Analysis of xx-mith-te3-00152151-base.sdk
Contents
Original Sudoku
level: medium
position: 1..........7.8...668.....51....3...5...5.4.1.9.567.....769....85.1....9789.7...6. initial
Autosolve
position: 1..........7.8...668.....51....3...5...5.4.1.9.567.....769....85.1....9789.7...6. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # F4: 1,8 => SOL * DIS # G5: 2,9 => CTR => G5: 3,6,7,8 * DIS # E1: 2,9 => CTR => E1: 4,5,6 * CNT 3 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # F4: 1,8 => SOL * STA F4: 1,8 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1..........7.8...668.....51....3...5...5.4.1.9.567.....769....85.1....9789.7...6. | initial |
| 1..........7.8...668.....51....3...5...5.4.1.9.567.....769....85.1....9789.7...6. | autosolve |
| 123456789457189236689327451264831975738594612915672843376945128541268397892713564 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (3) E5: 2,9 G7: 1,5 G9: 1,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,F2: 1.. / D2 = 1 => 7 pairs (_) / F2 = 1 => 11 pairs (_) B4,B6: 1.. / B4 = 1 => 8 pairs (_) / B6 = 1 => 10 pairs (_) E7,E9: 1.. / E7 = 1 => 2 pairs (_) / E9 = 1 => 2 pairs (_) G7,G9: 1.. / G7 = 1 => 2 pairs (_) / G9 = 1 => 2 pairs (_) B6,F6: 1.. / B6 = 1 => 10 pairs (_) / F6 = 1 => 8 pairs (_) E7,G7: 1.. / E7 = 1 => 2 pairs (_) / G7 = 1 => 2 pairs (_) E9,G9: 1.. / E9 = 1 => 2 pairs (_) / G9 = 1 => 2 pairs (_) D2,D4: 1.. / D2 = 1 => 7 pairs (_) / D4 = 1 => 11 pairs (_) B1,B2: 5.. / B1 = 5 => 17 pairs (_) / B2 = 5 => 7 pairs (_) G7,G9: 5.. / G7 = 5 => 2 pairs (_) / G9 = 5 => 2 pairs (_) B2,F2: 5.. / B2 = 5 => 7 pairs (_) / F2 = 5 => 17 pairs (_) E1,F1: 6.. / E1 = 6 => 13 pairs (_) / F1 = 6 => 5 pairs (_) B4,B5: 6.. / B4 = 6 => 10 pairs (_) / B5 = 6 => 8 pairs (_) G4,G5: 6.. / G4 = 6 => 8 pairs (_) / G5 = 6 => 10 pairs (_) E8,F8: 6.. / E8 = 6 => 5 pairs (_) / F8 = 6 => 13 pairs (_) B4,G4: 6.. / B4 = 6 => 10 pairs (_) / G4 = 6 => 8 pairs (_) B5,G5: 6.. / B5 = 6 => 8 pairs (_) / G5 = 6 => 10 pairs (_) E1,E8: 6.. / E1 = 6 => 13 pairs (_) / E8 = 6 => 5 pairs (_) F1,F8: 6.. / F1 = 6 => 5 pairs (_) / F8 = 6 => 13 pairs (_) F1,F3: 7.. / F1 = 7 => 0 pairs (X) / F3 = 7 => 5 pairs (_) A4,A5: 7.. / A4 = 7 => 9 pairs (_) / A5 = 7 => 4 pairs (_) F3,G3: 7.. / F3 = 7 => 5 pairs (_) / G3 = 7 => 0 pairs (X) A5,G5: 7.. / A5 = 7 => 4 pairs (_) / G5 = 7 => 9 pairs (_) H1,H4: 7.. / H1 = 7 => 11 pairs (_) / H4 = 7 => 4 pairs (_) G1,H1: 8.. / G1 = 8 => 4 pairs (_) / H1 = 8 => 4 pairs (_) C4,C5: 8.. / C4 = 8 => 9 pairs (_) / C5 = 8 => 4 pairs (_) D8,F8: 8.. / D8 = 8 => 9 pairs (_) / F8 = 8 => 10 pairs (_) C5,G5: 8.. / C5 = 8 => 4 pairs (_) / G5 = 8 => 9 pairs (_) D4,D8: 8.. / D4 = 8 => 10 pairs (_) / D8 = 8 => 9 pairs (_) C1,C3: 9.. / C1 = 9 => 8 pairs (_) / C3 = 9 => 11 pairs (_) F4,E5: 9.. / F4 = 9 => 9 pairs (_) / E5 = 9 => 0 pairs (*) F2,G2: 9.. / F2 = 9 => 0 pairs (*) / G2 = 9 => 0 pairs (X) F4,G4: 9.. / F4 = 9 => 9 pairs (_) / G4 = 9 => 0 pairs (*) I1,I5: 9.. / I1 = 9 => 0 pairs (*) / I5 = 9 => 0 pairs (X) * DURATION: 0:00:09.200105 START: 22:42:31.538118 END: 22:42:40.738223 2025-04-06 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (E5,G7,G9) * 1..........7.8...668.....51....3...5...5.4.1.9.567.....769....85.1....9789.7...6. * PAIR E5: 2,9 BLK 5 F4: 2,9,1,8 # reduction candidate for 2,9 F4: 1,8 => SOLVED * 123456789457189236689327451264831975738594612915672843376945128541268397892713564 F4: 2,9 # 6 pairs * PAIR E5: 2,9 ROW 5 G5: 2,9,3,6,7,8 # reduction candidate for 2,9 G5: 2,9 => CTR * 1.......9..7189..6689....51.1..3.675768594213935671..4.769....85.1....9789.7...62 G5: 3,6,7,8 # 3 pairs I5: 2,9,3 # reduction candidate for 2,9 I5: 2,9 # 7 pairs * PAIR E5: 2,9 COL E E1: 2,9,4,5,6 # reduction candidate for 2,9 E1: 2,9 => CTR * 15..9687..47185936689347251714839625368524719925671483.769....85.1468.9789.7...6. E1: 4,5,6 # 3 pairs E3: 2,9,4 # reduction candidate for 2,9 E3: 2,9 # 5 pairs * PAIR G7: 1,5 ROW 7 E7: 1,5,2,4 # reduction candidate for 1,5 E7: 2,4 # 5 pairs E7: 1,5 # 5 pairs * PAIR G9: 1,5 ROW 9 E9: 1,5,2,4 # reduction candidate for 1,5 E9: 2,4 # 5 pairs E9: 1,5 # 5 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-mith-te3-00152151-base-pr-000.dot * REASONING * PRF # F4: 1,8 => SOL * DIS # G5: 2,9 => CTR => G5: 3,6,7,8 * DIS # E1: 2,9 => CTR => E1: 4,5,6 * CNT 3 HDP CHAINS / 12 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (E5,G7,G9) * 1..........7.8...668.....51....3...5...5.4.1.9.567.....769....85.1....9789.7...6. * PAIR E5: 2,9 BLK 5 F4: 2,9,1,8 # reduction candidate for 2,9 F4: 1,8 => SOLVED * 123456789457189236689327451264831975738594612915672843376945128541268397892713564 * DURATION: 0:00:00.669042 START: 22:42:42.725601 END: 22:42:43.394643 2025-04-06 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00152151-base-pr-001.dot * REASONING * PRF # F4: 1,8 => SOL * STA F4: 1,8 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
rating: 41556; r2: 833093; index: 152151
Solution
position: 123456789457189236689327451264831975738594612915672843376945128541268397892713564 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 # F4: 2,9 => UNS * PRF # F4: 1,8 => SOL * DIS # G5: 2,9 => CTR => G5: 3,6,7,8 * INC # G5: 3,6,7,8 => UNS * INC # I5: 2,9 => UNS * DIS # E1: 2,9 => CTR => E1: 4,5,6 * INC # E1: 4,5,6 => UNS * INC # E3: 2,9 => UNS * INC # E7: 1,5 => UNS * INC # E7: 2,4 => UNS * INC # E9: 1,5 => UNS * INC # E9: 2,4 => UNS * CNT 12 HDP CHAINS / 12 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F4: 2,9 => UNS * PRF # F4: 1,8 => SOL * STA F4: 1,8 * CNT 2 HDP CHAINS / 2 HYP OPENED