Analysis of xx-mith-te3-00093276-base.sdk
Contents
Original Sudoku
level: medium
position: 1.3....8..5..8.....89....46....756.4.7.84...5.4.6.287...256.4.8....28..7......2.. initial
Autosolve
position: 1.3....8..5..8.....89....46....756.4.7.84...5.4.6.287...256.4.8....28..7......2.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 2,6 => CTR => A2: 4,7 * DIS # A2: 2,7 => CTR => A2: 4,6 * DIS # C8: 1,6 => CTR => C8: 4,5 * DIS # C8: 1,5 => CTR => C8: 4,6 * DIS # C8: 5,6 => CTR => C8: 1,4 * CNT 5 HDP CHAINS / 25 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 2,6 => CTR => A2: 4,7 * DIS A2: 4,7 # C8: 1,6 => CTR => C8: 4,5 * PRF A2: 4,7 + C8: 4,5 # C2: 6 => SOL * STA A2: 4,7 + C8: 4,5 + C2: 6 * CNT 3 HDP CHAINS / 25 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.3....8..5..8.....89....46....756.4.7.84...5.4.6.287...256.4.8....28..7......2.. | initial |
| 1.3....8..5..8.....89....46....756.4.7.84...5.4.6.287...256.4.8....28..7......2.. | autosolve |
| 123456789456789132789231546238975614671843925945612873312567498594128367867394251 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) B1: 2,6 A3: 2,7 E1: 5,9 I1: 2,9 C4: 1,8 C5: 1,6 C6: 1,5 H8: 5,6 H9: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I1,I2: 2.. / I1 = 2 => 11 pairs (_) / I2 = 2 => 15 pairs (_) H4,H5: 2.. / H4 = 2 => 0 pairs (X) / H5 = 2 => 9 pairs (_) A3,D3: 2.. / A3 = 2 => 13 pairs (_) / D3 = 2 => 16 pairs (_) A5,H5: 2.. / A5 = 2 => 0 pairs (X) / H5 = 2 => 9 pairs (_) B1,B4: 2.. / B1 = 2 => 16 pairs (_) / B4 = 2 => 13 pairs (_) A2,C2: 4.. / A2 = 4 => 10 pairs (_) / C2 = 4 => 0 pairs (X) D1,F1: 4.. / D1 = 4 => 9 pairs (_) / F1 = 4 => 12 pairs (_) F1,F9: 4.. / F1 = 4 => 12 pairs (_) / F9 = 4 => 9 pairs (_) E1,E3: 5.. / E1 = 5 => 10 pairs (_) / E3 = 5 => 14 pairs (_) G1,G3: 5.. / G1 = 5 => 14 pairs (_) / G3 = 5 => 10 pairs (_) A6,C6: 5.. / A6 = 5 => 12 pairs (_) / C6 = 5 => 9 pairs (_) H8,H9: 5.. / H8 = 5 => 12 pairs (_) / H9 = 5 => 7 pairs (_) E1,G1: 5.. / E1 = 5 => 10 pairs (_) / G1 = 5 => 14 pairs (_) E3,G3: 5.. / E3 = 5 => 14 pairs (_) / G3 = 5 => 10 pairs (_) F1,F2: 6.. / F1 = 6 => 16 pairs (_) / F2 = 6 => 13 pairs (_) A5,C5: 6.. / A5 = 6 => 9 pairs (_) / C5 = 6 => 9 pairs (_) H8,H9: 6.. / H8 = 6 => 7 pairs (_) / H9 = 6 => 12 pairs (_) B1,F1: 6.. / B1 = 6 => 13 pairs (_) / F1 = 6 => 16 pairs (_) A7,F7: 7.. / A7 = 7 => 13 pairs (_) / F7 = 7 => 16 pairs (_) C2,C9: 7.. / C2 = 7 => 13 pairs (_) / C9 = 7 => 16 pairs (_) A4,C4: 8.. / A4 = 8 => 15 pairs (_) / C4 = 8 => 8 pairs (_) A9,C9: 8.. / A9 = 8 => 8 pairs (_) / C9 = 8 => 15 pairs (_) A4,A9: 8.. / A4 = 8 => 15 pairs (_) / A9 = 8 => 8 pairs (_) C4,C9: 8.. / C4 = 8 => 8 pairs (_) / C9 = 8 => 15 pairs (_) * DURATION: 0:00:07.226360 START: 23:53:17.149396 END: 23:53:24.375756 2025-04-04 * CP COUNT: (24) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B1,C4,C5,C6,E1,H8,H9,I1) * 1.3....8..5..8.....89....46....756.4.7.84...5.4.6.287...256.4.8....28..7......2.. * PAIR B1: 2,6 BLK 1 A2: 2,6,4,7 # reduction candidate for 2,6 A2: 2,6 => CTR * 123456789654789..2789213546..83756143768419255416928739125674384.5.28.67867..4251 A2: 4,7 # 10 pairs * PAIR A3: 2,7 BLK 1 A2: 2,7,4,6 # reduction candidate for 2,7 A2: 2,7 => CTR * 163....8..54.86....89....46.28.756.4.7.84..25.4.6.287...25674.8....28..78.7...2.. A2: 4,6 # 10 pairs * PAIR A3: 2,7 ROW 3 D3: 2,7,1,3 # reduction candidate for 2,7 D3: 1,3 # 13 pairs D3: 2,7 # 11 pairs * PAIR E1: 5,9 ROW 1 G1: 5,9,7 # reduction candidate for 5,9 G1: 5,9 # 14 pairs G1: 7 # 9 pairs * PAIR I1: 2,9 BLK 3 I2: 2,9,1,3 # reduction candidate for 2,9 I2: 2,9 # 14 pairs I2: 1,3 # 12 pairs * PAIR I1: 2,9 ROW 1 D1: 2,9,4,7 # reduction candidate for 2,9 D1: 2,9 # 13 pairs D1: 4,7 # 10 pairs * PAIR C4: 1,8 COL C C9: 1,8,4,5,6,7 # reduction candidate for 1,8 C9: 1,8 # 15 pairs C9: 4,5,6,7 # 8 pairs * PAIR C5: 1,6 COL C C8: 1,6,4,5 # reduction candidate for 1,6 C8: 1,6 => CTR * 1.3....8..57.8....289....46.28.756.4.7184..25.456.287.7.256.4.8..6.28.57......2.. C8: 4,5 # 10 pairs C9: 1,6,4,5,7,8 # reduction candidate for 1,6 C9: 1,6 # 11 pairs * PAIR C6: 1,5 COL C C8: 1,5,4,6 # reduction candidate for 1,5 C8: 1,5 => CTR * 123456789654789..2789213546..83756143768419255416928739125674384.5.28.67867934251 C8: 4,6 # 10 pairs C9: 1,5,4,6,7,8 # reduction candidate for 1,5 C9: 1,5 # 11 pairs * PAIR H8: 5,6 ROW 8 A8: 5,6,3,4,9 # reduction candidate for 5,6 A8: 5,6 # 11 pairs C8: 5,6,1,4 # reduction candidate for 5,6 C8: 5,6 => CTR * 123456789654789..2789213546..83756143768419255416928739125674384.5.28.67867..4251 C8: 1,4 # 10 pairs * PAIR H9: 5,6 ROW 9 A9: 5,6,3,4,7,8,9 # reduction candidate for 5,6 A9: 5,6 # 15 pairs C9: 5,6,1,4,7,8 # reduction candidate for 5,6 C9: 5,6 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-mith-te3-00093276-base-pr-000.dot * REASONING * DIS # A2: 2,6 => CTR => A2: 4,7 * DIS # A2: 2,7 => CTR => A2: 4,6 * DIS # C8: 1,6 => CTR => C8: 4,5 * DIS # C8: 1,5 => CTR => C8: 4,6 * DIS # C8: 5,6 => CTR => C8: 1,4 * CNT 5 HDP CHAINS / 25 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B1,C4,C5,C6,E1,H8,H9,I1) * 1.3....8..5..8.....89....46....756.4.7.84...5.4.6.287...256.4.8....28..7......2.. * PAIR B1: 2,6 BLK 1 A2: 2,6,4,7 # reduction candidate for 2,6 A2: 2,6 => CTR * 123456789654789..2789213546..83756143768419255416928739125674384.5.28.67867..4251 * PAIR A3: 2,7 ROW 3 D3: 2,7,1,3 # reduction candidate for 2,7 D3: 1,3 # 13 pairs D3: 2,7 # 12 pairs * PAIR E1: 5,9 ROW 1 G1: 5,9,7 # reduction candidate for 5,9 G1: 5,9 # 14 pairs G1: 7 # 10 pairs * PAIR I1: 2,9 BLK 3 I2: 2,9,1,3 # reduction candidate for 2,9 I2: 2,9 # 15 pairs I2: 1,3 # 12 pairs * PAIR I1: 2,9 ROW 1 D1: 2,9,4,7 # reduction candidate for 2,9 D1: 2,9 # 13 pairs D1: 4,7 # 11 pairs * PAIR C4: 1,8 COL C C9: 1,8,4,5,6,7 # reduction candidate for 1,8 C9: 1,8 # 15 pairs C9: 4,5,6,7 # 9 pairs * PAIR C5: 1,6 COL C C8: 1,6,4,5 # reduction candidate for 1,6 C8: 1,6 => CTR * 163....8..57.86...289....46.28.756.467184..25.456.287.7.256.4.8..6.28.57......2.. C9: 1,6,4,5,7,8 # reduction candidate for 1,6 C9: 1,6 # 11 pairs * RESTART * PAIR C5: 1,6 COL C C9: 1,6,4,5,7,8 # reduction candidate for 1,6 C9: 4,5,7,8 # 11 pairs C9: 1,6 # 11 pairs * PAIR RESTART * PAIR C5: 1,6 COL C C9: 1,6,4,5,7,8 # reduction candidate for 1,6 C9: 4,5,7,8 # 11 pairs C9: 1,6 # 11 pairs * PAIR C6: 1,5 COL C C9: 1,5,4,6,7,8 # reduction candidate for 1,5 C9: 4,6,7,8 # 11 pairs C9: 1,5 # 11 pairs * PAIR H8: 5,6 ROW 8 A8: 5,6,3,4,9 # reduction candidate for 5,6 A8: 5,6 # 11 pairs A8: 3,4,9 # 11 pairs * PAIR H9: 5,6 ROW 9 A9: 5,6,3,4,7,8,9 # reduction candidate for 5,6 A9: 5,6 # 15 pairs C9: 5,6,1,4,7,8 # reduction candidate for 5,6 C9: 5,6 # 14 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,A3,B1,C4,C5,C6,C8,E1,H8,H9,I1) * 1.3....8..5..8.....89....46....756.4.7.84...5.4.6.287...256.4.8....28..7......2.. * PAIR A2: 4,7 BLK 1 C2: 4,7,6 # reduction candidate for 4,7 C2: 6 => SOLVED * 123456789456789132789231546238975614671843925945612873312567498594128367867394251 * DURATION: 0:00:04.524233 START: 23:53:28.482286 END: 23:53:33.006519 2025-04-04 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00093276-base-pr-001.dot * REASONING * DIS # A2: 2,6 => CTR => A2: 4,7 * DIS A2: 4,7 # C8: 1,6 => CTR => C8: 4,5 * PRF A2: 4,7 + C8: 4,5 # C2: 6 => SOL * STA A2: 4,7 + C8: 4,5 + C2: 6 * CNT 3 HDP CHAINS / 25 HYP OPENED
Header Info
rating: 23620; r2: 723724; index: 93276
Solution
position: 123456789456789132789231546238975614671843925945612873312567498594128367867394251 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:
* DIS # A2: 2,6 => CTR => A2: 4,7 * INC # A2: 4,7 => UNS * DIS # A2: 2,7 => CTR => A2: 4,6 * INC # A2: 4,6 => UNS * INC # D3: 2,7 => UNS * INC # D3: 1,3 => UNS * INC # G1: 5,9 => UNS * INC # G1: 7 => UNS * INC # I2: 2,9 => UNS * INC # I2: 1,3 => UNS * INC # D1: 2,9 => UNS * INC # D1: 4,7 => UNS * INC # C9: 1,8 => UNS * INC # C9: 4,5,6,7 => UNS * DIS # C8: 1,6 => CTR => C8: 4,5 * INC # C8: 4,5 => UNS * INC # C9: 1,6 => UNS * DIS # C8: 1,5 => CTR => C8: 4,6 * INC # C8: 4,6 => UNS * INC # C9: 1,5 => UNS * INC # A8: 5,6 => UNS * DIS # C8: 5,6 => CTR => C8: 1,4 * INC # C8: 1,4 => UNS * INC # A9: 5,6 => UNS * INC # C9: 5,6 => UNS * CNT 25 HDP CHAINS / 25 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A2: 2,6 => CTR => A2: 4,7 * INC A2: 4,7 # D3: 2,7 => UNS * INC A2: 4,7 # D3: 1,3 => UNS * INC A2: 4,7 # G1: 5,9 => UNS * INC A2: 4,7 # G1: 7 => UNS * INC A2: 4,7 # I2: 2,9 => UNS * INC A2: 4,7 # I2: 1,3 => UNS * INC A2: 4,7 # D1: 2,9 => UNS * INC A2: 4,7 # D1: 4,7 => UNS * INC A2: 4,7 # C9: 1,8 => UNS * INC A2: 4,7 # C9: 4,5,6,7 => UNS * DIS A2: 4,7 # C8: 1,6 => CTR => C8: 4,5 * INC A2: 4,7 + C8: 4,5 # C9: 1,6 => UNS * INC A2: 4,7 + C8: 4,5 # C9: 1,6 => UNS * INC A2: 4,7 + C8: 4,5 # C9: 4,5,7,8 => UNS * INC A2: 4,7 + C8: 4,5 # C9: 1,6 => UNS * INC A2: 4,7 + C8: 4,5 # C9: 4,5,7,8 => UNS * INC A2: 4,7 + C8: 4,5 # C9: 1,5 => UNS * INC A2: 4,7 + C8: 4,5 # C9: 4,6,7,8 => UNS * INC A2: 4,7 + C8: 4,5 # A8: 5,6 => UNS * INC A2: 4,7 + C8: 4,5 # A8: 3,4,9 => UNS * INC A2: 4,7 + C8: 4,5 # A9: 5,6 => UNS * INC A2: 4,7 + C8: 4,5 # C9: 5,6 => UNS * INC A2: 4,7 + C8: 4,5 # C2: 4,7 => UNS * PRF A2: 4,7 + C8: 4,5 # C2: 6 => SOL * STA A2: 4,7 + C8: 4,5 + C2: 6 * CNT 25 HDP CHAINS / 25 HYP OPENED