Analysis of xx-mith-te3-00082951-base.sdk
Contents
Original Sudoku
level: medium
position: 1.3..67.9.57..9.3696....15..........5.6.3..71..9.6...3.9...5........7315..584.... initial
Autosolve
position: 1.3..67.9.57..9.3696....15..........5.6.3..71..9.6...3.9...5........7315..584.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # D6: 2,4,5 => SOL * PRF # D8: 2,9 => SOL * PRF # E4: 2,9 => SOL * CNT 3 HDP CHAINS / 18 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # D6: 2,4,5 => SOL * STA D6: 2,4,5 * CNT 1 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.3..67.9.57..9.3696....15..........5.6.3..71..9.6...3.9...5........7315..584.... | initial |
| 1.3..67.9.57..9.3696....15..........5.6.3..71..9.6...3.9...5........7315..584.... | autosolve |
| 123456789457189236968372154231794568546238971879561423392615847684927315715843692 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) B6: 1,7 C7: 1,2 D7: 3,6 E7: 1,2 E8: 2,9 F9: 1,3 I9: 2,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,E2: 1.. / D2 = 1 => 8 pairs (_) / E2 = 1 => 12 pairs (_) C7,B9: 1.. / C7 = 1 => 11 pairs (_) / B9 = 1 => 0 pairs (*) E7,F9: 1.. / E7 = 1 => 0 pairs (*) / F9 = 1 => 0 pairs (X) C7,E7: 1.. / C7 = 1 => 11 pairs (_) / E7 = 1 => 0 pairs (*) B9,F9: 1.. / B9 = 1 => 0 pairs (*) / F9 = 1 => 0 pairs (X) C4,C7: 1.. / C4 = 1 => 0 pairs (*) / C7 = 1 => 0 pairs (X) C7,E7: 2.. / C7 = 2 => 0 pairs (*) / E7 = 2 => 0 pairs (X) D3,F3: 3.. / D3 = 3 => 0 pairs (*) / F3 = 3 => 0 pairs (X) A4,B4: 3.. / A4 = 3 => 11 pairs (_) / B4 = 3 => 8 pairs (_) D7,F9: 3.. / D7 = 3 => 11 pairs (_) / F9 = 3 => 0 pairs (*) A7,D7: 3.. / A7 = 3 => 0 pairs (*) / D7 = 3 => 0 pairs (X) B4,B9: 3.. / B4 = 3 => 8 pairs (_) / B9 = 3 => 11 pairs (_) D3,D7: 3.. / D3 = 3 => 0 pairs (*) / D7 = 3 => 0 pairs (X) F3,F9: 3.. / F3 = 3 => 11 pairs (_) / F9 = 3 => 0 pairs (*) D1,E1: 5.. / D1 = 5 => 8 pairs (_) / E1 = 5 => 8 pairs (_) G4,G6: 5.. / G4 = 5 => 0 pairs (*) / G6 = 5 => 0 pairs (X) D6,G6: 5.. / D6 = 5 => 0 pairs (*) / G6 = 5 => 0 pairs (X) E1,E4: 5.. / E1 = 5 => 8 pairs (_) / E4 = 5 => 8 pairs (_) G4,H4: 6.. / G4 = 6 => 9 pairs (_) / H4 = 6 => 9 pairs (_) D7,D8: 6.. / D7 = 6 => 0 pairs (*) / D8 = 6 => 0 pairs (X) A8,D8: 6.. / A8 = 6 => 0 pairs (*) / D8 = 6 => 0 pairs (X) D3,E3: 7.. / D3 = 7 => 9 pairs (_) / E3 = 7 => 7 pairs (_) I7,I9: 7.. / I7 = 7 => 15 pairs (_) / I9 = 7 => 11 pairs (_) A7,I7: 7.. / A7 = 7 => 11 pairs (_) / I7 = 7 => 15 pairs (_) E3,E4: 7.. / E3 = 7 => 7 pairs (_) / E4 = 7 => 9 pairs (_) D8,E8: 9.. / D8 = 9 => 0 pairs (*) / E8 = 9 => 0 pairs (X) G9,H9: 9.. / G9 = 9 => 9 pairs (_) / H9 = 9 => 8 pairs (_) D5,G5: 9.. / D5 = 9 => 9 pairs (_) / G5 = 9 => 0 pairs (*) E4,E8: 9.. / E4 = 9 => 0 pairs (*) / E8 = 9 => 0 pairs (X) H4,H9: 9.. / H4 = 9 => 9 pairs (_) / H9 = 9 => 8 pairs (_) * DURATION: 0:00:10.080356 START: 12:28:48.069555 END: 12:28:58.149911 2025-04-06 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,C7,D7,E7,E8,F9,I9) * 1.3..67.9.57..9.3696....15..........5.6.3..71..9.6...3.9...5........7315..584.... * PAIR B6: 1,7 BLK 4 B4: 1,7,3 # reduction candidate for 1,7 B4: 1,7 # 11 pairs B4: 3 # 8 pairs * PAIR B6: 1,7 ROW 6 D6: 1,7,2,4,5 # reduction candidate for 1,7 D6: 2,4,5 => SOLVED * 123456789457189236968372154231794568546238971879561423392615847684927315715843692 D6: 1,7 # 8 pairs * PAIR B6: 1,7 COL B B9: 1,7,3 # reduction candidate for 1,7 B9: 3 # 11 pairs B9: 1,7 # 8 pairs * PAIR C7: 1,2 COL C C4: 1,2,4,8 # reduction candidate for 1,2 C4: 4,8 # 12 pairs C4: 1,2 # 10 pairs * PAIR D7: 3,6 ROW 7 A7: 3,6,7 # reduction candidate for 3,6 A7: 3,6 # 15 pairs A7: 7 # 11 pairs * PAIR E7: 1,2 COL E E2: 1,2,8 # reduction candidate for 1,2 E2: 1,2 # 10 pairs E4: 1,2,5,7,8,9 # reduction candidate for 1,2 E4: 1,2 # 11 pairs * PAIR E8: 2,9 BLK 8 D8: 2,9,6 # reduction candidate for 2,9 D8: 2,9 => SOLVED * 123456789457189236968372154231794568546238971879561423392615847684927315715843692 D8: 6 # 11 pairs * PAIR E8: 2,9 COL E E4: 2,9,1,5,7,8 # reduction candidate for 2,9 E4: 2,9 => SOLVED * 123456789457189236968372154231794568546238971879561423392615847684927315715843692 E4: 1,5,7,8 # 7 pairs * PAIR F9: 1,3 ROW 9 B9: 1,3,7 # reduction candidate for 1,3 B9: 7 # 13 pairs B9: 1,3 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-mith-te3-00082951-base-pr-000.dot * REASONING * PRF # D6: 2,4,5 => SOL * PRF # D8: 2,9 => SOL * PRF # E4: 2,9 => SOL * CNT 3 HDP CHAINS / 18 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,C7,D7,E7,E8,F9,I9) * 1.3..67.9.57..9.3696....15..........5.6.3..71..9.6...3.9...5........7315..584.... * PAIR B6: 1,7 BLK 4 B4: 1,7,3 # reduction candidate for 1,7 B4: 1,7 # 11 pairs B4: 3 # 8 pairs * PAIR B6: 1,7 ROW 6 D6: 1,7,2,4,5 # reduction candidate for 1,7 D6: 2,4,5 => SOLVED * 123456789457189236968372154231794568546238971879561423392615847684927315715843692 * DURATION: 0:00:01.061907 START: 12:29:01.944312 END: 12:29:03.006219 2025-04-06 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00082951-base-pr-001.dot * REASONING * PRF # D6: 2,4,5 => SOL * STA D6: 2,4,5 * CNT 1 HDP CHAINS / 4 HYP OPENED
Header Info
rating: 20391; r2: 413992; index: 82951
Solution
position: 123456789457189236968372154231794568546238971879561423392615847684927315715843692 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 # B4: 1,7 => UNS * INC # B4: 3 => UNS * INC # D6: 1,7 => UNS * PRF # D6: 2,4,5 => SOL * INC # B9: 1,7 => UNS * INC # B9: 3 => UNS * INC # C4: 1,2 => UNS * INC # C4: 4,8 => UNS * INC # A7: 3,6 => UNS * INC # A7: 7 => UNS * INC # E2: 1,2 => UNS * INC # E4: 1,2 => UNS * PRF # D8: 2,9 => SOL * INC # D8: 6 => UNS * PRF # E4: 2,9 => SOL * INC # E4: 1,5,7,8 => UNS * INC # B9: 1,3 => UNS * INC # B9: 7 => UNS * CNT 18 HDP CHAINS / 18 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B4: 1,7 => UNS * INC # B4: 3 => UNS * INC # D6: 1,7 => UNS * PRF # D6: 2,4,5 => SOL * STA D6: 2,4,5 * CNT 4 HDP CHAINS / 4 HYP OPENED