Analysis of xx-mith-te3-00154974-base.sdk
Contents
Original Sudoku
level: medium
position: ..3.567.9..71.9..3......1..2.6...5.7.71......84......6...9...7.7...13.959....76.1 initial
Autosolve
position: ..3.567.9..71.9..3......1..2.6...5.7.71......84......6...9...7.7...13.959....76.1 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D5: 3,5 => CTR => D5: 2,4,6,8 * PRF # C3: 2,4,8 => SOL * CNT 2 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 # D5: 3,5 => CTR => D5: 2,4,6,8 * PRF D5: 2,4,6,8 # C3: 2,4,8 => SOL * STA D5: 2,4,6,8 + C3: 2,4,8 * CNT 2 HDP CHAINS / 19 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..3.567.9..71.9..3......1..2.6...5.7.71......84......6...9...7.7...13.959....76.1 | initial |
| ..3.567.9..71.9..3......1..2.6...5.7.71......84......6...9...7.7...13.959....76.1 | autosolve |
| 123456789457189263698372154236891547571634928849725316315968472764213895982547631 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) A1: 1,4 D3: 3,7 E3: 3,7 H2: 5,6 H3: 5,6 B4: 3,9 A5: 3,5 C6: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,B1: 1.. / A1 = 1 => 8 pairs (_) / B1 = 1 => 15 pairs (_) F4,F6: 1.. / F4 = 1 => 9 pairs (_) / F6 = 1 => 11 pairs (_) H4,H6: 1.. / H4 = 1 => 11 pairs (_) / H6 = 1 => 9 pairs (_) A7,B7: 1.. / A7 = 1 => 15 pairs (_) / B7 = 1 => 8 pairs (_) F4,H4: 1.. / F4 = 1 => 9 pairs (_) / H4 = 1 => 11 pairs (_) F6,H6: 1.. / F6 = 1 => 11 pairs (_) / H6 = 1 => 9 pairs (_) A1,A7: 1.. / A1 = 1 => 8 pairs (_) / A7 = 1 => 15 pairs (_) B1,B7: 1.. / B1 = 1 => 15 pairs (_) / B7 = 1 => 8 pairs (_) D3,E3: 3.. / D3 = 3 => 7 pairs (_) / E3 = 3 => 6 pairs (_) B4,A5: 3.. / B4 = 3 => 0 pairs (*) / A5 = 3 => 0 pairs (X) G7,H9: 3.. / G7 = 3 => 12 pairs (_) / H9 = 3 => 13 pairs (_) B9,H9: 3.. / B9 = 3 => 12 pairs (_) / H9 = 3 => 13 pairs (_) A5,A7: 3.. / A5 = 3 => 12 pairs (_) / A7 = 3 => 0 pairs (*) H2,H3: 5.. / H2 = 5 => 8 pairs (_) / H3 = 5 => 8 pairs (_) A5,C6: 5.. / A5 = 5 => 0 pairs (*) / C6 = 5 => 0 pairs (X) F7,D9: 5.. / F7 = 5 => 9 pairs (_) / D9 = 5 => 8 pairs (_) H2,H3: 6.. / H2 = 6 => 8 pairs (_) / H3 = 6 => 8 pairs (_) D5,E5: 6.. / D5 = 6 => 8 pairs (_) / E5 = 6 => 0 pairs (X) E7,D8: 6.. / E7 = 6 => 8 pairs (_) / D8 = 6 => 0 pairs (X) B8,D8: 6.. / B8 = 6 => 8 pairs (_) / D8 = 6 => 0 pairs (X) D5,D8: 6.. / D5 = 6 => 8 pairs (_) / D8 = 6 => 0 pairs (X) E5,E7: 6.. / E5 = 6 => 0 pairs (X) / E7 = 6 => 8 pairs (_) D3,E3: 7.. / D3 = 7 => 6 pairs (_) / E3 = 7 => 7 pairs (_) D6,E6: 7.. / D6 = 7 => 7 pairs (_) / E6 = 7 => 6 pairs (_) D3,D6: 7.. / D3 = 7 => 6 pairs (_) / D6 = 7 => 7 pairs (_) E3,E6: 7.. / E3 = 7 => 7 pairs (_) / E6 = 7 => 6 pairs (_) B3,C3: 9.. / B3 = 9 => 0 pairs (*) / C3 = 9 => 0 pairs (X) B4,C6: 9.. / B4 = 9 => 12 pairs (_) / C6 = 9 => 0 pairs (*) G5,G6: 9.. / G5 = 9 => 9 pairs (_) / G6 = 9 => 10 pairs (_) B4,E4: 9.. / B4 = 9 => 12 pairs (_) / E4 = 9 => 0 pairs (*) E5,G5: 9.. / E5 = 9 => 10 pairs (_) / G5 = 9 => 9 pairs (_) B3,B4: 9.. / B3 = 9 => 0 pairs (*) / B4 = 9 => 0 pairs (X) C3,C6: 9.. / C3 = 9 => 12 pairs (_) / C6 = 9 => 0 pairs (*) * DURATION: 0:00:09.410742 START: 15:32:52.447665 END: 15:33:01.858407 2025-04-05 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A5,B4,C6,D3,E3,H2,H3) * ..3.567.9..71.9..3......1..2.6...5.7.71......84......6...9...7.7...13.959....76.1 * PAIR A1: 1,4 COL A A7: 1,4,3,5,6 # reduction candidate for 1,4 A7: 1,4 # 15 pairs A7: 3,5,6 # 8 pairs * PAIR D3: 3,7 COL D D6: 3,7,2,5 # reduction candidate for 3,7 D6: 3,7 # 10 pairs D6: 2,5 # 7 pairs * PAIR E3: 3,7 COL E E6: 3,7,2,9 # reduction candidate for 3,7 E6: 3,7 # 9 pairs E6: 2,9 # 9 pairs * PAIR H2: 5,6 ROW 2 A2: 5,6,4 # reduction candidate for 5,6 A2: 5,6 # 10 pairs B2: 5,6,2,8 # reduction candidate for 5,6 B2: 5,6 # 12 pairs * PAIR H3: 5,6 ROW 3 A3: 5,6,4 # reduction candidate for 5,6 A3: 5,6 # 9 pairs B3: 5,6,2,8,9 # reduction candidate for 5,6 B3: 5,6 # 11 pairs * PAIR B4: 3,9 ROW 4 E4: 3,9,4,8 # reduction candidate for 3,9 E4: 4,8 # 12 pairs E4: 3,9 # 10 pairs * PAIR A5: 3,5 ROW 5 D5: 3,5,2,4,6,8 # reduction candidate for 3,5 D5: 3,5 => CTR * ..3.567.9..71.9..3......1..2.6...5.737156.9..845.9...6...9.537.7..613.9593...76.1 D5: 2,4,6,8 # 8 pairs * PAIR A5: 3,5 COL A A7: 3,5,1,4,6 # reduction candidate for 3,5 A7: 1,4,6 # 15 pairs A7: 3,5 # 11 pairs * PAIR C6: 5,9 COL C C3: 5,9,2,4,8 # reduction candidate for 5,9 C3: 2,4,8 => SOLVED * 123456789457189263698372154236891547571634928849725316315968472764213895982547631 C3: 5,9 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-mith-te3-00154974-base-pr-000.dot * REASONING * DIS # D5: 3,5 => CTR => D5: 2,4,6,8 * PRF # C3: 2,4,8 => SOL * CNT 2 HDP CHAINS / 18 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A5,B4,C6,D3,E3,H2,H3) * ..3.567.9..71.9..3......1..2.6...5.7.71......84......6...9...7.7...13.959....76.1 * PAIR A1: 1,4 COL A A7: 1,4,3,5,6 # reduction candidate for 1,4 A7: 1,4 # 15 pairs A7: 3,5,6 # 8 pairs * PAIR D3: 3,7 COL D D6: 3,7,2,5 # reduction candidate for 3,7 D6: 3,7 # 10 pairs D6: 2,5 # 7 pairs * PAIR E3: 3,7 COL E E6: 3,7,2,9 # reduction candidate for 3,7 E6: 3,7 # 9 pairs E6: 2,9 # 9 pairs * PAIR H2: 5,6 ROW 2 A2: 5,6,4 # reduction candidate for 5,6 A2: 5,6 # 10 pairs B2: 5,6,2,8 # reduction candidate for 5,6 B2: 5,6 # 12 pairs * PAIR H3: 5,6 ROW 3 A3: 5,6,4 # reduction candidate for 5,6 A3: 5,6 # 9 pairs B3: 5,6,2,8,9 # reduction candidate for 5,6 B3: 5,6 # 11 pairs * PAIR B4: 3,9 ROW 4 E4: 3,9,4,8 # reduction candidate for 3,9 E4: 4,8 # 12 pairs E4: 3,9 # 10 pairs * PAIR A5: 3,5 ROW 5 D5: 3,5,2,4,6,8 # reduction candidate for 3,5 D5: 3,5 => CTR * ..3.567.9..71.9..3......1..2.6...5.737156.9..845.9...6...9.537.7..613.9593...76.1 * PAIR A5: 3,5 COL A A7: 3,5,1,4,6 # reduction candidate for 3,5 A7: 1,4,6 # 15 pairs A7: 3,5 # 11 pairs * PAIR RESTART * PAIR A5: 3,5 COL A A7: 3,5,1,4,6 # reduction candidate for 3,5 A7: 1,4,6 # 15 pairs A7: 3,5 # 11 pairs * PAIR C6: 5,9 COL C C3: 5,9,2,4,8 # reduction candidate for 5,9 C3: 2,4,8 => SOLVED * 123456789457189263698372154236891547571634928849725316315968472764213895982547631 * DURATION: 0:00:03.334829 START: 15:33:04.873887 END: 15:33:08.208716 2025-04-05 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00154974-base-pr-001.dot * REASONING * DIS # D5: 3,5 => CTR => D5: 2,4,6,8 * PRF D5: 2,4,6,8 # C3: 2,4,8 => SOL * STA D5: 2,4,6,8 + C3: 2,4,8 * CNT 2 HDP CHAINS / 19 HYP OPENED
Header Info
rating: 42754; r2: 809141; index: 154974
Solution
position: 123456789457189263698372154236891547571634928849725316315968472764213895982547631 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 # A7: 1,4 => UNS * INC # A7: 3,5,6 => UNS * INC # D6: 3,7 => UNS * INC # D6: 2,5 => UNS * INC # E6: 3,7 => UNS * INC # E6: 2,9 => UNS * INC # A2: 5,6 => UNS * INC # B2: 5,6 => UNS * INC # A3: 5,6 => UNS * INC # B3: 5,6 => UNS * INC # E4: 3,9 => UNS * INC # E4: 4,8 => UNS * DIS # D5: 3,5 => CTR => D5: 2,4,6,8 * INC # D5: 2,4,6,8 => UNS * INC # A7: 3,5 => UNS * INC # A7: 1,4,6 => UNS * INC # C3: 5,9 => UNS * PRF # C3: 2,4,8 => SOL * CNT 18 HDP CHAINS / 18 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A7: 1,4 => UNS * INC # A7: 3,5,6 => UNS * INC # D6: 3,7 => UNS * INC # D6: 2,5 => UNS * INC # E6: 3,7 => UNS * INC # E6: 2,9 => UNS * INC # A2: 5,6 => UNS * INC # B2: 5,6 => UNS * INC # A3: 5,6 => UNS * INC # B3: 5,6 => UNS * INC # E4: 3,9 => UNS * INC # E4: 4,8 => UNS * DIS # D5: 3,5 => CTR => D5: 2,4,6,8 * INC D5: 2,4,6,8 # A7: 3,5 => UNS * INC D5: 2,4,6,8 # A7: 1,4,6 => UNS * INC D5: 2,4,6,8 # A7: 3,5 => UNS * INC D5: 2,4,6,8 # A7: 1,4,6 => UNS * INC D5: 2,4,6,8 # C3: 5,9 => UNS * PRF D5: 2,4,6,8 # C3: 2,4,8 => SOL * STA D5: 2,4,6,8 + C3: 2,4,8 * CNT 19 HDP CHAINS / 19 HYP OPENED