Analysis of xx-mith-te3-00041396-base.sdk
Contents
Original Sudoku
level: medium
position: ....56......1..23...9237.............14..3.92..8..41.3..18...24.92...3.884.3..91. initial
Autosolve
position: ....56......1..23...9237.............14..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: 1,2,4 * DIS # B1: 3,7 => CTR => B1: 2,8 * PRF # E2: 8 => 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:
* DIS # A1: 3,7 => CTR => A1: 1,2,4 * DIS A1: 1,2,4 # B1: 3,7 => CTR => B1: 2,8 * PRF A1: 1,2,4 + B1: 2,8 # E2: 8 => SOL * STA A1: 1,2,4 + B1: 2,8 + E2: 8 * CNT 3 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....56......1..23...9237.............14..3.92..8..41.3..18...24.92...3.884.3..91. | initial |
| ....56......1..23...9237.............14..3.92..8..41.3..18...24.92...3.884.3..91. | autosolve |
| 123456789457189236689237541235918467714563892968724153371895624592641378846372915 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) C1: 3,7 D1: 4,9 F2: 8,9 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 (_) E4,F4: 1.. / E4 = 1 => 5 pairs (_) / F4 = 1 => 13 pairs (_) E8,F8: 1.. / E8 = 1 => 13 pairs (_) / F8 = 1 => 5 pairs (_) A1,I1: 1.. / A1 = 1 => 8 pairs (_) / I1 = 1 => 11 pairs (_) A3,I3: 1.. / A3 = 1 => 11 pairs (_) / I3 = 1 => 8 pairs (_) E4,E8: 1.. / E4 = 1 => 5 pairs (_) / E8 = 1 => 13 pairs (_) F4,F8: 1.. / F4 = 1 => 13 pairs (_) / F8 = 1 => 5 pairs (_) A1,B1: 2.. / A1 = 2 => 0 pairs (X) / B1 = 2 => 8 pairs (_) E9,F9: 2.. / E9 = 2 => 8 pairs (_) / F9 = 2 => 6 pairs (_) F4,F9: 2.. / F4 = 2 => 8 pairs (_) / F9 = 2 => 6 pairs (_) A7,B7: 3.. / A7 = 3 => 6 pairs (_) / B7 = 3 => 0 pairs (X) C1,C4: 3.. / C1 = 3 => 5 pairs (_) / C4 = 3 => 0 pairs (X) D1,E2: 4.. / D1 = 4 => 10 pairs (_) / E2 = 4 => 11 pairs (_) G4,H4: 4.. / G4 = 4 => 7 pairs (_) / H4 = 4 => 8 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 (_) B1,B3: 8.. / B1 = 8 => 0 pairs (X) / B3 = 8 => 6 pairs (_) E2,F2: 8.. / E2 = 8 => 0 pairs (*) / F2 = 8 => 0 pairs (X) E5,G5: 8.. / E5 = 8 => 8 pairs (_) / G5 = 8 => 0 pairs (*) F2,F4: 8.. / F2 = 8 => 6 pairs (_) / F4 = 8 => 0 pairs (*) I1,I2: 9.. / I1 = 9 => 10 pairs (_) / I2 = 9 => 11 pairs (_) A4,A6: 9.. / A4 = 9 => 6 pairs (_) / A6 = 9 => 6 pairs (_) E7,F7: 9.. / E7 = 9 => 7 pairs (_) / F7 = 9 => 6 pairs (_) D1,I1: 9.. / D1 = 9 => 11 pairs (_) / I1 = 9 => 10 pairs (_) * DURATION: 0:00:06.748502 START: 13:44:27.064285 END: 13:44:33.812787 2025-04-04 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C1,D1,F2,F7,F8,F9) * ....56......1..23...9237.............14..3.92..8..41.3..18...24.92...3.884.3..91. * PAIR C1: 3,7 BLK 1 A1: 3,7,1,2,4 # reduction candidate for 3,7 A1: 3,7 => CTR * .2.956..14..18.239189237.............14..3.92..8..41.3..18...24.92...3.884.3..91. A1: 1,2,4 # 6 pairs B1: 3,7,2,8 # reduction candidate for 3,7 B1: 3,7 => CTR * 2..956..14..18.239189237.............14..3.92..8..41.3..18...24.92...3.884.3..91. B1: 2,8 # 7 pairs * PAIR C1: 3,7 COL C C4: 3,7,5,6 # reduction candidate for 3,7 C4: 3,7 # 9 pairs C4: 5,6 # 6 pairs * PAIR D1: 4,9 BLK 2 E2: 4,9,8 # reduction candidate for 4,9 E2: 8 => SOLVED * 123456789457189236689237541235918467714563892968724153371895624592641378846372915 E2: 4,9 # 6 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 # 7 pairs F4: 1,2,5 # 6 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 # 6 pairs * PAIR F8: 1,5 COL F F4: 1,5,2,8,9 # reduction candidate for 1,5 F4: 1,5 # 14 pairs F4: 2,8,9 # 5 pairs * PAIR F9: 2,5 COL F F4: 2,5,1,8,9 # reduction candidate for 2,5 F4: 2,5 # 8 pairs F4: 1,8,9 # 6 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-mith-te3-00041396-base-pr-000.dot * REASONING * DIS # A1: 3,7 => CTR => A1: 1,2,4 * DIS # B1: 3,7 => CTR => B1: 2,8 * PRF # E2: 8 => SOL * CNT 3 HDP CHAINS / 18 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C1,D1,F2,F7,F8,F9) * ....56......1..23...9237.............14..3.92..8..41.3..18...24.92...3.884.3..91. * PAIR C1: 3,7 BLK 1 A1: 3,7,1,2,4 # reduction candidate for 3,7 A1: 3,7 => CTR * .2.956..14..18.239189237.............14..3.92..8..41.3..18...24.92...3.884.3..91. B1: 3,7,2,8 # reduction candidate for 3,7 B1: 3,7 => CTR * 2..956..14..18.239189237.............14..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: 0:00:00.863514 START: 13:44:36.133030 END: 13:44:36.996544 2025-04-04 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00041396-base-pr-001.dot * REASONING * DIS # A1: 3,7 => CTR => A1: 1,2,4 * DIS A1: 1,2,4 # B1: 3,7 => CTR => B1: 2,8 * PRF A1: 1,2,4 + B1: 2,8 # E2: 8 => SOL * STA A1: 1,2,4 + B1: 2,8 + E2: 8 * CNT 3 HDP CHAINS / 4 HYP OPENED
Header Info
rating: 8591; r2: 257361; index: 41396
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: 1,2,4 * INC # A1: 1,2,4 => UNS * DIS # B1: 3,7 => CTR => B1: 2,8 * INC # B1: 2,8 => 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 # 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 18 HDP CHAINS / 18 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 3,7 => CTR => A1: 1,2,4 * DIS A1: 1,2,4 # B1: 3,7 => CTR => B1: 2,8 * INC A1: 1,2,4 + B1: 2,8 # E2: 4,9 => UNS * PRF A1: 1,2,4 + B1: 2,8 # E2: 8 => SOL * STA A1: 1,2,4 + B1: 2,8 + E2: 8 * CNT 4 HDP CHAINS / 4 HYP OPENED