Analysis of xx-mith-te3-00050838-base.sdk
Contents
Original Sudoku
level: medium
position: .2..567...5.1.926....27......576.19...19.5.2.......5.63.6...91.51..97...89....... initial
Autosolve
position: .2..567...5.1.926....27..5...576.19...19.5.2.......5.63.6...91.51..97...89....... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A6: 2,4 => CTR => A6: 7,9 * DIS # C9: 7 => CTR => C9: 2,4 * CNT 2 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A6: 2,4 => CTR => A6: 7,9 * DIS A6: 7,9 # C9: 7 => CTR => C9: 2,4 * PRF A6: 7,9 + C9: 2,4 # C6: 3,8 => SOL * STA A6: 7,9 + C9: 2,4 + C6: 3,8 * CNT 3 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2..567...5.1.926....27......576.19...19.5.2.......5.63.6...91.51..97...89....... | initial |
| .2..567...5.1.926....27..5...576.19...19.5.2.......5.63.6...91.51..97...89....... | autosolve |
| 123456789457189263689273451235768194761945328948312576376824915514697832892531647 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) A2: 4,7 I1: 1,9 I3: 1,9 A4: 2,4 B7: 4,7 C8: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A3: 1.. / A1 = 1 => 4 pairs (_) / A3 = 1 => 5 pairs (_) I1,I3: 1.. / I1 = 1 => 5 pairs (_) / I3 = 1 => 4 pairs (_) E6,F6: 1.. / E6 = 1 => 7 pairs (_) / F6 = 1 => 6 pairs (_) E9,F9: 1.. / E9 = 1 => 6 pairs (_) / F9 = 1 => 7 pairs (_) A1,I1: 1.. / A1 = 1 => 4 pairs (_) / I1 = 1 => 5 pairs (_) A3,I3: 1.. / A3 = 1 => 5 pairs (_) / I3 = 1 => 4 pairs (_) E6,E9: 1.. / E6 = 1 => 7 pairs (_) / E9 = 1 => 6 pairs (_) F6,F9: 1.. / F6 = 1 => 6 pairs (_) / F9 = 1 => 7 pairs (_) A4,A6: 2.. / A4 = 2 => 7 pairs (_) / A6 = 2 => 0 pairs (X) C8,C9: 2.. / C8 = 2 => 13 pairs (_) / C9 = 2 => 5 pairs (_) A4,F4: 2.. / A4 = 2 => 7 pairs (_) / F4 = 2 => 0 pairs (X) C8,I8: 2.. / C8 = 2 => 13 pairs (_) / I8 = 2 => 5 pairs (_) D7,D9: 5.. / D7 = 5 => 6 pairs (_) / D9 = 5 => 10 pairs (_) I7,I9: 5.. / I7 = 5 => 10 pairs (_) / I9 = 5 => 6 pairs (_) D7,I7: 5.. / D7 = 5 => 6 pairs (_) / I7 = 5 => 10 pairs (_) D9,I9: 5.. / D9 = 5 => 10 pairs (_) / I9 = 5 => 6 pairs (_) A3,B3: 6.. / A3 = 6 => 6 pairs (_) / B3 = 6 => 6 pairs (_) A5,B5: 6.. / A5 = 6 => 6 pairs (_) / B5 = 6 => 6 pairs (_) D8,D9: 6.. / D8 = 6 => 7 pairs (_) / D9 = 6 => 7 pairs (_) G8,G9: 6.. / G8 = 6 => 7 pairs (_) / G9 = 6 => 7 pairs (_) D8,G8: 6.. / D8 = 6 => 7 pairs (_) / G8 = 6 => 7 pairs (_) D9,G9: 6.. / D9 = 6 => 7 pairs (_) / G9 = 6 => 7 pairs (_) A3,A5: 6.. / A3 = 6 => 6 pairs (_) / A5 = 6 => 6 pairs (_) B3,B5: 6.. / B3 = 6 => 6 pairs (_) / B5 = 6 => 6 pairs (_) A2,C2: 7.. / A2 = 7 => 6 pairs (_) / C2 = 7 => 12 pairs (_) I5,H6: 7.. / I5 = 7 => 11 pairs (_) / H6 = 7 => 0 pairs (*) B7,C9: 7.. / B7 = 7 => 6 pairs (_) / C9 = 7 => 0 pairs (X) B7,I7: 7.. / B7 = 7 => 6 pairs (_) / I7 = 7 => 0 pairs (X) H6,H9: 7.. / H6 = 7 => 0 pairs (*) / H9 = 7 => 0 pairs (X) I1,I3: 9.. / I1 = 9 => 4 pairs (_) / I3 = 9 => 5 pairs (_) A6,C6: 9.. / A6 = 9 => 8 pairs (_) / C6 = 9 => 8 pairs (_) * DURATION: 0:00:08.262662 START: 15:30:20.941930 END: 15:30:29.204592 2025-04-04 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B7,C8,I1,I3) * .2..567...5.1.926....27..5...576.19...19.5.2.......5.63.6...91.51..97...89....... * PAIR A2: 4,7 BLK 1 C2: 4,7,3,8 # reduction candidate for 4,7 C2: 4,7 # 11 pairs C2: 3,8 # 7 pairs * PAIR A2: 4,7 COL A A5: 4,7,6 # reduction candidate for 4,7 A5: 4,7 # 6 pairs A6: 4,7,2,9 # reduction candidate for 4,7 A6: 4,7 # 10 pairs * PAIR I1: 1,9 ROW 1 A1: 1,9,4 # reduction candidate for 1,9 A1: 4 # 9 pairs A1: 1,9 # 7 pairs * PAIR I3: 1,9 ROW 3 A3: 1,9,4,6 # reduction candidate for 1,9 A3: 1,9 # 7 pairs A3: 4,6 # 6 pairs * PAIR A4: 2,4 BLK 4 A6: 2,4,7,9 # reduction candidate for 2,4 A6: 2,4 => CTR * .2..567..75.1.926..6.27..5...576.19.6.19.5.2...9...5.6346...917512.97...897...... A6: 7,9 # 8 pairs * PAIR A4: 2,4 ROW 4 F4: 2,4,3,8 # reduction candidate for 2,4 F4: 2,4 # 9 pairs F4: 3,8 # 8 pairs * PAIR B7: 4,7 BLK 7 C9: 4,7,2 # reduction candidate for 4,7 C9: 4,7 # 13 pairs C9: 2 # 5 pairs * PAIR B7: 4,7 ROW 7 I7: 4,7,2,5,8 # reduction candidate for 4,7 I7: 4,7 # 16 pairs I7: 2,5,8 # 6 pairs * PAIR B7: 4,7 COL B B5: 4,7,3,6,8 # reduction candidate for 4,7 B5: 4,7 # 9 pairs B6: 4,7,3,8 # reduction candidate for 4,7 B6: 4,7 # 8 pairs * PAIR C8: 2,4 BLK 7 C9: 2,4,7 # reduction candidate for 2,4 C9: 7 => CTR * .2..567..75.1.926....27..5...576.19...19.5.2.......576346...917512.97...897...... C9: 2,4 # 6 pairs * PAIR C8: 2,4 ROW 8 I8: 2,4,3,8 # reduction candidate for 2,4 I8: 3,8 # 14 pairs I8: 2,4 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-mith-te3-00050838-base-pr-000.dot * REASONING * DIS # A6: 2,4 => CTR => A6: 7,9 * DIS # C9: 7 => CTR => C9: 2,4 * CNT 2 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B7,C8,I1,I3) * .2..567...5.1.926....27..5...576.19...19.5.2.......5.63.6...91.51..97...89....... * PAIR A2: 4,7 BLK 1 C2: 4,7,3,8 # reduction candidate for 4,7 C2: 4,7 # 11 pairs C2: 3,8 # 7 pairs * PAIR A2: 4,7 COL A A5: 4,7,6 # reduction candidate for 4,7 A5: 4,7 # 6 pairs A6: 4,7,2,9 # reduction candidate for 4,7 A6: 4,7 # 10 pairs * PAIR I1: 1,9 ROW 1 A1: 1,9,4 # reduction candidate for 1,9 A1: 4 # 9 pairs A1: 1,9 # 7 pairs * PAIR I3: 1,9 ROW 3 A3: 1,9,4,6 # reduction candidate for 1,9 A3: 1,9 # 7 pairs A3: 4,6 # 6 pairs * PAIR A4: 2,4 BLK 4 A6: 2,4,7,9 # reduction candidate for 2,4 A6: 2,4 => CTR * .2..567..75.1.926..6.27..5...576.19.6.19.5.2...9...5.6346...917512.97...897...... * PAIR B7: 4,7 BLK 7 C9: 4,7,2 # reduction candidate for 4,7 C9: 4,7 # 13 pairs C9: 2 # 7 pairs * PAIR B7: 4,7 ROW 7 I7: 4,7,2,5,8 # reduction candidate for 4,7 I7: 4,7 # 16 pairs I7: 2,5,8 # 8 pairs * PAIR B7: 4,7 COL B B5: 4,7,3,6,8 # reduction candidate for 4,7 B5: 4,7 # 11 pairs B6: 4,7,3,8 # reduction candidate for 4,7 B6: 4,7 # 10 pairs * PAIR C8: 2,4 BLK 7 C9: 2,4,7 # reduction candidate for 2,4 C9: 7 => CTR * .2..567..75.1.926....27..5.2.576.19...19.5.2.9.....576346...917512.97...897...... * PAIR C8: 2,4 ROW 8 I8: 2,4,3,8 # reduction candidate for 2,4 I8: 3,8 # 14 pairs I8: 2,4 # 10 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,A6,C8,C9,E6,F6,I1,I3) * .2..567...5.1.926....27..5.2.576.19...19.5.2.......5.6376...91.51..97...89....... * PAIR A2: 4,7 COL A A5: 4,7,6 # reduction candidate for 4,7 A5: 6 # 9 pairs A5: 4,7 # 7 pairs * PAIR I1: 1,9 ROW 1 A1: 1,9,4 # reduction candidate for 1,9 A1: 1,9 # 10 pairs A1: 4 # 8 pairs * PAIR I3: 1,9 ROW 3 A3: 1,9,4,6 # reduction candidate for 1,9 A3: 1,9 # 11 pairs A3: 4,6 # 7 pairs * PAIR A6: 7,9 BLK 4 C6: 7,9,3,8 # reduction candidate for 7,9 C6: 3,8 => SOLVED * 123456789457189263689273451235768194761945328948312576376824915514697832892531647 * DURATION: 0:00:04.825804 START: 15:30:32.583583 END: 15:30:37.409387 2025-04-04 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00050838-base-pr-001.dot * REASONING * DIS # A6: 2,4 => CTR => A6: 7,9 * DIS A6: 7,9 # C9: 7 => CTR => C9: 2,4 * PRF A6: 7,9 + C9: 2,4 # C6: 3,8 => SOL * STA A6: 7,9 + C9: 2,4 + C6: 3,8 * CNT 3 HDP CHAINS / 27 HYP OPENED
Header Info
rating: 10416; r2: 254037; index: 50838
Solution
position: 123456789457189263689273451235768194761945328948312576376824915514697832892531647 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 # C2: 4,7 => UNS * INC # C2: 3,8 => UNS * INC # A5: 4,7 => UNS * INC # A6: 4,7 => UNS * INC # A1: 1,9 => UNS * INC # A1: 4 => UNS * INC # A3: 1,9 => UNS * INC # A3: 4,6 => UNS * DIS # A6: 2,4 => CTR => A6: 7,9 * INC # A6: 7,9 => UNS * INC # F4: 2,4 => UNS * INC # F4: 3,8 => UNS * INC # C9: 4,7 => UNS * INC # C9: 2 => UNS * INC # I7: 4,7 => UNS * INC # I7: 2,5,8 => UNS * INC # B5: 4,7 => UNS * INC # B6: 4,7 => UNS * INC # C9: 2,4 => UNS * DIS # C9: 7 => CTR => C9: 2,4 * INC # I8: 2,4 => UNS * INC # I8: 3,8 => UNS * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 4,7 => UNS * INC # C2: 3,8 => UNS * INC # A5: 4,7 => UNS * INC # A6: 4,7 => UNS * INC # A1: 1,9 => UNS * INC # A1: 4 => UNS * INC # A3: 1,9 => UNS * INC # A3: 4,6 => UNS * DIS # A6: 2,4 => CTR => A6: 7,9 * INC A6: 7,9 # C9: 4,7 => UNS * INC A6: 7,9 # C9: 2 => UNS * INC A6: 7,9 # I7: 4,7 => UNS * INC A6: 7,9 # I7: 2,5,8 => UNS * INC A6: 7,9 # B5: 4,7 => UNS * INC A6: 7,9 # B6: 4,7 => UNS * INC A6: 7,9 # C9: 2,4 => UNS * DIS A6: 7,9 # C9: 7 => CTR => C9: 2,4 * INC A6: 7,9 + C9: 2,4 # I8: 2,4 => UNS * INC A6: 7,9 + C9: 2,4 # I8: 3,8 => UNS * INC A6: 7,9 + C9: 2,4 # A5: 4,7 => UNS * INC A6: 7,9 + C9: 2,4 # A5: 6 => UNS * INC A6: 7,9 + C9: 2,4 # A1: 1,9 => UNS * INC A6: 7,9 + C9: 2,4 # A1: 4 => UNS * INC A6: 7,9 + C9: 2,4 # A3: 1,9 => UNS * INC A6: 7,9 + C9: 2,4 # A3: 4,6 => UNS * INC A6: 7,9 + C9: 2,4 # C6: 7,9 => UNS * PRF A6: 7,9 + C9: 2,4 # C6: 3,8 => SOL * STA A6: 7,9 + C9: 2,4 + C6: 3,8 * CNT 27 HDP CHAINS / 27 HYP OPENED