Analysis of xx-mith-te3-00081047-base.sdk
Contents
Original Sudoku
level: medium
position: 1.3.56....57.8....68...75...61....4.......192.....3..5........1.16.38..787.5.1.36 initial
Autosolve
position: 1.3.56....57.8....68...75...61....4.......192.....3..5........1.16.38..787.5.1.36 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A5: 3,4 => CTR => A5: 5,7 * DIS # G4: 7 => CTR => G4: 3,8 * CNT 2 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:
* DIS # A5: 3,4 => CTR => A5: 5,7 * DIS A5: 5,7 # G4: 7 => CTR => G4: 3,8 * PRF A5: 5,7 + G4: 3,8 # A4: 2,9 => SOL * STA A5: 5,7 + G4: 3,8 + A4: 2,9 * CNT 3 HDP CHAINS / 23 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.3.56....57.8....68...75...61....4.......192.....3..5........1.16.38..787.5.1.36 | initial |
| 1.3.56....57.8....68...75...61....4.......192.....3..5........1.16.38..787.5.1.36 | autosolve |
| 123456789457189263689327514261795348735864192948213675394672851516938427872541936 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) H3: 1,2 B5: 3,4 F5: 4,5 I4: 3,8 D7: 6,7 E7: 6,7 H8: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H2,H3: 1.. / H2 = 1 => 9 pairs (_) / H3 = 1 => 8 pairs (_) D6,E6: 1.. / D6 = 1 => 16 pairs (_) / E6 = 1 => 9 pairs (_) D2,H2: 1.. / D2 = 1 => 8 pairs (_) / H2 = 1 => 9 pairs (_) E3,E6: 1.. / E3 = 1 => 16 pairs (_) / E6 = 1 => 9 pairs (_) D2,D3: 3.. / D2 = 3 => 10 pairs (_) / D3 = 3 => 8 pairs (_) A5,B5: 3.. / A5 = 3 => 0 pairs (X) / B5 = 3 => 6 pairs (_) G4,I4: 3.. / G4 = 3 => 12 pairs (_) / I4 = 3 => 13 pairs (_) A7,B7: 3.. / A7 = 3 => 6 pairs (_) / B7 = 3 => 0 pairs (X) D3,I3: 3.. / D3 = 3 => 8 pairs (_) / I3 = 3 => 10 pairs (_) A5,A7: 3.. / A5 = 3 => 0 pairs (X) / A7 = 3 => 6 pairs (_) B5,B7: 3.. / B5 = 3 => 6 pairs (_) / B7 = 3 => 0 pairs (X) G2,G4: 3.. / G2 = 3 => 13 pairs (_) / G4 = 3 => 12 pairs (_) F4,F5: 5.. / F4 = 5 => 11 pairs (_) / F5 = 5 => 8 pairs (_) H7,H8: 5.. / H7 = 5 => 0 pairs (*) / H8 = 5 => 0 pairs (X) A4,F4: 5.. / A4 = 5 => 8 pairs (_) / F4 = 5 => 11 pairs (_) A8,H8: 5.. / A8 = 5 => 0 pairs (*) / H8 = 5 => 0 pairs (X) C5,C7: 5.. / C5 = 5 => 0 pairs (*) / C7 = 5 => 0 pairs (X) G2,H2: 6.. / G2 = 6 => 10 pairs (_) / H2 = 6 => 9 pairs (_) D5,E5: 6.. / D5 = 6 => 6 pairs (_) / E5 = 6 => 6 pairs (_) G6,H6: 6.. / G6 = 6 => 9 pairs (_) / H6 = 6 => 10 pairs (_) D7,E7: 6.. / D7 = 6 => 6 pairs (_) / E7 = 6 => 6 pairs (_) D5,D7: 6.. / D5 = 6 => 6 pairs (_) / D7 = 6 => 6 pairs (_) E5,E7: 6.. / E5 = 6 => 6 pairs (_) / E7 = 6 => 6 pairs (_) G2,G6: 6.. / G2 = 6 => 10 pairs (_) / G6 = 6 => 9 pairs (_) H2,H6: 6.. / H2 = 6 => 9 pairs (_) / H6 = 6 => 10 pairs (_) G1,H1: 7.. / G1 = 7 => 10 pairs (_) / H1 = 7 => 12 pairs (_) D7,E7: 7.. / D7 = 7 => 6 pairs (_) / E7 = 7 => 6 pairs (_) H1,H6: 7.. / H1 = 7 => 12 pairs (_) / H6 = 7 => 10 pairs (_) C5,C6: 8.. / C5 = 8 => 7 pairs (_) / C6 = 8 => 9 pairs (_) G7,H7: 8.. / G7 = 8 => 15 pairs (_) / H7 = 8 => 10 pairs (_) C5,D5: 8.. / C5 = 8 => 7 pairs (_) / D5 = 8 => 9 pairs (_) I1,I4: 8.. / I1 = 8 => 13 pairs (_) / I4 = 8 => 12 pairs (_) * DURATION: 0:00:08.899371 START: 21:23:01.011540 END: 21:23:09.910911 2025-04-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,D7,E7,F5,H3,H8,I4) * 1.3.56....57.8....68...75...61....4.......192.....3..5........1.16.38..787.5.1.36 * PAIR H3: 1,2 BLK 3 H2: 1,2,6 # reduction candidate for 1,2 H2: 1,2 # 10 pairs H2: 6 # 9 pairs * PAIR H3: 1,2 ROW 3 D3: 1,2,3,4,9 # reduction candidate for 1,2 D3: 1,2 # 11 pairs E3: 1,2,4,9 # reduction candidate for 1,2 E3: 1,2 # 9 pairs * PAIR B5: 3,4 BLK 4 A5: 3,4,5,7 # reduction candidate for 3,4 A5: 3,4 => CTR * 143.56278.5718.36.68.3.751.5618..743..8..5192729413685..5...821.16238.578725.1.36 A5: 5,7 # 7 pairs * PAIR B5: 3,4 COL B B7: 3,4,2,9 # reduction candidate for 3,4 B7: 3,4 # 10 pairs B7: 2,9 # 7 pairs * PAIR F5: 4,5 ROW 5 A5: 4,5,3,7 # reduction candidate for 4,5 A5: 4,5 # 10 pairs C5: 4,5,8 # reduction candidate for 4,5 C5: 4,5 # 9 pairs * PAIR I4: 3,8 BLK 6 G4: 3,8,7 # reduction candidate for 3,8 G4: 7 => CTR * 19345627825718.36.68.32751..61892743..8..5192.2..13685..5..9821916238457872541936 G4: 3,8 # 10 pairs * PAIR D7: 6,7 COL D D5: 6,7,4,8 # reduction candidate for 6,7 D5: 6,7 # 8 pairs D5: 4,8 # 7 pairs * PAIR E7: 6,7 COL E E5: 6,7,4 # reduction candidate for 6,7 E5: 6,7 # 9 pairs E5: 4 # 7 pairs * PAIR H8: 2,5 BLK 9 H7: 2,5,8 # reduction candidate for 2,5 H7: 2,5 # 15 pairs H7: 8 # 10 pairs * PAIR H8: 2,5 ROW 8 A8: 2,5,4,9 # reduction candidate for 2,5 A8: 2,5 # 10 pairs A8: 4,9 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-mith-te3-00081047-base-pr-000.dot * REASONING * DIS # A5: 3,4 => CTR => A5: 5,7 * DIS # G4: 7 => CTR => G4: 3,8 * CNT 2 HDP CHAINS / 20 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,D7,E7,F5,H3,H8,I4) * 1.3.56....57.8....68...75...61....4.......192.....3..5........1.16.38..787.5.1.36 * PAIR H3: 1,2 BLK 3 H2: 1,2,6 # reduction candidate for 1,2 H2: 1,2 # 10 pairs H2: 6 # 9 pairs * PAIR H3: 1,2 ROW 3 D3: 1,2,3,4,9 # reduction candidate for 1,2 D3: 1,2 # 11 pairs E3: 1,2,4,9 # reduction candidate for 1,2 E3: 1,2 # 9 pairs * PAIR B5: 3,4 BLK 4 A5: 3,4,5,7 # reduction candidate for 3,4 A5: 3,4 => CTR * 143.56278.5718.36.68.3.751.5618..743..8..5192729413685..5...821.16238.578725.1.36 * PAIR F5: 4,5 ROW 5 C5: 4,5,8 # reduction candidate for 4,5 C5: 4,5 # 9 pairs C5: 8 # 7 pairs * PAIR I4: 3,8 BLK 6 G4: 3,8,7 # reduction candidate for 3,8 G4: 7 => CTR * 19345627825718.36.68.32751..61892743.38..5192.2..136853.5..9821916238457872541936 * PAIR D7: 6,7 COL D D5: 6,7,4,8 # reduction candidate for 6,7 D5: 6,7 # 15 pairs D5: 4,8 # 9 pairs * PAIR E7: 6,7 COL E E5: 6,7,4 # reduction candidate for 6,7 E5: 6,7 # 12 pairs E5: 4 # 12 pairs * PAIR H8: 2,5 BLK 9 H7: 2,5,8 # reduction candidate for 2,5 H7: 8 # 15 pairs H7: 2,5 # 12 pairs * PAIR H8: 2,5 ROW 8 A8: 2,5,4,9 # reduction candidate for 2,5 A8: 4,9 # 14 pairs A8: 2,5 # 13 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A5,D7,E7,F5,G4,G6,H3,H6,H8,I4) * 1.3.56....57.8....68...75...61....4..3....192.....3..53.......1.16.38..787.5.1.36 * PAIR H3: 1,2 BLK 3 H2: 1,2,6 # reduction candidate for 1,2 H2: 6 # 10 pairs H2: 1,2 # 10 pairs * PAIR H3: 1,2 ROW 3 D3: 1,2,3,4,9 # reduction candidate for 1,2 D3: 1,2 # 11 pairs E3: 1,2,4,9 # reduction candidate for 1,2 E3: 1,2 # 12 pairs * PAIR A5: 5,7 BLK 4 A4: 5,7,2,9 # reduction candidate for 5,7 A4: 2,9 => SOLVED * 123456789457189263689327514261795348735864192948213675394672851516938427872541936 * DURATION: 0:00:04.360660 START: 21:23:13.055168 END: 21:23:17.415828 2025-04-04 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00081047-base-pr-001.dot * REASONING * DIS # A5: 3,4 => CTR => A5: 5,7 * DIS A5: 5,7 # G4: 7 => CTR => G4: 3,8 * PRF A5: 5,7 + G4: 3,8 # A4: 2,9 => SOL * STA A5: 5,7 + G4: 3,8 + A4: 2,9 * CNT 3 HDP CHAINS / 23 HYP OPENED
Header Info
rating: 19537; r2: 643377; index: 81047
Solution
position: 123456789457189263689327514261795348735864192948213675394672851516938427872541936 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 # H2: 1,2 => UNS * INC # H2: 6 => UNS * INC # D3: 1,2 => UNS * INC # E3: 1,2 => UNS * DIS # A5: 3,4 => CTR => A5: 5,7 * INC # A5: 5,7 => UNS * INC # B7: 3,4 => UNS * INC # B7: 2,9 => UNS * INC # A5: 4,5 => UNS * INC # C5: 4,5 => UNS * INC # G4: 3,8 => UNS * DIS # G4: 7 => CTR => G4: 3,8 * INC # D5: 6,7 => UNS * INC # D5: 4,8 => UNS * INC # E5: 6,7 => UNS * INC # E5: 4 => UNS * INC # H7: 2,5 => UNS * INC # H7: 8 => UNS * INC # A8: 2,5 => UNS * INC # A8: 4,9 => UNS * CNT 20 HDP CHAINS / 20 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # H2: 1,2 => UNS * INC # H2: 6 => UNS * INC # D3: 1,2 => UNS * INC # E3: 1,2 => UNS * DIS # A5: 3,4 => CTR => A5: 5,7 * INC A5: 5,7 # C5: 4,5 => UNS * INC A5: 5,7 # C5: 8 => UNS * INC A5: 5,7 # G4: 3,8 => UNS * DIS A5: 5,7 # G4: 7 => CTR => G4: 3,8 * INC A5: 5,7 + G4: 3,8 # D5: 6,7 => UNS * INC A5: 5,7 + G4: 3,8 # D5: 4,8 => UNS * INC A5: 5,7 + G4: 3,8 # E5: 6,7 => UNS * INC A5: 5,7 + G4: 3,8 # E5: 4 => UNS * INC A5: 5,7 + G4: 3,8 # H7: 2,5 => UNS * INC A5: 5,7 + G4: 3,8 # H7: 8 => UNS * INC A5: 5,7 + G4: 3,8 # A8: 2,5 => UNS * INC A5: 5,7 + G4: 3,8 # A8: 4,9 => UNS * INC A5: 5,7 + G4: 3,8 # H2: 1,2 => UNS * INC A5: 5,7 + G4: 3,8 # H2: 6 => UNS * INC A5: 5,7 + G4: 3,8 # D3: 1,2 => UNS * INC A5: 5,7 + G4: 3,8 # E3: 1,2 => UNS * INC A5: 5,7 + G4: 3,8 # A4: 5,7 => UNS * PRF A5: 5,7 + G4: 3,8 # A4: 2,9 => SOL * STA A5: 5,7 + G4: 3,8 + A4: 2,9 * CNT 23 HDP CHAINS / 23 HYP OPENED