Analysis of xx-mith-te3-00041395-base.sdk
Contents
Original Sudoku
level: medium
position: .2..56......1..23...9237..............4..3.92..8..41.3..18...24.92...3.884.3..91. initial
Autosolve
position: .2..56......1..23..89237..............4..3.92..8..41.3..18...24.92...3.884.3..91. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 3,7 => CTR => A1: 1,4 * PRF # E2: 8 => SOL * 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 # A1: 3,7 => CTR => A1: 1,4 * PRF A1: 1,4 # E2: 8 => SOL * STA A1: 1,4 + E2: 8 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2..56......1..23...9237..............4..3.92..8..41.3..18...24.92...3.884.3..91. | initial |
| .2..56......1..23..89237..............4..3.92..8..41.3..18...24.92...3.884.3..91. | autosolve |
| 123456789457189236689237541235918467714563892968724153371895624592641378846372915 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) C1: 3,7 D1: 4,9 F2: 8,9 A4: 2,9 A6: 2,9 F7: 5,9 F8: 1,5 F9: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A3: 1.. / A1 = 1 => 8 pairs (_) / A3 = 1 => 11 pairs (_) I1,I3: 1.. / I1 = 1 => 11 pairs (_) / I3 = 1 => 8 pairs (_) B4,B5: 1.. / B4 = 1 => 0 pairs (X) / B5 = 1 => 8 pairs (_) E8,F8: 1.. / E8 = 1 => 13 pairs (_) / F8 = 1 => 7 pairs (_) A1,I1: 1.. / A1 = 1 => 8 pairs (_) / I1 = 1 => 11 pairs (_) A3,I3: 1.. / A3 = 1 => 11 pairs (_) / I3 = 1 => 8 pairs (_) B5,E5: 1.. / B5 = 1 => 8 pairs (_) / E5 = 1 => 0 pairs (X) F4,F8: 1.. / F4 = 1 => 13 pairs (_) / F8 = 1 => 7 pairs (_) A4,A6: 2.. / A4 = 2 => 6 pairs (_) / A6 = 2 => 7 pairs (_) E9,F9: 2.. / E9 = 2 => 8 pairs (_) / F9 = 2 => 8 pairs (_) A6,E6: 2.. / A6 = 2 => 7 pairs (_) / E6 = 2 => 6 pairs (_) F4,F9: 2.. / F4 = 2 => 8 pairs (_) / F9 = 2 => 8 pairs (_) A1,C1: 3.. / A1 = 3 => 0 pairs (X) / C1 = 3 => 7 pairs (_) B4,C4: 3.. / B4 = 3 => 7 pairs (_) / C4 = 3 => 0 pairs (X) A7,B7: 3.. / A7 = 3 => 7 pairs (_) / B7 = 3 => 0 pairs (X) A1,A7: 3.. / A1 = 3 => 0 pairs (X) / A7 = 3 => 7 pairs (_) B4,B7: 3.. / B4 = 3 => 7 pairs (_) / B7 = 3 => 0 pairs (X) C1,C4: 3.. / C1 = 3 => 7 pairs (_) / C4 = 3 => 0 pairs (X) D1,E2: 4.. / D1 = 4 => 10 pairs (_) / E2 = 4 => 11 pairs (_) G4,H4: 4.. / G4 = 4 => 10 pairs (_) / H4 = 4 => 10 pairs (_) D8,E8: 4.. / D8 = 4 => 11 pairs (_) / E8 = 4 => 10 pairs (_) A2,E2: 4.. / A2 = 4 => 10 pairs (_) / E2 = 4 => 11 pairs (_) D1,D8: 4.. / D1 = 4 => 10 pairs (_) / D8 = 4 => 11 pairs (_) E2,E8: 4.. / E2 = 4 => 11 pairs (_) / E8 = 4 => 10 pairs (_) E2,F2: 8.. / E2 = 8 => 0 pairs (*) / F2 = 8 => 0 pairs (X) G1,H1: 8.. / G1 = 8 => 10 pairs (_) / H1 = 8 => 9 pairs (_) E5,G5: 8.. / E5 = 8 => 10 pairs (_) / G5 = 8 => 9 pairs (_) F2,F4: 8.. / F2 = 8 => 8 pairs (_) / F4 = 8 => 0 pairs (*) H1,H4: 8.. / H1 = 8 => 9 pairs (_) / H4 = 8 => 10 pairs (_) I1,I2: 9.. / I1 = 9 => 10 pairs (_) / I2 = 9 => 11 pairs (_) A4,A6: 9.. / A4 = 9 => 7 pairs (_) / A6 = 9 => 6 pairs (_) E7,F7: 9.. / E7 = 9 => 9 pairs (_) / F7 = 9 => 8 pairs (_) D1,I1: 9.. / D1 = 9 => 11 pairs (_) / I1 = 9 => 10 pairs (_) * DURATION: 0:00:09.223813 START: 07:48:40.591522 END: 07:48:49.815335 2025-04-06 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,C1,D1,F2,F7,F8,F9) * .2..56......1..23..89237..............4..3.92..8..41.3..18...24.92...3.884.3..91. * PAIR C1: 3,7 BLK 1 A1: 3,7,1,4 # reduction candidate for 3,7 A1: 3,7 => CTR * .2.956..14..18.239189237..............4..3.92..8..41.3..18...24.92...3.884.3..91. A1: 1,4 # 8 pairs * PAIR C1: 3,7 COL C C4: 3,7,5,6 # reduction candidate for 3,7 C4: 3,7 # 11 pairs C4: 5,6 # 8 pairs * PAIR D1: 4,9 BLK 2 E2: 4,9,8 # reduction candidate for 4,9 E2: 8 => SOLVED * 123456789457189236689237541235918467714563892968724153371895624592641378846372915 E2: 4,9 # 8 pairs * PAIR F2: 8,9 BLK 2 E2: 8,9,4 # reduction candidate for 8,9 E2: 4 # 11 pairs E2: 8,9 # 10 pairs * PAIR F2: 8,9 COL F F4: 8,9,1,2,5 # reduction candidate for 8,9 F4: 8,9 # 9 pairs F4: 1,2,5 # 8 pairs * PAIR A4: 2,9 ROW 4 E4: 2,9,1,6,7,8 # reduction candidate for 2,9 E4: 2,9 # 13 pairs F4: 2,9,1,5,8 # reduction candidate for 2,9 F4: 2,9 # 10 pairs * PAIR A6: 2,9 ROW 6 E6: 2,9,6,7 # reduction candidate for 2,9 E6: 6,7 # 11 pairs E6: 2,9 # 9 pairs * PAIR F7: 5,9 COL F F4: 5,9,1,2,8 # reduction candidate for 5,9 F4: 5,9 # 9 pairs F4: 1,2,8 # 8 pairs * PAIR F8: 1,5 COL F F4: 1,5,2,8,9 # reduction candidate for 1,5 F4: 1,5 # 15 pairs F4: 2,8,9 # 7 pairs * PAIR F9: 2,5 COL F F4: 2,5,1,8,9 # reduction candidate for 2,5 F4: 2,5 # 10 pairs F4: 1,8,9 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-mith-te3-00041395-base-pr-000.dot * REASONING * DIS # A1: 3,7 => CTR => A1: 1,4 * PRF # E2: 8 => SOL * CNT 2 HDP CHAINS / 20 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,C1,D1,F2,F7,F8,F9) * .2..56......1..23..89237..............4..3.92..8..41.3..18...24.92...3.884.3..91. * PAIR C1: 3,7 BLK 1 A1: 3,7,1,4 # reduction candidate for 3,7 A1: 3,7 => CTR * .2.956..14..18.239189237..............4..3.92..8..41.3..18...24.92...3.884.3..91. * PAIR D1: 4,9 BLK 2 E2: 4,9,8 # reduction candidate for 4,9 E2: 8 => SOLVED * 123456789457189236689237541235918467714563892968724153371895624592641378846372915 * DURATION: 0:00:00.942961 START: 07:48:53.140672 END: 07:48:54.083633 2025-04-06 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00041395-base-pr-001.dot * REASONING * DIS # A1: 3,7 => CTR => A1: 1,4 * PRF A1: 1,4 # E2: 8 => SOL * STA A1: 1,4 + E2: 8 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
rating: 8591; r2: 274270; index: 41395
Solution
position: 123456789457189236689237541235918467714563892968724153371895624592641378846372915 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 # A1: 3,7 => CTR => A1: 1,4 * INC # A1: 1,4 => UNS * INC # C4: 3,7 => UNS * INC # C4: 5,6 => UNS * INC # E2: 4,9 => UNS * PRF # E2: 8 => SOL * INC # E2: 8,9 => UNS * INC # E2: 4 => UNS * INC # F4: 8,9 => UNS * INC # F4: 1,2,5 => UNS * INC # E4: 2,9 => UNS * INC # F4: 2,9 => UNS * INC # E6: 2,9 => UNS * INC # E6: 6,7 => UNS * INC # F4: 5,9 => UNS * INC # F4: 1,2,8 => UNS * INC # F4: 1,5 => UNS * INC # F4: 2,8,9 => UNS * INC # F4: 2,5 => UNS * INC # F4: 1,8,9 => UNS * CNT 20 HDP CHAINS / 20 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 3,7 => CTR => A1: 1,4 * INC A1: 1,4 # E2: 4,9 => UNS * PRF A1: 1,4 # E2: 8 => SOL * STA A1: 1,4 + E2: 8 * CNT 3 HDP CHAINS / 3 HYP OPENED