Analysis of xx-mith-te3-00116705-base.sdk
Contents
Original Sudoku
level: medium
position: 12..56.8..5718....6.82.7.1.2.576.......8......8..1.6......28.73....719...72....5. initial
Autosolve
position: 12..56.8..5718....6.82.7.1.2.576.......8......8..1.6......28473....719...72....5. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # G4: 3 => SOL * CNT 1 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # G4: 3 => SOL * STA G4: 3 * CNT 1 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 12..56.8..5718....6.82.7.1.2.576.......8......8..1.6......28.73....719...72....5. | initial |
| 12..56.8..5718....6.82.7.1.2.576.......8......8..1.6......28473....719...72....5. | autosolve |
| 123456789457189236698237514215764398346895127789312645561928473834571962972643851 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) G1: 3,7 G2: 2,3 G3: 3,5 F5: 2,5 F6: 2,5 A7: 5,9 H8: 2,6 G9: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B7,C7: 1.. / B7 = 1 => 12 pairs (_) / C7 = 1 => 9 pairs (_) G9,I9: 1.. / G9 = 1 => 8 pairs (_) / I9 = 1 => 18 pairs (_) C5,C7: 1.. / C5 = 1 => 12 pairs (_) / C7 = 1 => 9 pairs (_) F5,F6: 2.. / F5 = 2 => 5 pairs (_) / F6 = 2 => 6 pairs (_) H8,I8: 2.. / H8 = 2 => 13 pairs (_) / I8 = 2 => 17 pairs (_) G2,G5: 2.. / G2 = 2 => 7 pairs (_) / G5 = 2 => 13 pairs (_) G3,I3: 5.. / G3 = 5 => 8 pairs (_) / I3 = 5 => 7 pairs (_) F5,F6: 5.. / F5 = 5 => 6 pairs (_) / F6 = 5 => 5 pairs (_) A7,A8: 5.. / A7 = 5 => 9 pairs (_) / A8 = 5 => 14 pairs (_) D7,D8: 5.. / D7 = 5 => 14 pairs (_) / D8 = 5 => 9 pairs (_) F6,I6: 5.. / F6 = 5 => 5 pairs (_) / I6 = 5 => 6 pairs (_) A7,D7: 5.. / A7 = 5 => 9 pairs (_) / D7 = 5 => 14 pairs (_) A8,D8: 5.. / A8 = 5 => 14 pairs (_) / D8 = 5 => 9 pairs (_) G3,G5: 5.. / G3 = 5 => 8 pairs (_) / G5 = 5 => 7 pairs (_) H2,I2: 6.. / H2 = 6 => 13 pairs (_) / I2 = 6 => 17 pairs (_) B5,C5: 6.. / B5 = 6 => 10 pairs (_) / C5 = 6 => 10 pairs (_) D9,I9: 6.. / D9 = 6 => 19 pairs (_) / I9 = 6 => 11 pairs (_) H2,H8: 6.. / H2 = 6 => 13 pairs (_) / H8 = 6 => 17 pairs (_) G1,I1: 7.. / G1 = 7 => 8 pairs (_) / I1 = 7 => 9 pairs (_) A5,A6: 7.. / A5 = 7 => 20 pairs (_) / A6 = 7 => 8 pairs (_) A6,I6: 7.. / A6 = 7 => 8 pairs (_) / I6 = 7 => 20 pairs (_) G1,G5: 7.. / G1 = 7 => 8 pairs (_) / G5 = 7 => 9 pairs (_) G4,I4: 8.. / G4 = 8 => 8 pairs (_) / I4 = 8 => 18 pairs (_) A8,A9: 8.. / A8 = 8 => 19 pairs (_) / A9 = 8 => 11 pairs (_) A8,I8: 8.. / A8 = 8 => 19 pairs (_) / I8 = 8 => 11 pairs (_) G4,G9: 8.. / G4 = 8 => 8 pairs (_) / G9 = 8 => 18 pairs (_) * DURATION: 0:00:07.176378 START: 18:44:22.885201 END: 18:44:30.061579 2025-04-06 * CP COUNT: (26) * INCONCLUSIVE -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,F5,F6,G1,G2,G3,G9,H8) * 12..56.8..5718....6.82.7.1.2.576.......8......8..1.6......28473....719...72....5. * PAIR G1: 3,7 COL G G5: 3,7,1,2,5 # reduction candidate for 3,7 G5: 3,7 # 9 pairs G5: 1,2,5 # 8 pairs * PAIR G2: 2,3 BLK 3 H2: 2,3,4,6,9 # reduction candidate for 2,3 H2: 2,3 # 27 pairs H2: 4,6,9 # 9 pairs * PAIR G2: 2,3 COL G G5: 2,3,1,5,7 # reduction candidate for 2,3 G5: 2,3 # 18 pairs G5: 1,5,7 # 7 pairs * PAIR G3: 3,5 COL G G5: 3,5,1,2,7 # reduction candidate for 3,5 G5: 3,5 # 9 pairs G5: 1,2,7 # 8 pairs * PAIR F5: 2,5 ROW 5 G5: 2,5,1,3,7 # reduction candidate for 2,5 G5: 2,5 # 10 pairs I5: 2,5,1,4,7,9 # reduction candidate for 2,5 I5: 2,5 # 8 pairs * PAIR F6: 2,5 ROW 6 I6: 2,5,4,7,9 # reduction candidate for 2,5 I6: 4,7,9 # 14 pairs I6: 2,5 # 9 pairs * PAIR A7: 5,9 ROW 7 D7: 5,9,6 # reduction candidate for 5,9 D7: 5,9 # 18 pairs D7: 6 # 11 pairs * PAIR H8: 2,6 BLK 9 I8: 2,6,8 # reduction candidate for 2,6 I8: 2,6 # 19 pairs I8: 8 # 11 pairs * PAIR H8: 2,6 COL H H2: 2,6,3,4,9 # reduction candidate for 2,6 H2: 3,4,9 # 16 pairs H2: 2,6 # 14 pairs * PAIR G9: 1,8 BLK 9 I9: 1,8,6 # reduction candidate for 1,8 I9: 1,8 # 19 pairs I9: 6 # 11 pairs * PAIR G9: 1,8 COL G G4: 1,8,3 # reduction candidate for 1,8 G4: 3 => SOLVED * 123456789457189236698237514215764398346895127789312645561928473834571962972643851 G4: 1,8 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-mith-te3-00116705-base-pr-000.dot * REASONING * PRF # G4: 3 => SOL * CNT 1 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,F5,F6,G1,G2,G3,G9,H8) * 12..56.8..5718....6.82.7.1.2.576.......8......8..1.6......28473....719...72....5. * PAIR G1: 3,7 COL G G5: 3,7,1,2,5 # reduction candidate for 3,7 G5: 3,7 # 9 pairs G5: 1,2,5 # 8 pairs * PAIR G2: 2,3 BLK 3 H2: 2,3,4,6,9 # reduction candidate for 2,3 H2: 2,3 # 27 pairs H2: 4,6,9 # 9 pairs * PAIR G2: 2,3 COL G G5: 2,3,1,5,7 # reduction candidate for 2,3 G5: 2,3 # 18 pairs G5: 1,5,7 # 7 pairs * PAIR G3: 3,5 COL G G5: 3,5,1,2,7 # reduction candidate for 3,5 G5: 3,5 # 9 pairs G5: 1,2,7 # 8 pairs * PAIR F5: 2,5 ROW 5 G5: 2,5,1,3,7 # reduction candidate for 2,5 G5: 2,5 # 10 pairs I5: 2,5,1,4,7,9 # reduction candidate for 2,5 I5: 2,5 # 8 pairs * PAIR F6: 2,5 ROW 6 I6: 2,5,4,7,9 # reduction candidate for 2,5 I6: 4,7,9 # 14 pairs I6: 2,5 # 9 pairs * PAIR A7: 5,9 ROW 7 D7: 5,9,6 # reduction candidate for 5,9 D7: 5,9 # 18 pairs D7: 6 # 11 pairs * PAIR H8: 2,6 BLK 9 I8: 2,6,8 # reduction candidate for 2,6 I8: 2,6 # 19 pairs I8: 8 # 11 pairs * PAIR H8: 2,6 COL H H2: 2,6,3,4,9 # reduction candidate for 2,6 H2: 3,4,9 # 16 pairs H2: 2,6 # 14 pairs * PAIR G9: 1,8 BLK 9 I9: 1,8,6 # reduction candidate for 1,8 I9: 1,8 # 19 pairs I9: 6 # 11 pairs * PAIR G9: 1,8 COL G G4: 1,8,3 # reduction candidate for 1,8 G4: 3 => SOLVED * 123456789457189236698237514215764398346895127789312645561928473834571962972643851 * DURATION: 0:00:03.589435 START: 18:44:33.689982 END: 18:44:37.279417 2025-04-06 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00116705-base-pr-001.dot * REASONING * PRF # G4: 3 => SOL * STA G4: 3 * CNT 1 HDP CHAINS / 22 HYP OPENED
Header Info
rating: 29863; r2: 566418; index: 116705
Solution
position: 123456789457189236698237514215764398346895127789312645561928473834571962972643851 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 # G5: 3,7 => UNS * INC # G5: 1,2,5 => UNS * INC # H2: 2,3 => UNS * INC # H2: 4,6,9 => UNS * INC # G5: 2,3 => UNS * INC # G5: 1,5,7 => UNS * INC # G5: 3,5 => UNS * INC # G5: 1,2,7 => UNS * INC # G5: 2,5 => UNS * INC # I5: 2,5 => UNS * INC # I6: 2,5 => UNS * INC # I6: 4,7,9 => UNS * INC # D7: 5,9 => UNS * INC # D7: 6 => UNS * INC # I8: 2,6 => UNS * INC # I8: 8 => UNS * INC # H2: 2,6 => UNS * INC # H2: 3,4,9 => UNS * INC # I9: 1,8 => UNS * INC # I9: 6 => UNS * INC # G4: 1,8 => UNS * PRF # G4: 3 => SOL * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G5: 3,7 => UNS * INC # G5: 1,2,5 => UNS * INC # H2: 2,3 => UNS * INC # H2: 4,6,9 => UNS * INC # G5: 2,3 => UNS * INC # G5: 1,5,7 => UNS * INC # G5: 3,5 => UNS * INC # G5: 1,2,7 => UNS * INC # G5: 2,5 => UNS * INC # I5: 2,5 => UNS * INC # I6: 2,5 => UNS * INC # I6: 4,7,9 => UNS * INC # D7: 5,9 => UNS * INC # D7: 6 => UNS * INC # I8: 2,6 => UNS * INC # I8: 8 => UNS * INC # H2: 2,6 => UNS * INC # H2: 3,4,9 => UNS * INC # I9: 1,8 => UNS * INC # I9: 6 => UNS * INC # G4: 1,8 => UNS * PRF # G4: 3 => SOL * STA G4: 3 * CNT 22 HDP CHAINS / 22 HYP OPENED