Analysis of zz-menneske-no-06902129-base.sdk
Contents
Sudoku from http://www.menneske.no/sudoku/utskrift.html?number=6902129
level: medium
position: ..6...32....1.89..7.1......6.4..9............1..7.34......5......9..4.......6.75. initial
Autosolve
position: ..6...321...1.89..7.1......6.4..9............1..7.34......5......9..4.......6.75. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D5: 4,5 => CTR => D5: 2,6,8 * PRF # D5: 2,6,8 => SOL * DIS # D3: 3 => CTR => D3: 2,6 * DIS # F5: 2,6 => CTR => F5: 1,5 * PRF # F5: 1,5 => SOL * DIS # D4: 2,8 => CTR => D4: 5 * PRF # D4: 5 => SOL * PRF # E4: 2,8 => SOL * DIS # D5: 2,8 => CTR => D5: 4,5,6 * DIS # E5: 2,8 => CTR => E5: 1,4 * DIS # I6: 2,8 => CTR => I6: 5,6,9 * DIS # E8: 2,8 => CTR => E8: 1,3,7 * DIS # F7: 1,2 => CTR => F7: 7 * PRF # F7: 7 => SOL * PRF # E8: 1,2 => SOL * DIS # B9: 3,4,8 => CTR => B9: 1,2 * PRF # F5: 1,2 => SOL * CNT 17 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D5: 4,5 => CTR => D5: 2,6,8 * PRF D5: 2,6,8 => SOL * STA D5: 2,6,8 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..6...32....1.89..7.1......6.4..9............1..7.34......5......9..4.......6.75. | initial |
| ..6...321...1.89..7.1......6.4..9............1..7.34......5......9..4.......6.75. | autosolve |
| 986475321245138967731296548624589173397641285158723496462357819579814632813962754 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) D1: 4,5 F1: 5,7 F3: 2,6 H2: 6,7 I2: 6,7 G3: 5,8 H3: 4,8 E6: 2,8 F9: 1,2 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B9,F9: 1.. / B9 = 1 => 0 pairs (*) / F9 = 1 => 0 pairs (X) H3,I3: 4.. / H3 = 4 => 9 pairs (_) / I3 = 4 => 9 pairs (_) D5,E5: 4.. / D5 = 4 => 0 pairs (X) / E5 = 4 => 0 pairs (_) D1,D5: 4.. / D1 = 4 => 0 pairs (*) / D5 = 4 => 0 pairs (X) H3,H7: 4.. / H3 = 4 => 9 pairs (_) / H7 = 4 => 9 pairs (_) D1,F1: 5.. / D1 = 5 => 0 pairs (X) / F1 = 5 => 0 pairs (_) G3,I3: 5.. / G3 = 5 => 9 pairs (_) / I3 = 5 => 7 pairs (_) A8,B8: 5.. / A8 = 5 => 9 pairs (_) / B8 = 5 => 0 pairs (X) F1,F5: 5.. / F1 = 5 => 0 pairs (*) / F5 = 5 => 0 pairs (X) D3,F3: 6.. / D3 = 6 => 0 pairs (X) / F3 = 6 => 0 pairs (_) H2,I2: 6.. / H2 = 6 => 8 pairs (_) / I2 = 6 => 7 pairs (_) D5,F5: 6.. / D5 = 6 => 0 pairs (*) / F5 = 6 => 0 pairs (X) H6,I6: 6.. / H6 = 6 => 7 pairs (_) / I6 = 6 => 8 pairs (_) B7,B8: 6.. / B7 = 6 => 9 pairs (_) / B8 = 6 => 0 pairs (X) G7,G8: 6.. / G7 = 6 => 0 pairs (X) / G8 = 6 => 9 pairs (_) B7,G7: 6.. / B7 = 6 => 9 pairs (_) / G7 = 6 => 0 pairs (X) B8,G8: 6.. / B8 = 6 => 0 pairs (X) / G8 = 6 => 9 pairs (_) D3,D5: 6.. / D3 = 6 => 0 pairs (X) / D5 = 6 => 0 pairs (_) F3,F5: 6.. / F3 = 6 => 0 pairs (*) / F5 = 6 => 0 pairs (X) H2,H6: 6.. / H2 = 6 => 8 pairs (_) / H6 = 6 => 7 pairs (_) I2,I6: 6.. / I2 = 6 => 7 pairs (_) / I6 = 6 => 8 pairs (_) E1,F1: 7.. / E1 = 7 => 0 pairs (*) / F1 = 7 => 0 pairs (X) H2,I2: 7.. / H2 = 7 => 7 pairs (_) / I2 = 7 => 8 pairs (_) F7,E8: 7.. / F7 = 7 => 0 pairs (*) / E8 = 7 => 0 pairs (X) B8,E8: 7.. / B8 = 7 => 0 pairs (*) / E8 = 7 => 0 pairs (X) C5,C7: 7.. / C5 = 7 => 0 pairs (*) / C7 = 7 => 0 pairs (X) E1,E8: 7.. / E1 = 7 => 0 pairs (*) / E8 = 7 => 0 pairs (X) F1,F7: 7.. / F1 = 7 => 0 pairs (X) / F7 = 7 => 0 pairs (_) A1,B1: 8.. / A1 = 8 => 12 pairs (_) / B1 = 8 => 10 pairs (_) E1,E3: 9.. / E1 = 9 => 0 pairs (X) / E3 = 9 => 14 pairs (_) D7,D9: 9.. / D7 = 9 => 9 pairs (_) / D9 = 9 => 9 pairs (_) B3,E3: 9.. / B3 = 9 => 0 pairs (X) / E3 = 9 => 14 pairs (_) D9,I9: 9.. / D9 = 9 => 9 pairs (_) / I9 = 9 => 9 pairs (_) A1,A5: 9.. / A1 = 9 => 12 pairs (_) / A5 = 9 => 12 pairs (_) * DURATION: 0:00:48.623792 START: 06:36:03.840200 END: 06:36:52.463992 2017-05-01 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D1,E6,F1,F3,F9,G3,H2,H3,I2) * ..6...321...1.89..7.1......6.4..9............1..7.34......5......9..4.......6.75. * PAIR D1: 4,5 COL D D5: 4,5,2,6,8 # reduction candidate for 4,5 D5: 4,5 => CTR * ..6..5321...1.89..7.16.2...6.4..9........6...1..7.34......57....79..461.....6175. D5: 2,6,8 => SOLVED * 986475321245138967731296548624589173397641285158723496462357819579814632813962754 * PAIR F3: 2,6 BLK 2 D3: 2,6,3 # reduction candidate for 2,6 D3: 3 => CTR * ..6475321...1289..721396...6.4519......642...1.27834......57....79.3461.....6175. D3: 2,6 # 13 pairs * PAIR F3: 2,6 COL F F5: 2,6,1,5 # reduction candidate for 2,6 F5: 2,6 => CTR * ..6..5321...1.89..7.1......6.4..9............1..7.34......57....79..46......6175. F5: 1,5 => SOLVED * 986475321245138967731296548624589173397641285158723496462357819579814632813962754 * PAIR G3: 5,8 BLK 3 I3: 5,8,4 # reduction candidate for 5,8 I3: 5,8 # 9 pairs I3: 4 # 9 pairs * PAIR G3: 5,8 COL G G4: 5,8,1,2 # reduction candidate for 5,8 G4: 5,8 # 11 pairs G5: 5,8,1,2 # reduction candidate for 5,8 G5: 5,8 # 11 pairs * PAIR H3: 4,8 BLK 3 I3: 4,8,5 # reduction candidate for 4,8 I3: 4,8 # 9 pairs I3: 5 # 7 pairs * PAIR H3: 4,8 COL H H7: 4,8,1,3,9 # reduction candidate for 4,8 H7: 4,8 # 12 pairs H7: 1,3,9 # 9 pairs * PAIR E6: 2,8 BLK 5 D4: 2,8,5 # reduction candidate for 2,8 D4: 2,8 => CTR * ..64.5321...1.89..7.1......6.4.19......546...1..7.34......57....79..461.....6175. D4: 5 => SOLVED * 986475321245138967731296548624589173397641285158723496462357819579814632813962754 E4: 2,8,1 # reduction candidate for 2,8 E4: 2,8 => SOLVED * 986475321245138967731296548624589173397641285158723496462357819579814632813962754 E4: 1 # 9 pairs D5: 2,8,4,5,6 # reduction candidate for 2,8 D5: 2,8 => CTR * ..64.5321...1.89..7.16.2...6.45.9.......46...1..7.34......57....79..46......6175. D5: 4,5,6 # 9 pairs E5: 2,8,1,4 # reduction candidate for 2,8 E5: 2,8 => CTR * ..65.7321...1.89..7.16.2...6.4.19......4.6...1..7.34......51.....9..4.......6.75. E5: 1,4 # 10 pairs * PAIR E6: 2,8 ROW 6 B6: 2,8,5,9 # reduction candidate for 2,8 B6: 2,8 # 13 pairs C6: 2,8,5 # reduction candidate for 2,8 C6: 2,8 # 12 pairs I6: 2,8,5,6,9 # reduction candidate for 2,8 I6: 2,8 => CTR * 986.47321...138976731.9....6.4..9......4.....1957.346...7.5......9.74.......6.75. I6: 5,6,9 # 9 pairs * PAIR E6: 2,8 COL E E8: 2,8,1,3,7 # reduction candidate for 2,8 E8: 2,8 => CTR * ..6.75321...1.89..7.1.9....6.4..9............1..7.34......57....79..461.....6175. E8: 1,3,7 # 10 pairs * PAIR F9: 1,2 BLK 8 F7: 1,2,7 # reduction candidate for 1,2 F7: 1,2 => CTR * ..65.7321...1.89..7.1..6...6.4..9........5...1..7.34......5......9.74.......6.75. F7: 7 => SOLVED * 986475321245138967731296548624589173397641285158723496462357819579814632813962754 E8: 1,2,3,7,8 # reduction candidate for 1,2 E8: 1,2 => SOLVED * 986475321245138967731296548624589173397641285158723496462357819579814632813962754 E8: 3,7,8 # 9 pairs * PAIR F9: 1,2 ROW 9 B9: 1,2,3,4,8 # reduction candidate for 1,2 B9: 3,4,8 => CTR * ..6..7321...1.89..7.1..6...6.4..9......645...1..7.34....7.52...5.9.74.......6175. B9: 1,2 # 11 pairs * PAIR F9: 1,2 COL F F5: 1,2,5,6 # reduction candidate for 1,2 F5: 1,2 => SOLVED * 986475321245138967731296548624589173397641285158723496462357819579814632813962754 F5: 5,6 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-menneske-no-06902129-base-pr-000.dot * REASONING * DIS # D5: 4,5 => CTR => D5: 2,6,8 * PRF # D5: 2,6,8 => SOL * DIS # D3: 3 => CTR => D3: 2,6 * DIS # F5: 2,6 => CTR => F5: 1,5 * PRF # F5: 1,5 => SOL * DIS # D4: 2,8 => CTR => D4: 5 * PRF # D4: 5 => SOL * PRF # E4: 2,8 => SOL * DIS # D5: 2,8 => CTR => D5: 4,5,6 * DIS # E5: 2,8 => CTR => E5: 1,4 * DIS # I6: 2,8 => CTR => I6: 5,6,9 * DIS # E8: 2,8 => CTR => E8: 1,3,7 * DIS # F7: 1,2 => CTR => F7: 7 * PRF # F7: 7 => SOL * PRF # E8: 1,2 => SOL * DIS # B9: 3,4,8 => CTR => B9: 1,2 * PRF # F5: 1,2 => SOL * CNT 17 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D1,E6,F1,F3,F9,G3,H2,H3,I2) * ..6...321...1.89..7.1......6.4..9............1..7.34......5......9..4.......6.75. * PAIR D1: 4,5 COL D D5: 4,5,2,6,8 # reduction candidate for 4,5 D5: 4,5 => CTR * ..6..5321...1.89..7.16.2...6.4..9........6...1..7.34......57....79..461.....6175. D5: 2,6,8 => SOLVED * 986475321245138967731296548624589173397641285158723496462357819579814632813962754 * DURATION: 0:00:03.318960 START: 06:37:23.349027 END: 06:37:26.667987 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-menneske-no-06902129-base-pr-001.dot * REASONING * DIS # D5: 4,5 => CTR => D5: 2,6,8 * PRF D5: 2,6,8 => SOL * STA D5: 2,6,8 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.menneske.no/sudoku/utskrift.html?number=6902129 umulig -------------------------------------------------- level: medium * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D1,E6,F1,F3,F9,G3,H2,H3,I2) * ..6...321...1.89..7.1......6.4..9............1..7.34......5......9..4.......6.75. * PAIR D1: 4,5 COL D D5: 4,5,2,6,8 # reduction candidate for 4,5 D5: 4,5 => CTR * ..6..5321...1.89..7.16.2...6.4..9........6...1..7.34......57....79..461.....6175. D5: 2,6,8 => SOLVED * 986475321245138967731296548624589173397641285158723496462357819579814632813962754 * PAIR F3: 2,6 BLK 2 D3: 2,6,3 # reduction candidate for 2,6 D3: 3 => CTR * ..6475321...1289..721396...6.4519......642...1.27834......57....79.3461.....6175. D3: 2,6 # 13 pairs * PAIR F3: 2,6 COL F F5: 2,6,1,5 # reduction candidate for 2,6 F5: 2,6 => CTR * ..6..5321...1.89..7.1......6.4..9............1..7.34......57....79..46......6175. F5: 1,5 => SOLVED * 986475321245138967731296548624589173397641285158723496462357819579814632813962754 * PAIR G3: 5,8 BLK 3 I3: 5,8,4 # reduction candidate for 5,8 I3: 5,8 # 9 pairs I3: 4 # 9 pairs * PAIR G3: 5,8 COL G G4: 5,8,1,2 # reduction candidate for 5,8 G4: 5,8 # 11 pairs G5: 5,8,1,2 # reduction candidate for 5,8 G5: 5,8 # 11 pairs * PAIR H3: 4,8 BLK 3 I3: 4,8,5 # reduction candidate for 4,8 I3: 4,8 # 9 pairs I3: 5 # 7 pairs * PAIR H3: 4,8 COL H H7: 4,8,1,3,9 # reduction candidate for 4,8 H7: 4,8 # 12 pairs H7: 1,3,9 # 9 pairs * PAIR E6: 2,8 BLK 5 D4: 2,8,5 # reduction candidate for 2,8 D4: 2,8 => CTR * ..64.5321...1.89..7.1......6.4.19......546...1..7.34......57....79..461.....6175. D4: 5 => SOLVED * 986475321245138967731296548624589173397641285158723496462357819579814632813962754 E4: 2,8,1 # reduction candidate for 2,8 E4: 2,8 => SOLVED * 986475321245138967731296548624589173397641285158723496462357819579814632813962754 E4: 1 # 9 pairs D5: 2,8,4,5,6 # reduction candidate for 2,8 D5: 2,8 => CTR * ..64.5321...1.89..7.16.2...6.45.9.......46...1..7.34......57....79..46......6175. D5: 4,5,6 # 9 pairs E5: 2,8,1,4 # reduction candidate for 2,8 E5: 2,8 => CTR * ..65.7321...1.89..7.16.2...6.4.19......4.6...1..7.34......51.....9..4.......6.75. E5: 1,4 # 10 pairs * PAIR E6: 2,8 ROW 6 B6: 2,8,5,9 # reduction candidate for 2,8 B6: 2,8 # 13 pairs C6: 2,8,5 # reduction candidate for 2,8 C6: 2,8 # 12 pairs I6: 2,8,5,6,9 # reduction candidate for 2,8 I6: 2,8 => CTR * 986.47321...138976731.9....6.4..9......4.....1957.346...7.5......9.74.......6.75. I6: 5,6,9 # 9 pairs * PAIR E6: 2,8 COL E E8: 2,8,1,3,7 # reduction candidate for 2,8 E8: 2,8 => CTR * ..6.75321...1.89..7.1.9....6.4..9............1..7.34......57....79..461.....6175. E8: 1,3,7 # 10 pairs * PAIR F9: 1,2 BLK 8 F7: 1,2,7 # reduction candidate for 1,2 F7: 1,2 => CTR * ..65.7321...1.89..7.1..6...6.4..9........5...1..7.34......5......9.74.......6.75. F7: 7 => SOLVED * 986475321245138967731296548624589173397641285158723496462357819579814632813962754 E8: 1,2,3,7,8 # reduction candidate for 1,2 E8: 1,2 => SOLVED * 986475321245138967731296548624589173397641285158723496462357819579814632813962754 E8: 3,7,8 # 9 pairs * PAIR F9: 1,2 ROW 9 B9: 1,2,3,4,8 # reduction candidate for 1,2 B9: 3,4,8 => CTR * ..6..7321...1.89..7.1..6...6.4..9......645...1..7.34....7.52...5.9.74.......6175. B9: 1,2 # 11 pairs * PAIR F9: 1,2 COL F F5: 1,2,5,6 # reduction candidate for 1,2 F5: 1,2 => SOLVED * 986475321245138967731296548624589173397641285158723496462357819579814632813962754 F5: 5,6 # 10 pairs * UNSOLVED! * SAVE PR GRAPH zz-menneske-no-06902129-base-pr-000.dot * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D1,E6,F1,F3,F9,G3,H2,H3,I2) * ..6...321...1.89..7.1......6.4..9............1..7.34......5......9..4.......6.75. * PAIR D1: 4,5 COL D D5: 4,5,2,6,8 # reduction candidate for 4,5 D5: 4,5 => CTR * ..6..5321...1.89..7.16.2...6.4..9........6...1..7.34......57....79..461.....6175. D5: 2,6,8 => SOLVED * 986475321245138967731296548624589173397641285158723496462357819579814632813962754 * SOLVED! * SAVE PR GRAPH zz-menneske-no-06902129-base-pr-001.dot
Solution
position: 986475321245138967731296548624589173397641285158723496462357819579814632813962754 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 # D5: 4,5 => CTR => D5: 2,6,8 * PRF # D5: 2,6,8 => SOL * INC # D3: 2,6 => UNS * DIS # D3: 3 => CTR => D3: 2,6 * DIS # F5: 2,6 => CTR => F5: 1,5 * PRF # F5: 1,5 => SOL * INC # I3: 5,8 => UNS * INC # I3: 4 => UNS * INC # G4: 5,8 => UNS * INC # G5: 5,8 => UNS * INC # I3: 4,8 => UNS * INC # I3: 5 => UNS * INC # H7: 4,8 => UNS * INC # H7: 1,3,9 => UNS * DIS # D4: 2,8 => CTR => D4: 5 * PRF # D4: 5 => SOL * PRF # E4: 2,8 => SOL * INC # E4: 1 => UNS * DIS # D5: 2,8 => CTR => D5: 4,5,6 * INC # D5: 4,5,6 => UNS * DIS # E5: 2,8 => CTR => E5: 1,4 * INC # E5: 1,4 => UNS * INC # B6: 2,8 => UNS * INC # C6: 2,8 => UNS * DIS # I6: 2,8 => CTR => I6: 5,6,9 * INC # I6: 5,6,9 => UNS * DIS # E8: 2,8 => CTR => E8: 1,3,7 * INC # E8: 1,3,7 => UNS * DIS # F7: 1,2 => CTR => F7: 7 * PRF # F7: 7 => SOL * PRF # E8: 1,2 => SOL * INC # E8: 3,7,8 => UNS * INC # B9: 1,2 => UNS * DIS # B9: 3,4,8 => CTR => B9: 1,2 * PRF # F5: 1,2 => SOL * INC # F5: 5,6 => UNS * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D5: 4,5 => CTR => D5: 2,6,8 * PRF D5: 2,6,8 => SOL * STA D5: 2,6,8 * CNT 2 HDP CHAINS / 1 HYP OPENED