Analysis of zz-www.sudokuwiki.org-0079-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=79
level: medium
position: ....6...268.1.2.4....4..5.......9.8...1.2.9...3.5.......4..3....1.2.4.562...7.... initial
Autosolve
position: ....6...268.1.2.4....4..56......9.8...1.2.9...3.5.......4..3....1.2.4.562...7.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F5: 7,8 => CTR => F5: 6 * DIS # G1: 3,7 => CTR => G1: 1,8 * DIS # G4: 3,7 => CTR => G4: 1,2,4,6 * DIS # G4: 3,7 => CTR => G4: 1,2,4,6 * DIS # G4: 3,7 => CTR => G4: 1,2,4,6 * PRF # I5: 3,7 => SOL * CNT 6 HDP CHAINS / 39 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F5: 7,8 => CTR => F5: 6 * DIS F5: 6 # G1: 3,7 => CTR => G1: 1,8 * DIS F5: 6 + G1: 1,8 # G4: 3,7 => CTR => G4: 1,2,4,6 * DIS F5: 6 + G1: 1,8 + G4: 1,2,4,6 # G8: 8 => CTR => G8: 3,7 * PRF F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # I5: 3,7 => SOL * STA F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 + I5: 3,7 * CNT 5 HDP CHAINS / 37 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....6...268.1.2.4....4..5.......9.8...1.2.9...3.5.......4..3....1.2.4.562...7.... | initial |
| ....6...268.1.2.4....4..56......9.8...1.2.9...3.5.......4..3....1.2.4.562...7.... | autosolve |
| 493765812685192347127438569762349185541826973938517624874653291319284756256971438 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) F3: 7,8 G2: 3,7 D4: 3,7 H5: 3,7 E7: 1,5 E8: 8,9 F9: 1,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A3: 1.. / A1 = 1 => 12 pairs (_) / A3 = 1 => 7 pairs (_) E7,F9: 1.. / E7 = 1 => 13 pairs (_) / F9 = 1 => 9 pairs (_) A3,I3: 1.. / A3 = 1 => 7 pairs (_) / I3 = 1 => 12 pairs (_) F6,F9: 1.. / F6 = 1 => 13 pairs (_) / F9 = 1 => 9 pairs (_) B3,C3: 2.. / B3 = 2 => 7 pairs (_) / C3 = 2 => 8 pairs (_) G7,H7: 2.. / G7 = 2 => 7 pairs (_) / H7 = 2 => 10 pairs (_) B3,B4: 2.. / B3 = 2 => 7 pairs (_) / B4 = 2 => 8 pairs (_) H6,H7: 2.. / H6 = 2 => 7 pairs (_) / H7 = 2 => 10 pairs (_) A1,B1: 4.. / A1 = 4 => 9 pairs (_) / B1 = 4 => 7 pairs (_) E4,E6: 4.. / E4 = 4 => 11 pairs (_) / E6 = 4 => 9 pairs (_) G9,I9: 4.. / G9 = 4 => 7 pairs (_) / I9 = 4 => 11 pairs (_) F1,E2: 5.. / F1 = 5 => 9 pairs (_) / E2 = 5 => 13 pairs (_) I4,I5: 5.. / I4 = 5 => 8 pairs (_) / I5 = 5 => 8 pairs (_) E7,F9: 5.. / E7 = 5 => 9 pairs (_) / F9 = 5 => 13 pairs (_) C2,E2: 5.. / C2 = 5 => 9 pairs (_) / E2 = 5 => 13 pairs (_) E2,E7: 5.. / E2 = 5 => 13 pairs (_) / E7 = 5 => 9 pairs (_) F1,F9: 5.. / F1 = 5 => 9 pairs (_) / F9 = 5 => 13 pairs (_) F5,F6: 6.. / F5 = 6 => 7 pairs (_) / F6 = 6 => 0 pairs (X) G4,G6: 6.. / G4 = 6 => 7 pairs (_) / G6 = 6 => 7 pairs (_) D7,D9: 6.. / D7 = 6 => 8 pairs (_) / D9 = 6 => 9 pairs (_) B5,F5: 6.. / B5 = 6 => 0 pairs (X) / F5 = 6 => 7 pairs (_) B7,D7: 6.. / B7 = 6 => 9 pairs (_) / D7 = 6 => 8 pairs (_) G1,I3: 8.. / G1 = 8 => 11 pairs (_) / I3 = 8 => 10 pairs (_) A6,C6: 9.. / A6 = 9 => 7 pairs (_) / C6 = 9 => 7 pairs (_) * DURATION: 0:00:26.268704 START: 04:50:44.421450 END: 04:51:10.690154 2017-05-01 * CP COUNT: (24) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D4,E7,E8,F3,F9,G2,H5) * ....6...268.1.2.4....4..56......9.8...1.2.9...3.5.......4..3....1.2.4.562...7.... * PAIR F3: 7,8 BLK 2 D1: 7,8,3,9 # reduction candidate for 7,8 D1: 7,8 # 18 pairs F1: 7,8,5 # reduction candidate for 7,8 F1: 7,8 # 13 pairs * PAIR F3: 7,8 ROW 3 I3: 7,8,1,3,9 # reduction candidate for 7,8 I3: 1,3,9 # 11 pairs I3: 7,8 # 10 pairs * PAIR F3: 7,8 COL F F5: 7,8,6 # reduction candidate for 7,8 F5: 7,8 => CTR * ...96581268513274....4..56....3.968..61.2.93..3.5.6.....4653....1.2.4.56256.71.9. F5: 6 # 7 pairs F6: 7,8,1,6 # reduction candidate for 7,8 F6: 7,8 # 11 pairs * PAIR G2: 3,7 BLK 3 G1: 3,7,1,8 # reduction candidate for 3,7 G1: 3,7 => CTR * 4..968.1268.152.49129437568752349.8.8.1.269...3.581.24564813297.1.294856298675431 G1: 1,8 # 8 pairs H1: 3,7,1,9 # reduction candidate for 3,7 H1: 3,7 # 13 pairs I2: 3,7,9 # reduction candidate for 3,7 I2: 3,7 # 12 pairs I3: 3,7,1,8,9 # reduction candidate for 3,7 I3: 3,7 # 15 pairs * PAIR G2: 3,7 ROW 2 C2: 3,7,5,9 # reduction candidate for 3,7 C2: 3,7 # 15 pairs C2: 5,9 # 8 pairs * PAIR G2: 3,7 COL G G4: 3,7,1,2,4,6 # reduction candidate for 3,7 G4: 3,7 => CTR * ...9681.268.152.491..437568..6.49.818.1.269.5.3.581624.64813297.1.294856298675413 G4: 1,2,4,6 # 7 pairs G8: 3,7,8 # reduction candidate for 3,7 G8: 3,7 # 9 pairs * PAIR D4: 3,7 BLK 5 D5: 3,7,8 # reduction candidate for 3,7 D5: 8 # 17 pairs D5: 3,7 # 12 pairs * PAIR D4: 3,7 ROW 4 G4: 3,7,1,2,4,6 # reduction candidate for 3,7 G4: 3,7 => CTR * ...9681.268.152.491..437568..6.49.818.1.269.5.3.581624.64813297.1.294856298675413 G4: 1,2,4,6 # 7 pairs I4: 3,7,1,4,5 # reduction candidate for 3,7 I4: 3,7 # 14 pairs * PAIR D4: 3,7 COL D D1: 3,7,8,9 # reduction candidate for 3,7 D1: 3,7 # 17 pairs D1: 8,9 # 12 pairs * PAIR H5: 3,7 BLK 6 G4: 3,7,1,2,4,6 # reduction candidate for 3,7 G4: 3,7 => CTR * ...9681.268.152.491..437568..6.49.818.1.269.5.3.581624.64813297.1.294856298675413 G4: 1,2,4,6 # 7 pairs I4: 3,7,1,4,5 # reduction candidate for 3,7 I4: 3,7 # 14 pairs I5: 3,7,4,5 # reduction candidate for 3,7 I5: 3,7 => SOLVED * 493765812685192347127438569762349185541826973938517624874653291319284756256971438 I5: 4,5 # 8 pairs * PAIR H5: 3,7 ROW 5 D5: 3,7,8 # reduction candidate for 3,7 D5: 8 # 17 pairs D5: 3,7 # 12 pairs * PAIR H5: 3,7 COL H H1: 3,7,1,9 # reduction candidate for 3,7 H1: 3,7 # 13 pairs H1: 1,9 # 8 pairs * PAIR E8: 8,9 BLK 8 D7: 8,9,6 # reduction candidate for 8,9 D7: 8,9 # 9 pairs D9: 8,9,6 # reduction candidate for 8,9 D9: 8,9 # 8 pairs * PAIR E8: 8,9 ROW 8 A8: 8,9,3,7 # reduction candidate for 8,9 A8: 8,9 # 13 pairs C8: 8,9,3,7 # reduction candidate for 8,9 C8: 8,9 # 11 pairs * PAIR E8: 8,9 COL E E3: 8,9,3 # reduction candidate for 8,9 E3: 8,9 # 10 pairs E3: 3 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0079-base-pr-000.dot * REASONING * DIS # F5: 7,8 => CTR => F5: 6 * DIS # G1: 3,7 => CTR => G1: 1,8 * DIS # G4: 3,7 => CTR => G4: 1,2,4,6 * DIS # G4: 3,7 => CTR => G4: 1,2,4,6 * DIS # G4: 3,7 => CTR => G4: 1,2,4,6 * PRF # I5: 3,7 => SOL * CNT 6 HDP CHAINS / 39 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D4,E7,E8,F3,F9,G2,H5) * ....6...268.1.2.4....4..56......9.8...1.2.9...3.5.......4..3....1.2.4.562...7.... * PAIR F3: 7,8 BLK 2 D1: 7,8,3,9 # reduction candidate for 7,8 D1: 7,8 # 18 pairs F1: 7,8,5 # reduction candidate for 7,8 F1: 7,8 # 13 pairs * PAIR F3: 7,8 ROW 3 I3: 7,8,1,3,9 # reduction candidate for 7,8 I3: 1,3,9 # 11 pairs I3: 7,8 # 10 pairs * PAIR F3: 7,8 COL F F5: 7,8,6 # reduction candidate for 7,8 F5: 7,8 => CTR * ...96581268513274....4..56....3.968..61.2.93..3.5.6.....4653....1.2.4.56256.71.9. F6: 7,8,1 # reduction candidate for 7,8 F6: 7,8 # 11 pairs * RESTART * PAIR F3: 7,8 COL F F6: 7,8,1 # reduction candidate for 7,8 F6: 1 # 13 pairs F6: 7,8 # 11 pairs * PAIR RESTART * PAIR F3: 7,8 BLK 2 D1: 7,8,3,9 # reduction candidate for 7,8 D1: 7,8 # 20 pairs F1: 7,8,5 # reduction candidate for 7,8 F1: 7,8 # 13 pairs * PAIR F3: 7,8 ROW 3 I3: 7,8,1,3,9 # reduction candidate for 7,8 I3: 1,3,9 # 11 pairs I3: 7,8 # 10 pairs * PAIR F3: 7,8 COL F F6: 7,8,1 # reduction candidate for 7,8 F6: 1 # 13 pairs F6: 7,8 # 11 pairs * PAIR G2: 3,7 BLK 3 G1: 3,7,1,8 # reduction candidate for 3,7 G1: 3,7 => CTR * 4..968.1268.152.49129437568..2.49.8.8.1.269...3.581.24.64813297.1.294856298675431 H1: 3,7,1,9 # reduction candidate for 3,7 H1: 3,7 # 13 pairs I2: 3,7,9 # reduction candidate for 3,7 I2: 3,7 # 12 pairs I3: 3,7,1,8,9 # reduction candidate for 3,7 I3: 3,7 # 15 pairs * PAIR G2: 3,7 ROW 2 C2: 3,7,5,9 # reduction candidate for 3,7 C2: 3,7 # 16 pairs C2: 5,9 # 9 pairs * PAIR G2: 3,7 COL G G4: 3,7,1,2,4,6 # reduction candidate for 3,7 G4: 3,7 => CTR * ...9681.268.152.491..437568..6.49.818.1.269.5.3.581624.64813297.1.294856298675413 G8: 3,7,8 # reduction candidate for 3,7 G8: 3,7 # 9 pairs * RESTART * PAIR G2: 3,7 COL G G8: 3,7,8 # reduction candidate for 3,7 G8: 8 => CTR * 4.39681726871523491..437568...349.81841726935.3.581724564813297.1.294856298675413 * PAIR RESTART * PAIR G2: 3,7 BLK 3 H1: 3,7,1,9 # reduction candidate for 3,7 H1: 3,7 # 14 pairs I2: 3,7,9 # reduction candidate for 3,7 I2: 3,7 # 13 pairs I3: 3,7,1,8,9 # reduction candidate for 3,7 I3: 3,7 # 15 pairs * PAIR G2: 3,7 ROW 2 C2: 3,7,5,9 # reduction candidate for 3,7 C2: 3,7 # 18 pairs C2: 5,9 # 10 pairs * PAIR D4: 3,7 BLK 5 D5: 3,7,8 # reduction candidate for 3,7 D5: 8 # 20 pairs D5: 3,7 # 15 pairs * PAIR D4: 3,7 ROW 4 I4: 3,7,1,4,5 # reduction candidate for 3,7 I4: 3,7 # 16 pairs I4: 1,4,5 # 10 pairs * PAIR D4: 3,7 COL D D1: 3,7,8,9 # reduction candidate for 3,7 D1: 3,7 # 20 pairs D1: 8,9 # 15 pairs * PAIR H5: 3,7 BLK 6 I4: 3,7,1,4,5 # reduction candidate for 3,7 I4: 3,7 # 16 pairs I5: 3,7,4,5 # reduction candidate for 3,7 I5: 3,7 => SOLVED * 493765812685192347127438569762349185541826973938517624874653291319284756256971438 * DURATION: 0:00:28.036762 START: 04:51:36.561488 END: 04:52:04.598250 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0079-base-pr-001.dot * REASONING * DIS # F5: 7,8 => CTR => F5: 6 * DIS F5: 6 # G1: 3,7 => CTR => G1: 1,8 * DIS F5: 6 + G1: 1,8 # G4: 3,7 => CTR => G4: 1,2,4,6 * DIS F5: 6 + G1: 1,8 + G4: 1,2,4,6 # G8: 8 => CTR => G8: 3,7 * PRF F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # I5: 3,7 => SOL * STA F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 + I5: 3,7 * CNT 5 HDP CHAINS / 37 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=79
Solution
position: 493765812685192347127438569762349185541826973938517624874653291319284756256971438 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 # D1: 7,8 => UNS * INC # F1: 7,8 => UNS * INC # I3: 7,8 => UNS * INC # I3: 1,3,9 => UNS * DIS # F5: 7,8 => CTR => F5: 6 * INC # F5: 6 => UNS * INC # F6: 7,8 => UNS * DIS # G1: 3,7 => CTR => G1: 1,8 * INC # G1: 1,8 => UNS * INC # H1: 3,7 => UNS * INC # I2: 3,7 => UNS * INC # I3: 3,7 => UNS * INC # C2: 3,7 => UNS * INC # C2: 5,9 => UNS * DIS # G4: 3,7 => CTR => G4: 1,2,4,6 * INC # G4: 1,2,4,6 => UNS * INC # G8: 3,7 => UNS * INC # D5: 3,7 => UNS * INC # D5: 8 => UNS * DIS # G4: 3,7 => CTR => G4: 1,2,4,6 * INC # G4: 1,2,4,6 => UNS * INC # I4: 3,7 => UNS * INC # D1: 3,7 => UNS * INC # D1: 8,9 => UNS * DIS # G4: 3,7 => CTR => G4: 1,2,4,6 * INC # G4: 1,2,4,6 => UNS * INC # I4: 3,7 => UNS * PRF # I5: 3,7 => SOL * INC # I5: 4,5 => UNS * INC # D5: 3,7 => UNS * INC # D5: 8 => UNS * INC # H1: 3,7 => UNS * INC # H1: 1,9 => UNS * INC # D7: 8,9 => UNS * INC # D9: 8,9 => UNS * INC # A8: 8,9 => UNS * INC # C8: 8,9 => UNS * INC # E3: 8,9 => UNS * INC # E3: 3 => UNS * CNT 39 HDP CHAINS / 39 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D1: 7,8 => UNS * INC # F1: 7,8 => UNS * INC # I3: 7,8 => UNS * INC # I3: 1,3,9 => UNS * DIS # F5: 7,8 => CTR => F5: 6 * INC F5: 6 # F6: 7,8 => UNS * INC F5: 6 # F6: 7,8 => UNS * INC F5: 6 # F6: 1 => UNS * INC F5: 6 # D1: 7,8 => UNS * INC F5: 6 # F1: 7,8 => UNS * INC F5: 6 # I3: 7,8 => UNS * INC F5: 6 # I3: 1,3,9 => UNS * INC F5: 6 # F6: 7,8 => UNS * INC F5: 6 # F6: 1 => UNS * DIS F5: 6 # G1: 3,7 => CTR => G1: 1,8 * INC F5: 6 + G1: 1,8 # H1: 3,7 => UNS * INC F5: 6 + G1: 1,8 # I2: 3,7 => UNS * INC F5: 6 + G1: 1,8 # I3: 3,7 => UNS * INC F5: 6 + G1: 1,8 # C2: 3,7 => UNS * INC F5: 6 + G1: 1,8 # C2: 5,9 => UNS * DIS F5: 6 + G1: 1,8 # G4: 3,7 => CTR => G4: 1,2,4,6 * INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 # G8: 3,7 => UNS * INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 # G8: 3,7 => UNS * DIS F5: 6 + G1: 1,8 + G4: 1,2,4,6 # G8: 8 => CTR => G8: 3,7 * INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # H1: 3,7 => UNS * INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # I2: 3,7 => UNS * INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # I3: 3,7 => UNS * INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # C2: 3,7 => UNS * INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # C2: 5,9 => UNS * INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # D5: 3,7 => UNS * INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # D5: 8 => UNS * INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # I4: 3,7 => UNS * INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # I4: 1,4,5 => UNS * INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # D1: 3,7 => UNS * INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # D1: 8,9 => UNS * INC F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # I4: 3,7 => UNS * PRF F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 # I5: 3,7 => SOL * STA F5: 6 + G1: 1,8 + G4: 1,2,4,6 + G8: 3,7 + I5: 3,7 * CNT 37 HDP CHAINS / 37 HYP OPENED