Analysis of xx-mith-te3-00147741-base.sdk
Contents
Original Sudoku
level: medium
position: ...4.6.8.4..18....6...27.41......1...6.8.1.72.7..42.6..462.8....39......81......7 initial
Autosolve
position: ...4.6.8.4..18...66...27.41......1...6.8.1.72.7..42.6..462.8....39......81......7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # I4: 3,5,9 => SOL * CNT 1 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # I4: 3,5,9 => SOL * STA I4: 3,5,9 * CNT 1 HDP CHAINS / 25 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...4.6.8.4..18....6...27.41......1...6.8.1.72.7..42.6..462.8....39......81......7 | initial |
| ...4.6.8.4..18...66...27.41......1...6.8.1.72.7..42.6..462.8....39......81......7 | autosolve |
| 123456789457189236698327541284763195365891472971542368546278913739615824812934657 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) G1: 2,7 G2: 2,7 D4: 6,7 E4: 6,7 A7: 5,7 C9: 2,5 F8: 4,5 I8: 4,8 G9: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,C1: 1.. / A1 = 1 => 10 pairs (_) / C1 = 1 => 8 pairs (_) A6,C6: 1.. / A6 = 1 => 8 pairs (_) / C6 = 1 => 10 pairs (_) E7,E8: 1.. / E7 = 1 => 12 pairs (_) / E8 = 1 => 10 pairs (_) H7,H8: 1.. / H7 = 1 => 10 pairs (_) / H8 = 1 => 12 pairs (_) E7,H7: 1.. / E7 = 1 => 12 pairs (_) / H7 = 1 => 10 pairs (_) E8,H8: 1.. / E8 = 1 => 10 pairs (_) / H8 = 1 => 12 pairs (_) A1,A6: 1.. / A1 = 1 => 10 pairs (_) / A6 = 1 => 8 pairs (_) C1,C6: 1.. / C1 = 1 => 8 pairs (_) / C6 = 1 => 10 pairs (_) G1,G2: 2.. / G1 = 2 => 9 pairs (_) / G2 = 2 => 8 pairs (_) A8,C9: 2.. / A8 = 2 => 14 pairs (_) / C9 = 2 => 10 pairs (_) H8,H9: 2.. / H8 = 2 => 10 pairs (_) / H9 = 2 => 14 pairs (_) A8,H8: 2.. / A8 = 2 => 14 pairs (_) / H8 = 2 => 10 pairs (_) C9,H9: 2.. / C9 = 2 => 10 pairs (_) / H9 = 2 => 14 pairs (_) C4,C5: 4.. / C4 = 4 => 16 pairs (_) / C5 = 4 => 9 pairs (_) I4,G5: 4.. / I4 = 4 => 9 pairs (_) / G5 = 4 => 16 pairs (_) F8,F9: 4.. / F8 = 4 => 7 pairs (_) / F9 = 4 => 17 pairs (_) C4,I4: 4.. / C4 = 4 => 16 pairs (_) / I4 = 4 => 9 pairs (_) C5,G5: 4.. / C5 = 4 => 9 pairs (_) / G5 = 4 => 16 pairs (_) F9,G9: 4.. / F9 = 4 => 17 pairs (_) / G9 = 4 => 7 pairs (_) I4,I8: 4.. / I4 = 4 => 9 pairs (_) / I8 = 4 => 16 pairs (_) D4,E4: 6.. / D4 = 6 => 7 pairs (_) / E4 = 6 => 14 pairs (_) G8,G9: 6.. / G8 = 6 => 7 pairs (_) / G9 = 6 => 17 pairs (_) C1,C2: 7.. / C1 = 7 => 9 pairs (_) / C2 = 7 => 8 pairs (_) G1,G2: 7.. / G1 = 7 => 8 pairs (_) / G2 = 7 => 9 pairs (_) D4,E4: 7.. / D4 = 7 => 14 pairs (_) / E4 = 7 => 7 pairs (_) A7,A8: 7.. / A7 = 7 => 9 pairs (_) / A8 = 7 => 12 pairs (_) C1,G1: 7.. / C1 = 7 => 9 pairs (_) / G1 = 7 => 8 pairs (_) C2,G2: 7.. / C2 = 7 => 8 pairs (_) / G2 = 7 => 9 pairs (_) A7,E7: 7.. / A7 = 7 => 9 pairs (_) / E7 = 7 => 12 pairs (_) D4,D8: 7.. / D4 = 7 => 14 pairs (_) / D8 = 7 => 7 pairs (_) B3,C3: 8.. / B3 = 8 => 12 pairs (_) / C3 = 8 => 12 pairs (_) G8,I8: 8.. / G8 = 8 => 16 pairs (_) / I8 = 8 => 9 pairs (_) B3,B4: 8.. / B3 = 8 => 12 pairs (_) / B4 = 8 => 12 pairs (_) G6,G8: 8.. / G6 = 8 => 9 pairs (_) / G8 = 8 => 16 pairs (_) * DURATION: 0:00:10.636129 START: 22:20:41.700808 END: 22:20:52.336937 2025-04-06 * CP COUNT: (34) * INCONCLUSIVE -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,C9,D4,E4,F8,G1,G2,G9,I8) * ...4.6.8.4..18...66...27.41......1...6.8.1.72.7..42.6..462.8....39......81......7 * PAIR G1: 2,7 ROW 1 C1: 2,7,1,3,5 # reduction candidate for 2,7 C1: 2,7 # 12 pairs C1: 1,3,5 # 8 pairs * PAIR G2: 2,7 ROW 2 C2: 2,7,3,5 # reduction candidate for 2,7 C2: 3,5 # 11 pairs C2: 2,7 # 11 pairs * PAIR D4: 6,7 COL D D8: 6,7,5 # reduction candidate for 6,7 D8: 5 # 13 pairs D8: 6,7 # 10 pairs * PAIR E4: 6,7 COL E E8: 6,7,1,5 # reduction candidate for 6,7 E8: 6,7 # 14 pairs E8: 1,5 # 10 pairs * PAIR A7: 5,7 BLK 7 A8: 5,7,2 # reduction candidate for 5,7 A8: 2 # 14 pairs A8: 5,7 # 10 pairs * PAIR A7: 5,7 ROW 7 E7: 5,7,1,3,9 # reduction candidate for 5,7 E7: 5,7 # 16 pairs E7: 1,3,9 # 10 pairs * PAIR C9: 2,5 BLK 7 A8: 2,5,7 # reduction candidate for 2,5 A8: 7 # 12 pairs A8: 2,5 # 9 pairs * PAIR C9: 2,5 ROW 9 H9: 2,5,3,9 # reduction candidate for 2,5 H9: 2,5 # 10 pairs H9: 3,9 # 5 pairs * PAIR C9: 2,5 COL C C1: 2,5,1,3,7 # reduction candidate for 2,5 C1: 2,5 # 12 pairs C2: 2,5,3,7 # reduction candidate for 2,5 C2: 2,5 # 12 pairs C4: 2,5,3,4,8 # reduction candidate for 2,5 C4: 2,5 # 14 pairs * PAIR F8: 4,5 BLK 8 F9: 4,5,3,9 # reduction candidate for 4,5 F9: 4,5 # 14 pairs F9: 3,9 # 8 pairs * PAIR I8: 4,8 BLK 9 G8: 4,8,6 # reduction candidate for 4,8 G8: 4,8 # 17 pairs G8: 6 # 7 pairs * PAIR I8: 4,8 COL I I4: 4,8,3,5,9 # reduction candidate for 4,8 I4: 3,5,9 => SOLVED * 123456789457189236698327541284763195365891472971542368546278913739615824812934657 I4: 4,8 # 10 pairs * PAIR G9: 4,6 BLK 9 G8: 4,6,8 # reduction candidate for 4,6 G8: 8 # 16 pairs G8: 4,6 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-mith-te3-00147741-base-pr-000.dot * REASONING * PRF # I4: 3,5,9 => SOL * CNT 1 HDP CHAINS / 27 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,C9,D4,E4,F8,G1,G2,G9,I8) * ...4.6.8.4..18...66...27.41......1...6.8.1.72.7..42.6..462.8....39......81......7 * PAIR G1: 2,7 ROW 1 C1: 2,7,1,3,5 # reduction candidate for 2,7 C1: 2,7 # 12 pairs C1: 1,3,5 # 8 pairs * PAIR G2: 2,7 ROW 2 C2: 2,7,3,5 # reduction candidate for 2,7 C2: 3,5 # 11 pairs C2: 2,7 # 11 pairs * PAIR D4: 6,7 COL D D8: 6,7,5 # reduction candidate for 6,7 D8: 5 # 13 pairs D8: 6,7 # 10 pairs * PAIR E4: 6,7 COL E E8: 6,7,1,5 # reduction candidate for 6,7 E8: 6,7 # 14 pairs E8: 1,5 # 10 pairs * PAIR A7: 5,7 BLK 7 A8: 5,7,2 # reduction candidate for 5,7 A8: 2 # 14 pairs A8: 5,7 # 10 pairs * PAIR A7: 5,7 ROW 7 E7: 5,7,1,3,9 # reduction candidate for 5,7 E7: 5,7 # 16 pairs E7: 1,3,9 # 10 pairs * PAIR C9: 2,5 BLK 7 A8: 2,5,7 # reduction candidate for 2,5 A8: 7 # 12 pairs A8: 2,5 # 9 pairs * PAIR C9: 2,5 ROW 9 H9: 2,5,3,9 # reduction candidate for 2,5 H9: 2,5 # 10 pairs H9: 3,9 # 5 pairs * PAIR C9: 2,5 COL C C1: 2,5,1,3,7 # reduction candidate for 2,5 C1: 2,5 # 12 pairs C2: 2,5,3,7 # reduction candidate for 2,5 C2: 2,5 # 12 pairs C4: 2,5,3,4,8 # reduction candidate for 2,5 C4: 2,5 # 14 pairs * PAIR F8: 4,5 BLK 8 F9: 4,5,3,9 # reduction candidate for 4,5 F9: 4,5 # 14 pairs F9: 3,9 # 8 pairs * PAIR I8: 4,8 BLK 9 G8: 4,8,6 # reduction candidate for 4,8 G8: 4,8 # 17 pairs G8: 6 # 7 pairs * PAIR I8: 4,8 COL I I4: 4,8,3,5,9 # reduction candidate for 4,8 I4: 3,5,9 => SOLVED * 123456789457189236698327541284763195365891472971542368546278913739615824812934657 * DURATION: 0:00:04.619922 START: 22:20:57.295102 END: 22:21:01.915024 2025-04-06 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00147741-base-pr-001.dot * REASONING * PRF # I4: 3,5,9 => SOL * STA I4: 3,5,9 * CNT 1 HDP CHAINS / 25 HYP OPENED
Header Info
rating: 39622; r2: 748057; index: 147741
Solution
position: 123456789457189236698327541284763195365891472971542368546278913739615824812934657 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 # C1: 2,7 => UNS * INC # C1: 1,3,5 => UNS * INC # C2: 2,7 => UNS * INC # C2: 3,5 => UNS * INC # D8: 6,7 => UNS * INC # D8: 5 => UNS * INC # E8: 6,7 => UNS * INC # E8: 1,5 => UNS * INC # A8: 5,7 => UNS * INC # A8: 2 => UNS * INC # E7: 5,7 => UNS * INC # E7: 1,3,9 => UNS * INC # A8: 2,5 => UNS * INC # A8: 7 => UNS * INC # H9: 2,5 => UNS * INC # H9: 3,9 => UNS * INC # C1: 2,5 => UNS * INC # C2: 2,5 => UNS * INC # C4: 2,5 => UNS * INC # F9: 4,5 => UNS * INC # F9: 3,9 => UNS * INC # G8: 4,8 => UNS * INC # G8: 6 => UNS * INC # I4: 4,8 => UNS * PRF # I4: 3,5,9 => SOL * INC # G8: 4,6 => UNS * INC # G8: 8 => UNS * CNT 27 HDP CHAINS / 27 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 2,7 => UNS * INC # C1: 1,3,5 => UNS * INC # C2: 2,7 => UNS * INC # C2: 3,5 => UNS * INC # D8: 6,7 => UNS * INC # D8: 5 => UNS * INC # E8: 6,7 => UNS * INC # E8: 1,5 => UNS * INC # A8: 5,7 => UNS * INC # A8: 2 => UNS * INC # E7: 5,7 => UNS * INC # E7: 1,3,9 => UNS * INC # A8: 2,5 => UNS * INC # A8: 7 => UNS * INC # H9: 2,5 => UNS * INC # H9: 3,9 => UNS * INC # C1: 2,5 => UNS * INC # C2: 2,5 => UNS * INC # C4: 2,5 => UNS * INC # F9: 4,5 => UNS * INC # F9: 3,9 => UNS * INC # G8: 4,8 => UNS * INC # G8: 6 => UNS * INC # I4: 4,8 => UNS * PRF # I4: 3,5,9 => SOL * STA I4: 3,5,9 * CNT 25 HDP CHAINS / 25 HYP OPENED