Analysis of xx-mith-te3-00011095-base.sdk
Contents
Original Sudoku
level: medium
position: .......8.4.7.8..6368..3.4.5....71.3676..........692..43.67....857........485....7 initial
Autosolve
position: .......8.4.7.8..6368..3.4.5....71.3676..........692..43.67....857........485....7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F1: 5,9 => CTR => F1: 4,6,7 * DIS # F1: 7,9 => CTR => F1: 4,5,6 * PRF # D8: 4,9 => SOL * DIS # H7: 4,9 => CTR => H7: 1,2,5 * CNT 4 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F1: 5,9 => CTR => F1: 4,6,7 * PRF F1: 4,6,7 # D8: 4,9 => SOL * STA F1: 4,6,7 + D8: 4,9 * CNT 2 HDP CHAINS / 16 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .......8.4.7.8..6368..3.4.5....71.3676..........692..43.67....857........485....7 | initial |
| .......8.4.7.8..6368..3.4.5....71.3676..........692..43.67....857........485....7 | autosolve |
| 123456789457189263689237415294871536761345892835692174316724958572968341948513627 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) F2: 5,9 F3: 7,9 A6: 1,8 D4: 4,8 E5: 4,5 F7: 4,9 G8: 3,6 G9: 3,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,C1: 3.. / B1 = 3 => 9 pairs (_) / C1 = 3 => 10 pairs (_) B6,C6: 3.. / B6 = 3 => 10 pairs (_) / C6 = 3 => 9 pairs (_) D5,F5: 3.. / D5 = 3 => 8 pairs (_) / F5 = 3 => 10 pairs (_) G8,G9: 3.. / G8 = 3 => 7 pairs (_) / G9 = 3 => 12 pairs (_) F9,G9: 3.. / F9 = 3 => 7 pairs (_) / G9 = 3 => 12 pairs (_) B1,B6: 3.. / B1 = 3 => 9 pairs (_) / B6 = 3 => 10 pairs (_) C1,C6: 3.. / C1 = 3 => 10 pairs (_) / C6 = 3 => 9 pairs (_) D5,D8: 3.. / D5 = 3 => 8 pairs (_) / D8 = 3 => 10 pairs (_) C4,C5: 4.. / C4 = 4 => 10 pairs (_) / C5 = 4 => 13 pairs (_) H7,H8: 4.. / H7 = 4 => 0 pairs (X) / H8 = 4 => 8 pairs (_) C4,D4: 4.. / C4 = 4 => 10 pairs (_) / D4 = 4 => 13 pairs (_) E5,F5: 5.. / E5 = 5 => 7 pairs (_) / F5 = 5 => 0 pairs (*) G7,H7: 5.. / G7 = 5 => 0 pairs (X) / H7 = 5 => 9 pairs (_) B2,F2: 5.. / B2 = 5 => 0 pairs (*) / F2 = 5 => 0 pairs (X) E1,E5: 5.. / E1 = 5 => 0 pairs (*) / E5 = 5 => 0 pairs (X) H6,H7: 5.. / H6 = 5 => 0 pairs (X) / H7 = 5 => 9 pairs (_) E1,F1: 6.. / E1 = 6 => 13 pairs (_) / F1 = 6 => 8 pairs (_) G8,G9: 6.. / G8 = 6 => 12 pairs (_) / G9 = 6 => 7 pairs (_) F1,F3: 7.. / F1 = 7 => 0 pairs (X) / F3 = 7 => 7 pairs (_) G1,H3: 7.. / G1 = 7 => 7 pairs (_) / H3 = 7 => 0 pairs (X) G6,H6: 7.. / G6 = 7 => 0 pairs (X) / H6 = 7 => 7 pairs (_) F1,G1: 7.. / F1 = 7 => 0 pairs (X) / G1 = 7 => 7 pairs (_) F3,H3: 7.. / F3 = 7 => 7 pairs (_) / H3 = 7 => 0 pairs (X) G1,G6: 7.. / G1 = 7 => 7 pairs (_) / G6 = 7 => 0 pairs (X) H3,H6: 7.. / H3 = 7 => 0 pairs (X) / H6 = 7 => 7 pairs (_) A4,A6: 8.. / A4 = 8 => 16 pairs (_) / A6 = 8 => 8 pairs (_) D8,F8: 8.. / D8 = 8 => 10 pairs (_) / F8 = 8 => 8 pairs (_) A6,G6: 8.. / A6 = 8 => 8 pairs (_) / G6 = 8 => 16 pairs (_) F5,F8: 8.. / F5 = 8 => 10 pairs (_) / F8 = 8 => 8 pairs (_) * DURATION: 0:00:07.497739 START: 04:17:42.645062 END: 04:17:50.142801 2025-04-06 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,D4,E5,F2,F3,F7,G8,G9) * .......8.4.7.8..6368..3.4.5....71.3676..........692..43.67....857........485....7 * PAIR F2: 5,9 BLK 2 F1: 5,9,4,6,7 # reduction candidate for 5,9 F1: 5,9 => CTR * ...46.78.4.7.8..6368..374.5..4871.3676.3548..8..692.743.6749.5857...8.4..485....7 F1: 4,6,7 # 8 pairs * PAIR F2: 5,9 ROW 2 B2: 5,9,1,2 # reduction candidate for 5,9 B2: 5,9 # 11 pairs B2: 1,2 # 9 pairs * PAIR F3: 7,9 BLK 2 F1: 7,9,4,5,6 # reduction candidate for 7,9 F1: 7,9 => CTR * ...46..8.4.7.85.6368..3.4.5..4871.3676.3548..8..692..43.67.9..857...8....485....7 F1: 4,5,6 # 7 pairs * PAIR F3: 7,9 ROW 3 H3: 7,9,1,2 # reduction candidate for 7,9 H3: 7,9 # 11 pairs H3: 1,2 # 8 pairs * PAIR A6: 1,8 ROW 6 G6: 1,8,5,7 # reduction candidate for 1,8 G6: 1,8 # 13 pairs G6: 5,7 # 9 pairs * PAIR D4: 4,8 BLK 5 D5: 4,8,3 # reduction candidate for 4,8 D5: 4,8 # 10 pairs F5: 4,8,3,5 # reduction candidate for 4,8 F5: 4,8 # 8 pairs * PAIR D4: 4,8 COL D D8: 4,8,1,2,3,9 # reduction candidate for 4,8 D8: 4,8 # 10 pairs D8: 1,2,3,9 # 8 pairs * PAIR E5: 4,5 BLK 5 F5: 4,5,3,8 # reduction candidate for 4,5 F5: 3,8 # 11 pairs F5: 4,5 # 9 pairs * PAIR E5: 4,5 COL E E1: 4,5,1,2,6 # reduction candidate for 4,5 E1: 1,2,6 # 11 pairs E1: 4,5 # 9 pairs * PAIR F7: 4,9 BLK 8 D8: 4,9,1,2,3,8 # reduction candidate for 4,9 D8: 4,9 => SOLVED * 123456789457189263689237415294871536761345892835692174316724958572968341948513627 D8: 1,2,3,8 # 8 pairs F8: 4,9,3,6,8 # reduction candidate for 4,9 F8: 4,9 # 9 pairs * PAIR F7: 4,9 ROW 7 H7: 4,9,1,2,5 # reduction candidate for 4,9 H7: 4,9 => CTR * .....7.8.4.7.8..6368..39475....71.3676.......8..6927543.67.459857.9.834.9485....7 H7: 1,2,5 # 8 pairs * PAIR F7: 4,9 COL F F1: 4,9,5,6,7 # reduction candidate for 4,9 F1: 4,9 # 13 pairs F1: 5,6,7 # 8 pairs * PAIR G8: 3,6 ROW 8 F8: 3,6,4,8,9 # reduction candidate for 3,6 F8: 3,6 # 12 pairs F8: 4,8,9 # 8 pairs * PAIR G9: 3,6 ROW 9 F9: 3,6,9 # reduction candidate for 3,6 F9: 9 # 11 pairs F9: 3,6 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-mith-te3-00011095-base-pr-000.dot * REASONING * DIS # F1: 5,9 => CTR => F1: 4,6,7 * DIS # F1: 7,9 => CTR => F1: 4,5,6 * PRF # D8: 4,9 => SOL * DIS # H7: 4,9 => CTR => H7: 1,2,5 * CNT 4 HDP CHAINS / 29 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,D4,E5,F2,F3,F7,G8,G9) * .......8.4.7.8..6368..3.4.5....71.3676..........692..43.67....857........485....7 * PAIR F2: 5,9 BLK 2 F1: 5,9,4,6,7 # reduction candidate for 5,9 F1: 5,9 => CTR * ...46.78.4.7.8..6368..374.5..4871.3676.3548..8..692.743.6749.5857...8.4..485....7 * PAIR F2: 5,9 ROW 2 B2: 5,9,1,2 # reduction candidate for 5,9 B2: 5,9 # 11 pairs B2: 1,2 # 9 pairs * PAIR F3: 7,9 ROW 3 H3: 7,9,1,2 # reduction candidate for 7,9 H3: 7,9 # 11 pairs H3: 1,2 # 9 pairs * PAIR A6: 1,8 ROW 6 G6: 1,8,5,7 # reduction candidate for 1,8 G6: 1,8 # 14 pairs G6: 5,7 # 9 pairs * PAIR D4: 4,8 BLK 5 D5: 4,8,3 # reduction candidate for 4,8 D5: 4,8 # 10 pairs F5: 4,8,3,5 # reduction candidate for 4,8 F5: 4,8 # 9 pairs * PAIR D4: 4,8 COL D D8: 4,8,1,2,3,9 # reduction candidate for 4,8 D8: 4,8 # 10 pairs D8: 1,2,3,9 # 8 pairs * PAIR E5: 4,5 BLK 5 F5: 4,5,3,8 # reduction candidate for 4,5 F5: 3,8 # 11 pairs F5: 4,5 # 9 pairs * PAIR E5: 4,5 COL E E1: 4,5,1,2,6 # reduction candidate for 4,5 E1: 1,2,6 # 11 pairs E1: 4,5 # 9 pairs * PAIR F7: 4,9 BLK 8 D8: 4,9,1,2,3,8 # reduction candidate for 4,9 D8: 4,9 => SOLVED * 123456789457189263689237415294871536761345892835692174316724958572968341948513627 * DURATION: 0:00:02.863059 START: 04:17:54.631144 END: 04:17:57.494203 2025-04-06 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00011095-base-pr-001.dot * REASONING * DIS # F1: 5,9 => CTR => F1: 4,6,7 * PRF F1: 4,6,7 # D8: 4,9 => SOL * STA F1: 4,6,7 + D8: 4,9 * CNT 2 HDP CHAINS / 16 HYP OPENED
Header Info
rating: 2593; r2: 43394; index: 11095
Solution
position: 123456789457189263689237415294871536761345892835692174316724958572968341948513627 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 # F1: 5,9 => CTR => F1: 4,6,7 * INC # F1: 4,6,7 => UNS * INC # B2: 5,9 => UNS * INC # B2: 1,2 => UNS * DIS # F1: 7,9 => CTR => F1: 4,5,6 * INC # F1: 4,5,6 => UNS * INC # H3: 7,9 => UNS * INC # H3: 1,2 => UNS * INC # G6: 1,8 => UNS * INC # G6: 5,7 => UNS * INC # D5: 4,8 => UNS * INC # F5: 4,8 => UNS * INC # D8: 4,8 => UNS * INC # D8: 1,2,3,9 => UNS * INC # F5: 4,5 => UNS * INC # F5: 3,8 => UNS * INC # E1: 4,5 => UNS * INC # E1: 1,2,6 => UNS * PRF # D8: 4,9 => SOL * INC # D8: 1,2,3,8 => UNS * INC # F8: 4,9 => UNS * DIS # H7: 4,9 => CTR => H7: 1,2,5 * INC # H7: 1,2,5 => UNS * INC # F1: 4,9 => UNS * INC # F1: 5,6,7 => UNS * INC # F8: 3,6 => UNS * INC # F8: 4,8,9 => UNS * INC # F9: 3,6 => UNS * INC # F9: 9 => UNS * CNT 29 HDP CHAINS / 29 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # F1: 5,9 => CTR => F1: 4,6,7 * INC F1: 4,6,7 # B2: 5,9 => UNS * INC F1: 4,6,7 # B2: 1,2 => UNS * INC F1: 4,6,7 # H3: 7,9 => UNS * INC F1: 4,6,7 # H3: 1,2 => UNS * INC F1: 4,6,7 # G6: 1,8 => UNS * INC F1: 4,6,7 # G6: 5,7 => UNS * INC F1: 4,6,7 # D5: 4,8 => UNS * INC F1: 4,6,7 # F5: 4,8 => UNS * INC F1: 4,6,7 # D8: 4,8 => UNS * INC F1: 4,6,7 # D8: 1,2,3,9 => UNS * INC F1: 4,6,7 # F5: 4,5 => UNS * INC F1: 4,6,7 # F5: 3,8 => UNS * INC F1: 4,6,7 # E1: 4,5 => UNS * INC F1: 4,6,7 # E1: 1,2,6 => UNS * PRF F1: 4,6,7 # D8: 4,9 => SOL * STA F1: 4,6,7 + D8: 4,9 * CNT 16 HDP CHAINS / 16 HYP OPENED