Analysis of xx-mith-te3-00106337-base.sdk
Contents
Original Sudoku
level: medium
position: 1..4....94..1.9.3.....72.14285..7...7.6......9.1....27.1.7..49..7.9.31.2.......73 initial
Autosolve
position: 1..4....94..1.9.3.....72.14285..7...7.6......9.1....27.1.7..49..7.9.31.2.......73 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C9: 4,8 => SOL * CNT 1 HDP CHAINS / 23 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C9: 4,8 => SOL * STA C9: 4,8 * CNT 1 HDP CHAINS / 20 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1..4....94..1.9.3.....72.14285..7...7.6......9.1....27.1.7..49..7.9.31.2.......73 | initial |
| 1..4....94..1.9.3.....72.14285..7...7.6......9.1....27.1.7..49..7.9.31.2.......73 | autosolve |
| 123456789457189236869372514285697341736214958941835627312768495578943162694521873 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) G1: 2,7 G2: 2,7 B5: 3,4 B6: 3,4 D4: 3,6 H4: 4,6 I4: 1,6 C8: 4,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I4,I5: 1.. / I4 = 1 => 8 pairs (_) / I5 = 1 => 11 pairs (_) E9,F9: 1.. / E9 = 1 => 8 pairs (_) / F9 = 1 => 13 pairs (_) E4,I4: 1.. / E4 = 1 => 11 pairs (_) / I4 = 1 => 8 pairs (_) F5,F9: 1.. / F5 = 1 => 8 pairs (_) / F9 = 1 => 13 pairs (_) G1,G2: 2.. / G1 = 2 => 8 pairs (_) / G2 = 2 => 7 pairs (_) D5,E5: 2.. / D5 = 2 => 11 pairs (_) / E5 = 2 => 15 pairs (_) C7,E7: 2.. / C7 = 2 => 11 pairs (_) / E7 = 2 => 13 pairs (_) D5,D9: 2.. / D5 = 2 => 11 pairs (_) / D9 = 2 => 15 pairs (_) E1,D3: 3.. / E1 = 3 => 8 pairs (_) / D3 = 3 => 0 pairs (*) B5,B6: 3.. / B5 = 3 => 11 pairs (_) / B6 = 3 => 9 pairs (_) A7,C7: 3.. / A7 = 3 => 9 pairs (_) / C7 = 3 => 12 pairs (_) C1,E1: 3.. / C1 = 3 => 0 pairs (*) / E1 = 3 => 0 pairs (X) A3,A7: 3.. / A3 = 3 => 12 pairs (_) / A7 = 3 => 9 pairs (_) B5,B6: 4.. / B5 = 4 => 9 pairs (_) / B6 = 4 => 11 pairs (_) H4,H5: 4.. / H4 = 4 => 8 pairs (_) / H5 = 4 => 10 pairs (_) C8,C9: 4.. / C8 = 4 => 9 pairs (_) / C9 = 4 => 0 pairs (*) E4,H4: 4.. / E4 = 4 => 10 pairs (_) / H4 = 4 => 8 pairs (_) C8,E8: 4.. / C8 = 4 => 9 pairs (_) / E8 = 4 => 0 pairs (*) C1,C2: 7.. / C1 = 7 => 8 pairs (_) / C2 = 7 => 7 pairs (_) G1,G2: 7.. / G1 = 7 => 7 pairs (_) / G2 = 7 => 8 pairs (_) C1,G1: 7.. / C1 = 7 => 8 pairs (_) / G1 = 7 => 7 pairs (_) C2,G2: 7.. / C2 = 7 => 7 pairs (_) / G2 = 7 => 8 pairs (_) B3,C3: 9.. / B3 = 9 => 10 pairs (_) / C3 = 9 => 11 pairs (_) E4,E5: 9.. / E4 = 9 => 14 pairs (_) / E5 = 9 => 11 pairs (_) G4,G5: 9.. / G4 = 9 => 11 pairs (_) / G5 = 9 => 14 pairs (_) B9,C9: 9.. / B9 = 9 => 11 pairs (_) / C9 = 9 => 10 pairs (_) E4,G4: 9.. / E4 = 9 => 14 pairs (_) / G4 = 9 => 11 pairs (_) E5,G5: 9.. / E5 = 9 => 11 pairs (_) / G5 = 9 => 14 pairs (_) B3,B9: 9.. / B3 = 9 => 10 pairs (_) / B9 = 9 => 11 pairs (_) C3,C9: 9.. / C3 = 9 => 11 pairs (_) / C9 = 9 => 10 pairs (_) * DURATION: 0:00:08.185017 START: 02:09:48.832152 END: 02:09:57.017169 2025-04-05 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,B6,C8,D4,G1,G2,H4,I4) * 1..4....94..1.9.3.....72.14285..7...7.6......9.1....27.1.7..49..7.9.31.2.......73 * PAIR G1: 2,7 ROW 1 C1: 2,7,3,8 # reduction candidate for 2,7 C1: 2,7 # 10 pairs C1: 3,8 # 8 pairs * PAIR G2: 2,7 ROW 2 C2: 2,7,8 # reduction candidate for 2,7 C2: 8 # 13 pairs C2: 2,7 # 10 pairs * PAIR B5: 3,4 ROW 5 E5: 3,4,1,2,5,8,9 # reduction candidate for 3,4 E5: 3,4 # 16 pairs E5: 1,2,5,8,9 # 8 pairs * PAIR B6: 3,4 ROW 6 E6: 3,4,5,6,8 # reduction candidate for 3,4 E6: 3,4 # 13 pairs E6: 5,6,8 # 8 pairs * PAIR D4: 3,6 BLK 5 E4: 3,6,1,4,9 # reduction candidate for 3,6 E4: 3,6 # 14 pairs D6: 3,6,5,8 # reduction candidate for 3,6 D6: 3,6 # 10 pairs E6: 3,6,4,5,8 # reduction candidate for 3,6 E6: 3,6 # 10 pairs * PAIR D4: 3,6 ROW 4 G4: 3,6,9 # reduction candidate for 3,6 G4: 3,6 # 14 pairs G4: 9 # 11 pairs * PAIR D4: 3,6 COL D D3: 3,6,5,8 # reduction candidate for 3,6 D3: 3,6 # 10 pairs D3: 5,8 # 9 pairs * PAIR H4: 4,6 ROW 4 E4: 4,6,1,3,9 # reduction candidate for 4,6 E4: 4,6 # 12 pairs E4: 1,3,9 # 8 pairs * PAIR I4: 1,6 ROW 4 E4: 1,6,3,4,9 # reduction candidate for 1,6 E4: 1,6 # 11 pairs E4: 3,4,9 # 8 pairs * PAIR C8: 4,8 BLK 7 C9: 4,8,2,9 # reduction candidate for 4,8 C9: 4,8 => SOLVED * 123456789457189236869372514285697341736214958941835627312768495578943162694521873 C9: 2,9 # 10 pairs * PAIR C8: 4,8 ROW 8 E8: 4,8,5,6 # reduction candidate for 4,8 E8: 4,8 # 11 pairs E8: 5,6 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-mith-te3-00106337-base-pr-000.dot * REASONING * PRF # C9: 4,8 => SOL * CNT 1 HDP CHAINS / 23 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,B6,C8,D4,G1,G2,H4,I4) * 1..4....94..1.9.3.....72.14285..7...7.6......9.1....27.1.7..49..7.9.31.2.......73 * PAIR G1: 2,7 ROW 1 C1: 2,7,3,8 # reduction candidate for 2,7 C1: 2,7 # 10 pairs C1: 3,8 # 8 pairs * PAIR G2: 2,7 ROW 2 C2: 2,7,8 # reduction candidate for 2,7 C2: 8 # 13 pairs C2: 2,7 # 10 pairs * PAIR B5: 3,4 ROW 5 E5: 3,4,1,2,5,8,9 # reduction candidate for 3,4 E5: 3,4 # 16 pairs E5: 1,2,5,8,9 # 8 pairs * PAIR B6: 3,4 ROW 6 E6: 3,4,5,6,8 # reduction candidate for 3,4 E6: 3,4 # 13 pairs E6: 5,6,8 # 8 pairs * PAIR D4: 3,6 BLK 5 E4: 3,6,1,4,9 # reduction candidate for 3,6 E4: 3,6 # 14 pairs D6: 3,6,5,8 # reduction candidate for 3,6 D6: 3,6 # 10 pairs E6: 3,6,4,5,8 # reduction candidate for 3,6 E6: 3,6 # 10 pairs * PAIR D4: 3,6 ROW 4 G4: 3,6,9 # reduction candidate for 3,6 G4: 3,6 # 14 pairs G4: 9 # 11 pairs * PAIR D4: 3,6 COL D D3: 3,6,5,8 # reduction candidate for 3,6 D3: 3,6 # 10 pairs D3: 5,8 # 9 pairs * PAIR H4: 4,6 ROW 4 E4: 4,6,1,3,9 # reduction candidate for 4,6 E4: 4,6 # 12 pairs E4: 1,3,9 # 8 pairs * PAIR I4: 1,6 ROW 4 E4: 1,6,3,4,9 # reduction candidate for 1,6 E4: 1,6 # 11 pairs E4: 3,4,9 # 8 pairs * PAIR C8: 4,8 BLK 7 C9: 4,8,2,9 # reduction candidate for 4,8 C9: 4,8 => SOLVED * 123456789457189236869372514285697341736214958941835627312768495578943162694521873 * DURATION: 0:00:03.054358 START: 02:10:00.408161 END: 02:10:03.462519 2025-04-05 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00106337-base-pr-001.dot * REASONING * PRF # C9: 4,8 => SOL * STA C9: 4,8 * CNT 1 HDP CHAINS / 20 HYP OPENED
Header Info
rating: 26652; r2: 519392; index: 106337
Solution
position: 123456789457189236869372514285697341736214958941835627312768495578943162694521873 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 # C1: 2,7 => UNS * INC # C1: 3,8 => UNS * INC # C2: 2,7 => UNS * INC # C2: 8 => UNS * INC # E5: 3,4 => UNS * INC # E5: 1,2,5,8,9 => UNS * INC # E6: 3,4 => UNS * INC # E6: 5,6,8 => UNS * INC # E4: 3,6 => UNS * INC # D6: 3,6 => UNS * INC # E6: 3,6 => UNS * INC # G4: 3,6 => UNS * INC # G4: 9 => UNS * INC # D3: 3,6 => UNS * INC # D3: 5,8 => UNS * INC # E4: 4,6 => UNS * INC # E4: 1,3,9 => UNS * INC # E4: 1,6 => UNS * INC # E4: 3,4,9 => UNS * PRF # C9: 4,8 => SOL * INC # C9: 2,9 => UNS * INC # E8: 4,8 => UNS * INC # E8: 5,6 => UNS * CNT 23 HDP CHAINS / 23 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 2,7 => UNS * INC # C1: 3,8 => UNS * INC # C2: 2,7 => UNS * INC # C2: 8 => UNS * INC # E5: 3,4 => UNS * INC # E5: 1,2,5,8,9 => UNS * INC # E6: 3,4 => UNS * INC # E6: 5,6,8 => UNS * INC # E4: 3,6 => UNS * INC # D6: 3,6 => UNS * INC # E6: 3,6 => UNS * INC # G4: 3,6 => UNS * INC # G4: 9 => UNS * INC # D3: 3,6 => UNS * INC # D3: 5,8 => UNS * INC # E4: 4,6 => UNS * INC # E4: 1,3,9 => UNS * INC # E4: 1,6 => UNS * INC # E4: 3,4,9 => UNS * PRF # C9: 4,8 => SOL * STA C9: 4,8 * CNT 20 HDP CHAINS / 20 HYP OPENED