795...795684.8.5...79.9...7.46.6...9.3..1..53..7....7.9..6...82... B2: 5,7 => SOLVED * 956348172874621395321795684783564219192837546465219738219453867548176923637982451 * DURATION: 0:00:03.507946 START: 06:52:06.841116 END: 06:52:10.349062 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-menneske-no-06911767-base-pr-001.dot * REASONING * DIS # A1: 2,3 => CTR => A1: 5,7,9 * DIS A1: 5,7,9 # B1: 2,3 => CTR => B1: 5,7 * DIS A1: 5,7,9 + B1: 5,7 # B2: 2,3 => CTR => B2: 5,7 * PRF A1: 5,7,9 + B1: 5,7 + B2: 5,7 => SOL * STA A1: 5,7,9 + B1: 5,7 + B2: 5,7 * CNT 4 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.menneske.no/sudoku/utskrift.html?number=6911767 umulig
Solution
position: 956348172874621395321795684783564219192837546465219738219453867548176923637982451 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 # A1: 2,3 => CTR => A1: 5,7,9 * INC # A1: 5,7,9 => UNS * DIS # B1: 2,3 => CTR => B1: 5,7 * INC # B1: 5,7 => UNS * DIS # B2: 2,3 => CTR => B2: 5,7 * INC # B2: 5,7 => UNS * PRF # A3: 2,3 => SOL * INC # A3: 1,9 => UNS * DIS # C3: 2,3 => CTR => C3: 1,9 * INC # C3: 1,9 => UNS * DIS # E3: 2,3 => CTR => E3: 9 * PRF # E3: 9 => SOL * DIS # B8: 2,3 => CTR => B8: 4,5 * INC # B8: 4,5 => UNS * INC # E4: 6,7 => UNS * DIS # F4: 6,7 => CTR => F4: 4 * INC # F4: 4 => UNS * DIS # E5: 6,7 => CTR => E5: 1,2,3 * INC # E5: 1,2,3 => UNS * INC # F8: 6,7 => UNS * DIS # F8: 4 => CTR => F8: 6,7 * DIS # H8: 1,5 => CTR => H8: 2,6 * INC # H8: 2,6 => UNS * DIS # I8: 1,5 => CTR => I8: 2,3,6,8 * INC # I8: 2,3,6,8 => UNS * DIS # G9: 1,5 => CTR => G9: 3,4 * INC # G9: 3,4 => UNS * PRF # I9: 1,5 => SOL * INC # I9: 3 => UNS * DIS # H1: 1,5 => CTR => H1: 2,7 * INC # H1: 2,7 => UNS * CNT 31 HDP CHAINS / 31 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 2,3 => CTR => A1: 5,7,9 * DIS A1: 5,7,9 # B1: 2,3 => CTR => B1: 5,7 * DIS A1: 5,7,9 + B1: 5,7 # B2: 2,3 => CTR => B2: 5,7 * PRF A1: 5,7,9 + B1: 5,7 + B2: 5,7 => SOL * STA A1: 5,7,9 + B1: 5,7 + B2: 5,7 * CNT 4 HDP CHAINS / 3 HYP OPENED