Analysis of zz-www.sudokuwiki.org-0115-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=115
level: medium
position: .......4..15..72....8.....75..4....9....3....67...1..89...5.7....43..69..6....... initial
Autosolve
position: 7.6....4..15..72....8.....75..4...79...73....67...14.89...5.7...5437.69..67...... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G9: 1,3 => CTR => G9: 5,8 * PRF # H5: 1,5 => SOL * DIS # I5: 1,5 => CTR => I5: 2,6 * DIS # D7: 2,8 => CTR => D7: 1,6 * DIS # F7: 2,8 => CTR => F7: 4,6 * DIS # F9: 2,8 => CTR => F9: 4,9 * DIS # F1: 2,8 => CTR => F1: 3,5 * DIS # F4: 2,8 => CTR => F4: 6 * PRF # F5: 2,8 => SOL * DIS # I9: 1,2 => CTR => I9: 3,4,5 * CNT 10 HDP CHAINS / 48 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G9: 1,3 => CTR => G9: 5,8 * DIS G9: 5,8 # C4: 2 => CTR => C4: 1,3 * PRF G9: 5,8 + C4: 1,3 # H5: 1,5 => SOL * STA G9: 5,8 + C4: 1,3 + H5: 1,5 * CNT 3 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .......4..15..72....8.....75..4....9....3....67...1..89...5.7....43..69..6....... | initial |
| 7.6....4..15..72....8.....75..4...79...73....67...14.89...5.7...5437.69..67...... | autosolve |
| 796823145415967283238145967521486379849732516673591428982654731154378692367219854 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) A2: 3,4 I2: 3,6 E6: 2,9 G4: 1,3 G5: 1,5 F8: 2,8 I8: 1,2 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C4,G4: 1.. / C4 = 1 => 10 pairs (_) / G4 = 1 => 20 pairs (_) A8,I8: 1.. / A8 = 1 => 14 pairs (_) / I8 = 1 => 8 pairs (_) F1,F3: 3.. / F1 = 3 => 9 pairs (_) / F3 = 3 => 8 pairs (_) G4,H6: 3.. / G4 = 3 => 10 pairs (_) / H6 = 3 => 20 pairs (_) C6,H6: 3.. / C6 = 3 => 10 pairs (_) / H6 = 3 => 20 pairs (_) A5,B5: 4.. / A5 = 4 => 0 pairs (X) / B5 = 4 => 7 pairs (_) I7,I9: 4.. / I7 = 4 => 21 pairs (_) / I9 = 4 => 8 pairs (_) A2,E2: 4.. / A2 = 4 => 8 pairs (_) / E2 = 4 => 0 pairs (X) F7,I7: 4.. / F7 = 4 => 8 pairs (_) / I7 = 4 => 21 pairs (_) B3,B5: 4.. / B3 = 4 => 0 pairs (X) / B5 = 4 => 7 pairs (_) F5,D6: 5.. / F5 = 5 => 17 pairs (_) / D6 = 5 => 10 pairs (_) D6,H6: 5.. / D6 = 5 => 10 pairs (_) / H6 = 5 => 17 pairs (_) E4,F4: 6.. / E4 = 6 => 0 pairs (X) / F4 = 6 => 9 pairs (_) H5,I5: 6.. / H5 = 6 => 8 pairs (_) / I5 = 6 => 8 pairs (_) D7,F7: 6.. / D7 = 6 => 8 pairs (_) / F7 = 6 => 0 pairs (X) I2,I5: 6.. / I2 = 6 => 8 pairs (_) / I5 = 6 => 8 pairs (_) G1,H2: 8.. / G1 = 8 => 14 pairs (_) / H2 = 8 => 8 pairs (_) A8,F8: 8.. / A8 = 8 => 8 pairs (_) / F8 = 8 => 14 pairs (_) G1,G9: 8.. / G1 = 8 => 14 pairs (_) / G9 = 8 => 8 pairs (_) B1,B3: 9.. / B1 = 9 => 7 pairs (_) / B3 = 9 => 9 pairs (_) D2,E2: 9.. / D2 = 9 => 8 pairs (_) / E2 = 9 => 0 pairs (X) G1,G3: 9.. / G1 = 9 => 9 pairs (_) / G3 = 9 => 7 pairs (_) C5,C6: 9.. / C5 = 9 => 8 pairs (_) / C6 = 9 => 22 pairs (_) B1,G1: 9.. / B1 = 9 => 7 pairs (_) / G1 = 9 => 9 pairs (_) B3,G3: 9.. / B3 = 9 => 9 pairs (_) / G3 = 9 => 7 pairs (_) C5,F5: 9.. / C5 = 9 => 8 pairs (_) / F5 = 9 => 22 pairs (_) F5,F9: 9.. / F5 = 9 => 22 pairs (_) / F9 = 9 => 8 pairs (_) * DURATION: 0:00:35.485860 START: 05:34:00.692136 END: 05:34:36.177996 2017-05-01 * CP COUNT: (27) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,E6,F8,G4,G5,I2,I8) * 7.6....4..15..72....8.....75..4...79...73....67...14.89...5.7...5437.69..67...... * PAIR A2: 3,4 BLK 1 A3: 3,4,2 # reduction candidate for 3,4 A3: 3,4 # 12 pairs B3: 3,4,2,9 # reduction candidate for 3,4 B3: 3,4 # 9 pairs * PAIR I2: 3,6 BLK 3 H2: 3,6,8 # reduction candidate for 3,6 H2: 3,6 # 14 pairs H3: 3,6,1,5 # reduction candidate for 3,6 H3: 3,6 # 16 pairs * PAIR E6: 2,9 BLK 5 F5: 2,9,5,8 # reduction candidate for 2,9 F5: 2,9 # 19 pairs D6: 2,9,5 # reduction candidate for 2,9 D6: 2,9 # 17 pairs * PAIR E6: 2,9 ROW 6 C6: 2,9,3 # reduction candidate for 2,9 C6: 2,9 # 20 pairs C6: 3 # 10 pairs * PAIR E6: 2,9 COL E E9: 2,9,1,4,8 # reduction candidate for 2,9 E9: 2,9 # 11 pairs E9: 1,4,8 # 7 pairs * PAIR G4: 1,3 ROW 4 C4: 1,3,2 # reduction candidate for 1,3 C4: 2 # 21 pairs C4: 1,3 # 10 pairs * PAIR G4: 1,3 COL G G1: 1,3,5,8,9 # reduction candidate for 1,3 G1: 1,3 # 14 pairs G3: 1,3,5,9 # reduction candidate for 1,3 G3: 1,3 # 12 pairs G9: 1,3,5,8 # reduction candidate for 1,3 G9: 1,3 => CTR * 796213845415..726332864591758.46..79.4.7395..6795214389...56784.54372691.67..4352 G9: 5,8 # 8 pairs * PAIR G5: 1,5 BLK 6 H5: 1,5,2,6 # reduction candidate for 1,5 H5: 1,5 => SOLVED * 796823145415967283238145967521486379849732516673591428982654731154378692367219854 H5: 2,6 # 8 pairs I5: 1,5,2,6 # reduction candidate for 1,5 I5: 1,5 => CTR * 7.6....4..15947286..8.6...75.14.6379..9732.6.6735914289826547..154378692367..9..4 I5: 2,6 # 8 pairs * PAIR G5: 1,5 COL G G1: 1,5,3,8,9 # reduction candidate for 1,5 G1: 1,5 # 15 pairs G3: 1,5,3,9 # reduction candidate for 1,5 G3: 1,5 # 17 pairs G9: 1,5,3,8 # reduction candidate for 1,5 G9: 1,5 # 19 pairs * PAIR F8: 2,8 BLK 8 D7: 2,8,1,6 # reduction candidate for 2,8 D7: 2,8 => CTR * 7.6....4..15..72....8.....75..468.791..73....67...14.89...567.4854372691.67...... D7: 1,6 # 8 pairs F7: 2,8,4,6 # reduction candidate for 2,8 F7: 2,8 => CTR * 7.6....41.15..72....8.....75.24861798417395266795214.89..65.7.4154378692267...... F7: 4,6 # 8 pairs D9: 2,8,1,9 # reduction candidate for 2,8 D9: 2,8 # 11 pairs E9: 2,8,1,4,9 # reduction candidate for 2,8 E9: 2,8 # 13 pairs F9: 2,8,4,9 # reduction candidate for 2,8 F9: 2,8 => CTR * 7.6.1..45.15..72....8265.175..486179..17395..6795214389..6547.1154378692267.....4 F9: 4,9 # 8 pairs * PAIR F8: 2,8 ROW 8 A8: 2,8,1 # reduction candidate for 2,8 A8: 1 # 14 pairs A8: 2,8 # 8 pairs * PAIR F8: 2,8 COL F F1: 2,8,3,5 # reduction candidate for 2,8 F1: 2,8 => CTR * 7.6....45.15..72....85.39175.14.6379..97351..673..14589.26547.1154378692.67..95.4 F1: 3,5 # 8 pairs F4: 2,8,6 # reduction candidate for 2,8 F4: 2,8 => CTR * 796....4.315.472.6248.1.9.75..468.7948.73....67...14.89...5.7..854372691167...... F4: 6 # 9 pairs F5: 2,8,5,9 # reduction candidate for 2,8 F5: 2,8 => SOLVED * 796823145415967283238145967521486379849732516673591428982654731154378692367219854 F5: 5,9 # 19 pairs * PAIR I8: 1,2 BLK 9 H7: 1,2,3,8 # reduction candidate for 1,2 H7: 1,2 # 9 pairs I7: 1,2,3,4 # reduction candidate for 1,2 I7: 1,2 # 13 pairs H9: 1,2,3,5,8 # reduction candidate for 1,2 H9: 1,2 # 10 pairs I9: 1,2,3,4,5 # reduction candidate for 1,2 I9: 1,2 => CTR * 7.6....45.15..72.3..8.....75..4...79...73..2667...14.89..1567.4.54372691167.....2 I9: 3,4,5 # 7 pairs * PAIR I8: 1,2 ROW 8 A8: 1,2,8 # reduction candidate for 1,2 A8: 1,2 # 14 pairs A8: 8 # 8 pairs * PAIR I8: 1,2 COL I I5: 1,2,5,6 # reduction candidate for 1,2 I5: 1,2 # 11 pairs I5: 5,6 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0115-base-pr-000.dot * REASONING * DIS # G9: 1,3 => CTR => G9: 5,8 * PRF # H5: 1,5 => SOL * DIS # I5: 1,5 => CTR => I5: 2,6 * DIS # D7: 2,8 => CTR => D7: 1,6 * DIS # F7: 2,8 => CTR => F7: 4,6 * DIS # F9: 2,8 => CTR => F9: 4,9 * DIS # F1: 2,8 => CTR => F1: 3,5 * DIS # F4: 2,8 => CTR => F4: 6 * PRF # F5: 2,8 => SOL * DIS # I9: 1,2 => CTR => I9: 3,4,5 * CNT 10 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,E6,F8,G4,G5,I2,I8) * 7.6....4..15..72....8.....75..4...79...73....67...14.89...5.7...5437.69..67...... * PAIR A2: 3,4 BLK 1 A3: 3,4,2 # reduction candidate for 3,4 A3: 3,4 # 12 pairs B3: 3,4,2,9 # reduction candidate for 3,4 B3: 3,4 # 9 pairs * PAIR I2: 3,6 BLK 3 H2: 3,6,8 # reduction candidate for 3,6 H2: 3,6 # 14 pairs H3: 3,6,1,5 # reduction candidate for 3,6 H3: 3,6 # 16 pairs * PAIR E6: 2,9 BLK 5 F5: 2,9,5,8 # reduction candidate for 2,9 F5: 2,9 # 19 pairs D6: 2,9,5 # reduction candidate for 2,9 D6: 2,9 # 17 pairs * PAIR E6: 2,9 ROW 6 C6: 2,9,3 # reduction candidate for 2,9 C6: 2,9 # 20 pairs C6: 3 # 10 pairs * PAIR E6: 2,9 COL E E9: 2,9,1,4,8 # reduction candidate for 2,9 E9: 2,9 # 11 pairs E9: 1,4,8 # 7 pairs * PAIR G4: 1,3 ROW 4 C4: 1,3,2 # reduction candidate for 1,3 C4: 2 # 21 pairs C4: 1,3 # 10 pairs * PAIR G4: 1,3 COL G G1: 1,3,5,8,9 # reduction candidate for 1,3 G1: 1,3 # 14 pairs G3: 1,3,5,9 # reduction candidate for 1,3 G3: 1,3 # 12 pairs G9: 1,3,5,8 # reduction candidate for 1,3 G9: 1,3 => CTR * 796213845415..726332864591758.46..79.4.7395..6795214389...56784.54372691.67..4352 * PAIR RESTART * PAIR G4: 1,3 ROW 4 C4: 1,3,2 # reduction candidate for 1,3 C4: 2 => CTR * 7.6.13945315947286.98.65317532486179.41739562679521438983.5.724.5437.691167.94853 * PAIR G4: 1,3 COL G G1: 1,3,5,8,9 # reduction candidate for 1,3 G1: 1,3 # 17 pairs G3: 1,3,5,9 # reduction candidate for 1,3 G3: 1,3 # 15 pairs * PAIR RESTART * PAIR G4: 1,3 COL G G1: 1,3,5,8,9 # reduction candidate for 1,3 G1: 1,3 # 17 pairs G3: 1,3,5,9 # reduction candidate for 1,3 G3: 1,3 # 15 pairs * PAIR G5: 1,5 BLK 6 H5: 1,5,2,6 # reduction candidate for 1,5 H5: 1,5 => SOLVED * 796823145415967283238145967521486379849732516673591428982654731154378692367219854 * DURATION: 0:00:19.043941 START: 05:35:13.441094 END: 05:35:32.485035 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0115-base-pr-001.dot * REASONING * DIS # G9: 1,3 => CTR => G9: 5,8 * DIS G9: 5,8 # C4: 2 => CTR => C4: 1,3 * PRF G9: 5,8 + C4: 1,3 # H5: 1,5 => SOL * STA G9: 5,8 + C4: 1,3 + H5: 1,5 * CNT 3 HDP CHAINS / 22 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=115
Solution
position: 796823145415967283238145967521486379849732516673591428982654731154378692367219854 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 # A3: 3,4 => UNS * INC # B3: 3,4 => UNS * INC # H2: 3,6 => UNS * INC # H3: 3,6 => UNS * INC # F5: 2,9 => UNS * INC # D6: 2,9 => UNS * INC # C6: 2,9 => UNS * INC # C6: 3 => UNS * INC # E9: 2,9 => UNS * INC # E9: 1,4,8 => UNS * INC # C4: 1,3 => UNS * INC # C4: 2 => UNS * INC # G1: 1,3 => UNS * INC # G3: 1,3 => UNS * DIS # G9: 1,3 => CTR => G9: 5,8 * INC # G9: 5,8 => UNS * PRF # H5: 1,5 => SOL * INC # H5: 2,6 => UNS * DIS # I5: 1,5 => CTR => I5: 2,6 * INC # I5: 2,6 => UNS * INC # G1: 1,5 => UNS * INC # G3: 1,5 => UNS * INC # G9: 1,5 => UNS * DIS # D7: 2,8 => CTR => D7: 1,6 * INC # D7: 1,6 => UNS * DIS # F7: 2,8 => CTR => F7: 4,6 * INC # F7: 4,6 => UNS * INC # D9: 2,8 => UNS * INC # E9: 2,8 => UNS * DIS # F9: 2,8 => CTR => F9: 4,9 * INC # F9: 4,9 => UNS * INC # A8: 2,8 => UNS * INC # A8: 1 => UNS * DIS # F1: 2,8 => CTR => F1: 3,5 * INC # F1: 3,5 => UNS * DIS # F4: 2,8 => CTR => F4: 6 * INC # F4: 6 => UNS * PRF # F5: 2,8 => SOL * INC # F5: 5,9 => UNS * INC # H7: 1,2 => UNS * INC # I7: 1,2 => UNS * INC # H9: 1,2 => UNS * DIS # I9: 1,2 => CTR => I9: 3,4,5 * INC # I9: 3,4,5 => UNS * INC # A8: 1,2 => UNS * INC # A8: 8 => UNS * INC # I5: 1,2 => UNS * INC # I5: 5,6 => UNS * CNT 48 HDP CHAINS / 48 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 3,4 => UNS * INC # B3: 3,4 => UNS * INC # H2: 3,6 => UNS * INC # H3: 3,6 => UNS * INC # F5: 2,9 => UNS * INC # D6: 2,9 => UNS * INC # C6: 2,9 => UNS * INC # C6: 3 => UNS * INC # E9: 2,9 => UNS * INC # E9: 1,4,8 => UNS * INC # C4: 1,3 => UNS * INC # C4: 2 => UNS * INC # G1: 1,3 => UNS * INC # G3: 1,3 => UNS * DIS # G9: 1,3 => CTR => G9: 5,8 * INC G9: 5,8 # C4: 1,3 => UNS * DIS G9: 5,8 # C4: 2 => CTR => C4: 1,3 * INC G9: 5,8 + C4: 1,3 # G1: 1,3 => UNS * INC G9: 5,8 + C4: 1,3 # G3: 1,3 => UNS * INC G9: 5,8 + C4: 1,3 # G1: 1,3 => UNS * INC G9: 5,8 + C4: 1,3 # G3: 1,3 => UNS * PRF G9: 5,8 + C4: 1,3 # H5: 1,5 => SOL * STA G9: 5,8 + C4: 1,3 + H5: 1,5 * CNT 22 HDP CHAINS / 22 HYP OPENED