Analysis of xx-mith-te3-00153131-base.sdk
Contents
Original Sudoku
level: medium
position: ...4.6.89..71........23.....61..5...57...1.6.9.8....15...7..6..71.....588.65...9. initial
Autosolve
position: ...4.6.89..71........23.....61..5...57...1.6.9.8....15...7..6..71.....588.65...9. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # E2: 8,9 => SOL * PRF # B2: 2,3,4,5 => SOL * PRF # F7: 8,9 => SOL * DIS # G3: 4,7 => CTR => G3: 1,5 * CNT 4 HDP CHAINS / 20 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # E2: 8,9 => SOL * STA E2: 8,9 * CNT 1 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...4.6.89..71........23.....61..5...57...1.6.9.8....15...7..6..71.....588.65...9. | initial |
| ...4.6.89..71........23.....61..5...57...1.6.9.8....15...7..6..71.....588.65...9. | autosolve |
| 123456789457189236689237541261845973574391862938672415395718624712964358846523197 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) E1: 5,7 F2: 8,9 H3: 4,7 D6: 3,6 G4: 8,9 G5: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A3: 1.. / A1 = 1 => 7 pairs (_) / A3 = 1 => 12 pairs (_) E7,E9: 1.. / E7 = 1 => 0 pairs (*) / E9 = 1 => 0 pairs (X) A1,G1: 1.. / A1 = 1 => 7 pairs (_) / G1 = 1 => 12 pairs (_) E7,I7: 1.. / E7 = 1 => 0 pairs (*) / I7 = 1 => 0 pairs (X) E1,E2: 5.. / E1 = 5 => 0 pairs (*) / E2 = 5 => 0 pairs (X) B7,C7: 5.. / B7 = 5 => 15 pairs (_) / C7 = 5 => 8 pairs (_) A2,A3: 6.. / A2 = 6 => 7 pairs (_) / A3 = 6 => 6 pairs (_) I2,I3: 6.. / I2 = 6 => 6 pairs (_) / I3 = 6 => 7 pairs (_) D6,E6: 6.. / D6 = 6 => 6 pairs (_) / E6 = 6 => 9 pairs (_) D8,E8: 6.. / D8 = 6 => 9 pairs (_) / E8 = 6 => 6 pairs (_) A2,I2: 6.. / A2 = 6 => 7 pairs (_) / I2 = 6 => 6 pairs (_) A3,I3: 6.. / A3 = 6 => 6 pairs (_) / I3 = 6 => 7 pairs (_) D6,D8: 6.. / D6 = 6 => 6 pairs (_) / D8 = 6 => 9 pairs (_) E6,E8: 6.. / E6 = 6 => 9 pairs (_) / E8 = 6 => 6 pairs (_) E1,F3: 7.. / E1 = 7 => 14 pairs (_) / F3 = 7 => 0 pairs (*) G9,I9: 7.. / G9 = 7 => 14 pairs (_) / I9 = 7 => 6 pairs (_) E1,G1: 7.. / E1 = 7 => 14 pairs (_) / G1 = 7 => 0 pairs (*) F3,F6: 7.. / F3 = 7 => 0 pairs (*) / F6 = 7 => 0 pairs (X) H3,H4: 7.. / H3 = 7 => 14 pairs (_) / H4 = 7 => 9 pairs (_) B2,B3: 8.. / B2 = 8 => 11 pairs (_) / B3 = 8 => 7 pairs (_) D4,D5: 8.. / D4 = 8 => 5 pairs (_) / D5 = 8 => 6 pairs (_) G4,G5: 8.. / G4 = 8 => 6 pairs (_) / G5 = 8 => 5 pairs (_) E7,F7: 8.. / E7 = 8 => 7 pairs (_) / F7 = 8 => 0 pairs (*) B3,F3: 8.. / B3 = 8 => 7 pairs (_) / F3 = 8 => 11 pairs (_) D4,G4: 8.. / D4 = 8 => 5 pairs (_) / G4 = 8 => 6 pairs (_) D5,G5: 8.. / D5 = 8 => 6 pairs (_) / G5 = 8 => 5 pairs (_) E2,E7: 8.. / E2 = 8 => 0 pairs (*) / E7 = 8 => 0 pairs (X) G4,G5: 9.. / G4 = 9 => 5 pairs (_) / G5 = 9 => 6 pairs (_) * DURATION: 0:00:07.618491 START: 22:42:31.561993 END: 22:42:39.180484 2025-04-06 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D6,E1,F2,G4,G5,H3) * ...4.6.89..71........23.....61..5...57...1.6.9.8....15...7..6..71.....588.65...9. * PAIR E1: 5,7 ROW 1 G1: 5,7,1,2,3 # reduction candidate for 5,7 G1: 5,7 # 15 pairs G1: 1,2,3 # 12 pairs * PAIR F2: 8,9 BLK 2 E2: 8,9,5 # reduction candidate for 8,9 E2: 8,9 => SOLVED * 123456789457189236689237541261845973574391862938672415395718624712964358846523197 E2: 5 # 14 pairs F3: 8,9,7 # reduction candidate for 8,9 F3: 8,9 # 14 pairs * PAIR F2: 8,9 ROW 2 B2: 8,9,2,3,4,5 # reduction candidate for 8,9 B2: 2,3,4,5 => SOLVED * 123456789457189236689237541261845973574391862938672415395718624712964358846523197 B2: 8,9 # 14 pairs * PAIR F2: 8,9 COL F F7: 8,9,2,3,4 # reduction candidate for 8,9 F7: 8,9 => SOLVED * 123456789457189236689237541261845973574391862938672415395718624712964358846523197 F7: 2,3,4 # 9 pairs * PAIR H3: 4,7 BLK 3 G3: 4,7,1,5 # reduction candidate for 4,7 G3: 4,7 => CTR * 1..4765894.715...66..23...1.61..5...57...1.6.9.8..7.15...7..6..71.....588.65...9. G3: 1,5 # 7 pairs I3: 4,7,1,6 # reduction candidate for 4,7 I3: 4,7 # 19 pairs * PAIR H3: 4,7 COL H H4: 4,7,2,3 # reduction candidate for 4,7 H4: 2,3 # 15 pairs H4: 4,7 # 9 pairs * PAIR D6: 3,6 COL D D8: 3,6,9 # reduction candidate for 3,6 D8: 3,6 # 11 pairs D8: 9 # 10 pairs * PAIR G4: 8,9 ROW 4 D4: 8,9,3 # reduction candidate for 8,9 D4: 3 # 8 pairs D4: 8,9 # 7 pairs * PAIR G5: 8,9 ROW 5 D5: 8,9,3 # reduction candidate for 8,9 D5: 8,9 # 8 pairs D5: 3 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-mith-te3-00153131-base-pr-000.dot * REASONING * PRF # E2: 8,9 => SOL * PRF # B2: 2,3,4,5 => SOL * PRF # F7: 8,9 => SOL * DIS # G3: 4,7 => CTR => G3: 1,5 * CNT 4 HDP CHAINS / 20 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D6,E1,F2,G4,G5,H3) * ...4.6.89..71........23.....61..5...57...1.6.9.8....15...7..6..71.....588.65...9. * PAIR E1: 5,7 ROW 1 G1: 5,7,1,2,3 # reduction candidate for 5,7 G1: 5,7 # 15 pairs G1: 1,2,3 # 12 pairs * PAIR F2: 8,9 BLK 2 E2: 8,9,5 # reduction candidate for 8,9 E2: 8,9 => SOLVED * 123456789457189236689237541261845973574391862938672415395718624712964358846523197 * DURATION: 0:00:00.834208 START: 22:42:42.781247 END: 22:42:43.615455 2025-04-06 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00153131-base-pr-001.dot * REASONING * PRF # E2: 8,9 => SOL * STA E2: 8,9 * CNT 1 HDP CHAINS / 3 HYP OPENED
Header Info
rating: 42076; r2: 757907; index: 153131
Solution
position: 123456789457189236689237541261845973574391862938672415395718624712964358846523197 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 # G1: 5,7 => UNS * INC # G1: 1,2,3 => UNS * PRF # E2: 8,9 => SOL * INC # E2: 5 => UNS * INC # F3: 8,9 => UNS * INC # B2: 8,9 => UNS * PRF # B2: 2,3,4,5 => SOL * PRF # F7: 8,9 => SOL * INC # F7: 2,3,4 => UNS * DIS # G3: 4,7 => CTR => G3: 1,5 * INC # G3: 1,5 => UNS * INC # I3: 4,7 => UNS * INC # H4: 4,7 => UNS * INC # H4: 2,3 => UNS * INC # D8: 3,6 => UNS * INC # D8: 9 => UNS * INC # D4: 8,9 => UNS * INC # D4: 3 => UNS * INC # D5: 8,9 => UNS * INC # D5: 3 => UNS * CNT 20 HDP CHAINS / 20 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G1: 5,7 => UNS * INC # G1: 1,2,3 => UNS * PRF # E2: 8,9 => SOL * STA E2: 8,9 * CNT 3 HDP CHAINS / 3 HYP OPENED