Analysis of xx-mith-te3-00033843-base.sdk
Contents
Original Sudoku
level: medium
position: ..34.6..94.7.89..669.7........87..943.9...1........52...6.489..8........9.43.78.. initial
Autosolve
position: ..34.6..94.7.89..669.7........87..943.9...1........52...6.489..8........9.43.78.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B6: 1,7 => CTR => B6: 4,6,8 * DIS # B6: 1,8 => CTR => B6: 4,6,7 * PRF # I6: 7,8 => SOL * PRF # B5: 7,8 => SOL * CNT 4 HDP CHAINS / 21 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B6: 1,7 => CTR => B6: 4,6,8 * PRF B6: 4,6,8 # I6: 7,8 => SOL * STA B6: 4,6,8 + I6: 7,8 * CNT 2 HDP CHAINS / 15 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..34.6..94.7.89..669.7........87..943.9...1........52...6.489..8........9.43.78.. | initial |
| ..34.6..94.7.89..669.7........87..943.9...1........52...6.489..8........9.43.78.. | autosolve |
| 123456789457189236698732415265871394389524167741693528536248971872915643914367852 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) G1: 2,7 G2: 2,3 G3: 2,4 A6: 1,7 C6: 1,8 G4: 3,6 I5: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E3,F3: 3.. / E3 = 3 => 7 pairs (_) / F3 = 3 => 0 pairs (X) G2,H2: 3.. / G2 = 3 => 10 pairs (_) / H2 = 3 => 7 pairs (_) G4,I6: 3.. / G4 = 3 => 0 pairs (*) / I6 = 3 => 0 pairs (X) B7,B8: 3.. / B7 = 3 => 7 pairs (_) / B8 = 3 => 7 pairs (_) F4,G4: 3.. / F4 = 3 => 10 pairs (_) / G4 = 3 => 0 pairs (*) E3,E6: 3.. / E3 = 3 => 7 pairs (_) / E6 = 3 => 0 pairs (X) G3,H3: 4.. / G3 = 4 => 6 pairs (_) / H3 = 4 => 13 pairs (_) B5,B6: 4.. / B5 = 4 => 10 pairs (_) / B6 = 4 => 16 pairs (_) F5,F6: 4.. / F5 = 4 => 16 pairs (_) / F6 = 4 => 10 pairs (_) G8,H8: 4.. / G8 = 4 => 13 pairs (_) / H8 = 4 => 6 pairs (_) B5,F5: 4.. / B5 = 4 => 10 pairs (_) / F5 = 4 => 16 pairs (_) B6,F6: 4.. / B6 = 4 => 16 pairs (_) / F6 = 4 => 10 pairs (_) G3,G8: 4.. / G3 = 4 => 6 pairs (_) / G8 = 4 => 13 pairs (_) H3,H8: 4.. / H3 = 4 => 13 pairs (_) / H8 = 4 => 6 pairs (_) G4,H5: 6.. / G4 = 6 => 10 pairs (_) / H5 = 6 => 0 pairs (*) B4,G4: 6.. / B4 = 6 => 0 pairs (*) / G4 = 6 => 0 pairs (X) E9,H9: 6.. / E9 = 6 => 15 pairs (_) / H9 = 6 => 12 pairs (_) G4,G8: 6.. / G4 = 6 => 10 pairs (_) / G8 = 6 => 0 pairs (*) G1,H1: 7.. / G1 = 7 => 6 pairs (_) / H1 = 7 => 9 pairs (_) A6,A7: 7.. / A6 = 7 => 9 pairs (_) / A7 = 7 => 0 pairs (X) G1,G8: 7.. / G1 = 7 => 6 pairs (_) / G8 = 7 => 9 pairs (_) B1,C3: 8.. / B1 = 8 => 7 pairs (_) / C3 = 8 => 0 pairs (*) B1,H1: 8.. / B1 = 8 => 7 pairs (_) / H1 = 8 => 0 pairs (*) C3,C6: 8.. / C3 = 8 => 0 pairs (*) / C6 = 8 => 0 pairs (X) D6,E6: 9.. / D6 = 9 => 7 pairs (_) / E6 = 9 => 9 pairs (_) D8,E8: 9.. / D8 = 9 => 9 pairs (_) / E8 = 9 => 7 pairs (_) D6,D8: 9.. / D6 = 9 => 7 pairs (_) / D8 = 9 => 9 pairs (_) E6,E8: 9.. / E6 = 9 => 9 pairs (_) / E8 = 9 => 7 pairs (_) * DURATION: 0:00:07.387752 START: 12:05:03.218138 END: 12:05:10.605890 2025-04-04 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,C6,G1,G2,G3,G4,I5) * ..34.6..94.7.89..669.7........87..943.9...1........52...6.489..8........9.43.78.. * PAIR G1: 2,7 COL G G8: 2,7,3,4,6 # reduction candidate for 2,7 G8: 2,7 # 11 pairs G8: 3,4,6 # 6 pairs * PAIR G2: 2,3 COL G G8: 2,3,4,6,7 # reduction candidate for 2,3 G8: 2,3 # 12 pairs G8: 4,6,7 # 7 pairs * PAIR G3: 2,4 COL G G8: 2,4,3,6,7 # reduction candidate for 2,4 G8: 2,4 # 18 pairs G8: 3,6,7 # 6 pairs * PAIR A6: 1,7 BLK 4 B6: 1,7,4,6,8 # reduction candidate for 1,7 B6: 1,7 => CTR * .834.6..94.7.89..669.7......6.87.394349...16...8..452...6.489..8........9.43.78.. B6: 4,6,8 # 7 pairs * PAIR A6: 1,7 COL A A7: 1,7,2,5 # reduction candidate for 1,7 A7: 2,5 # 10 pairs A7: 1,7 # 10 pairs * PAIR C6: 1,8 BLK 4 B6: 1,8,4,6,7 # reduction candidate for 1,8 B6: 1,8 => CTR * ..34.6..94.7.89..669.7......6.87.394349...16.7....452...6.489..8........9.43.78.. B6: 4,6,7 # 7 pairs * PAIR C6: 1,8 COL C C3: 1,8,2,5 # reduction candidate for 1,8 C3: 1,8 # 10 pairs C3: 2,5 # 8 pairs * PAIR G4: 3,6 COL G G8: 3,6,2,4,7 # reduction candidate for 3,6 G8: 2,4,7 # 10 pairs G8: 3,6 # 7 pairs * PAIR I5: 7,8 BLK 6 H5: 7,8,6 # reduction candidate for 7,8 H5: 7,8 # 10 pairs I6: 7,8,3 # reduction candidate for 7,8 I6: 7,8 => SOLVED * 123456789457189236698732415265871394389524167741693528536248971872915643914367852 I6: 3 # 10 pairs * PAIR I5: 7,8 ROW 5 B5: 7,8,2,4,5,6 # reduction candidate for 7,8 B5: 7,8 => SOLVED * 123456789457189236698732415265871394389524167741693528536248971872915643914367852 B5: 2,4,5,6 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-mith-te3-00033843-base-pr-000.dot * REASONING * DIS # B6: 1,7 => CTR => B6: 4,6,8 * DIS # B6: 1,8 => CTR => B6: 4,6,7 * PRF # I6: 7,8 => SOL * PRF # B5: 7,8 => SOL * CNT 4 HDP CHAINS / 21 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,C6,G1,G2,G3,G4,I5) * ..34.6..94.7.89..669.7........87..943.9...1........52...6.489..8........9.43.78.. * PAIR G1: 2,7 COL G G8: 2,7,3,4,6 # reduction candidate for 2,7 G8: 2,7 # 11 pairs G8: 3,4,6 # 6 pairs * PAIR G2: 2,3 COL G G8: 2,3,4,6,7 # reduction candidate for 2,3 G8: 2,3 # 12 pairs G8: 4,6,7 # 7 pairs * PAIR G3: 2,4 COL G G8: 2,4,3,6,7 # reduction candidate for 2,4 G8: 2,4 # 18 pairs G8: 3,6,7 # 6 pairs * PAIR A6: 1,7 BLK 4 B6: 1,7,4,6,8 # reduction candidate for 1,7 B6: 1,7 => CTR * .834.6..94.7.89..669.7......6.87.394349...16...8..452...6.489..8........9.43.78.. * PAIR A6: 1,7 COL A A7: 1,7,2,5 # reduction candidate for 1,7 A7: 2,5 # 10 pairs A7: 1,7 # 10 pairs * PAIR C6: 1,8 COL C C3: 1,8,2,5 # reduction candidate for 1,8 C3: 1,8 # 10 pairs C3: 2,5 # 9 pairs * PAIR G4: 3,6 COL G G8: 3,6,2,4,7 # reduction candidate for 3,6 G8: 2,4,7 # 10 pairs G8: 3,6 # 7 pairs * PAIR I5: 7,8 BLK 6 H5: 7,8,6 # reduction candidate for 7,8 H5: 7,8 # 10 pairs I6: 7,8,3 # reduction candidate for 7,8 I6: 7,8 => SOLVED * 123456789457189236698732415265871394389524167741693528536248971872915643914367852 * DURATION: 0:00:02.346648 START: 12:05:13.663519 END: 12:05:16.010167 2025-04-04 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00033843-base-pr-001.dot * REASONING * DIS # B6: 1,7 => CTR => B6: 4,6,8 * PRF B6: 4,6,8 # I6: 7,8 => SOL * STA B6: 4,6,8 + I6: 7,8 * CNT 2 HDP CHAINS / 15 HYP OPENED
Header Info
rating: 6837; r2: 133050; index: 33843
Solution
position: 123456789457189236698732415265871394389524167741693528536248971872915643914367852 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 # G8: 2,7 => UNS * INC # G8: 3,4,6 => UNS * INC # G8: 2,3 => UNS * INC # G8: 4,6,7 => UNS * INC # G8: 2,4 => UNS * INC # G8: 3,6,7 => UNS * DIS # B6: 1,7 => CTR => B6: 4,6,8 * INC # B6: 4,6,8 => UNS * INC # A7: 1,7 => UNS * INC # A7: 2,5 => UNS * DIS # B6: 1,8 => CTR => B6: 4,6,7 * INC # B6: 4,6,7 => UNS * INC # C3: 1,8 => UNS * INC # C3: 2,5 => UNS * INC # G8: 3,6 => UNS * INC # G8: 2,4,7 => UNS * INC # H5: 7,8 => UNS * PRF # I6: 7,8 => SOL * INC # I6: 3 => UNS * PRF # B5: 7,8 => SOL * INC # B5: 2,4,5,6 => UNS * CNT 21 HDP CHAINS / 21 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G8: 2,7 => UNS * INC # G8: 3,4,6 => UNS * INC # G8: 2,3 => UNS * INC # G8: 4,6,7 => UNS * INC # G8: 2,4 => UNS * INC # G8: 3,6,7 => UNS * DIS # B6: 1,7 => CTR => B6: 4,6,8 * INC B6: 4,6,8 # A7: 1,7 => UNS * INC B6: 4,6,8 # A7: 2,5 => UNS * INC B6: 4,6,8 # C3: 1,8 => UNS * INC B6: 4,6,8 # C3: 2,5 => UNS * INC B6: 4,6,8 # G8: 3,6 => UNS * INC B6: 4,6,8 # G8: 2,4,7 => UNS * INC B6: 4,6,8 # H5: 7,8 => UNS * PRF B6: 4,6,8 # I6: 7,8 => SOL * STA B6: 4,6,8 + I6: 7,8 * CNT 15 HDP CHAINS / 15 HYP OPENED