Analysis of xx-mith-te3-00111178-base.sdk
Contents
Original Sudoku
level: hard
position: .234.....45.78....7.........14....98...94.61......1......69.84.6...7.9.19..1...76 initial
Autosolve
position: .234.....45.78....7.........14.67.98...94.61......1......69.84.6...7.9.19..1...76 autosolve
Pair Reduction Variants
Deep Pair Reduction
Time used: 0:00:23.130027
The following important HDP chains were detected:
* DIS # E3: 1,5 # H3: 2,3 => CTR => H3: 5,6,8 * PRF # E3: 1,5 + H3: 5,6,8 # D6: 2,3 => SOL * STA # E3: 1,5 + H3: 5,6,8 + D6: 2,3 * CNT 2 HDP CHAINS / 102 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .234.....45.78....7.........14....98...94.61......1......69.84.6...7.9.19..1...76 | initial |
| .234.....45.78....7.........14.67.98...94.61......1......69.84.6...7.9.19..1...76 | autosolve |
| 123456789456789123798213564214567398537948612869321457371692845642875931985134276 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (8) A1: 1,8 B3: 6,9 E1: 1,5 B6: 6,9 C6: 6,9 G6: 4,7 I6: 4,7 B7: 3,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,E3: 1.. / E1 = 1 => 12 pairs (_) / E3 = 1 => 14 pairs (_) A7,C7: 1.. / A7 = 1 => 12 pairs (_) / C7 = 1 => 19 pairs (_) C2,G2: 1.. / C2 = 1 => 19 pairs (_) / G2 = 1 => 11 pairs (_) A1,A7: 1.. / A1 = 1 => 19 pairs (_) / A7 = 1 => 12 pairs (_) G3,I3: 4.. / G3 = 4 => 11 pairs (_) / I3 = 4 => 7 pairs (_) G6,I6: 4.. / G6 = 4 => 7 pairs (_) / I6 = 4 => 11 pairs (_) B8,B9: 4.. / B8 = 4 => 10 pairs (_) / B9 = 4 => 9 pairs (_) F8,F9: 4.. / F8 = 4 => 9 pairs (_) / F9 = 4 => 10 pairs (_) B8,F8: 4.. / B8 = 4 => 10 pairs (_) / F8 = 4 => 9 pairs (_) B9,F9: 4.. / B9 = 4 => 9 pairs (_) / F9 = 4 => 10 pairs (_) G3,G6: 4.. / G3 = 4 => 11 pairs (_) / G6 = 4 => 7 pairs (_) I3,I6: 4.. / I3 = 4 => 7 pairs (_) / I6 = 4 => 11 pairs (_) B6,C6: 6.. / B6 = 6 => 6 pairs (_) / C6 = 6 => 6 pairs (_) F1,H1: 6.. / F1 = 6 => 8 pairs (_) / H1 = 6 => 13 pairs (_) B3,B6: 6.. / B3 = 6 => 6 pairs (_) / B6 = 6 => 6 pairs (_) G1,I1: 7.. / G1 = 7 => 7 pairs (_) / I1 = 7 => 11 pairs (_) B5,C5: 7.. / B5 = 7 => 15 pairs (_) / C5 = 7 => 9 pairs (_) G6,I6: 7.. / G6 = 7 => 11 pairs (_) / I6 = 7 => 7 pairs (_) B7,C7: 7.. / B7 = 7 => 9 pairs (_) / C7 = 7 => 15 pairs (_) B5,B7: 7.. / B5 = 7 => 15 pairs (_) / B7 = 7 => 9 pairs (_) C5,C7: 7.. / C5 = 7 => 9 pairs (_) / C7 = 7 => 15 pairs (_) G1,G6: 7.. / G1 = 7 => 7 pairs (_) / G6 = 7 => 11 pairs (_) I1,I6: 7.. / I1 = 7 => 11 pairs (_) / I6 = 7 => 7 pairs (_) A1,C3: 8.. / A1 = 8 => 12 pairs (_) / C3 = 8 => 19 pairs (_) H1,H3: 8.. / H1 = 8 => 19 pairs (_) / H3 = 8 => 12 pairs (_) F5,D6: 8.. / F5 = 8 => 17 pairs (_) / D6 = 8 => 10 pairs (_) A1,H1: 8.. / A1 = 8 => 12 pairs (_) / H1 = 8 => 19 pairs (_) C3,H3: 8.. / C3 = 8 => 19 pairs (_) / H3 = 8 => 12 pairs (_) A6,D6: 8.. / A6 = 8 => 17 pairs (_) / D6 = 8 => 10 pairs (_) D6,D8: 8.. / D6 = 8 => 10 pairs (_) / D8 = 8 => 17 pairs (_) B6,C6: 9.. / B6 = 9 => 6 pairs (_) / C6 = 9 => 6 pairs (_) F1,I1: 9.. / F1 = 9 => 13 pairs (_) / I1 = 9 => 8 pairs (_) B3,B6: 9.. / B3 = 9 => 6 pairs (_) / B6 = 9 => 6 pairs (_) * DURATION: 0:00:10.314918 START: 17:25:20.410748 END: 17:25:30.725666 2025-04-06 * CP COUNT: (33) * INCONCLUSIVE * DEEP PAIR REDUCTION * DURATION: 0:00:22.791587 START: 17:25:35.548591 END: 17:25:58.340178 2025-04-06 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00111178-base-pr-002.dot * REASONING * DIS # E3: 1,5 # H3: 2,3 => CTR => H3: 5,6,8 * PRF # E3: 1,5 + H3: 5,6,8 # D6: 2,3 => SOL * STA # E3: 1,5 + H3: 5,6,8 + D6: 2,3 * CNT 2 HDP CHAINS / 102 HYP OPENED
Header Info
rating: 28318; r2: 540029; index: 111178
Solution
position: 123456789456789123798213564214567398537948612869321457371692845642875931985134276 solved
See section Deep 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 # C3: 1,8 => UNS * INC # C3: 6,9 => UNS * INC # C2: 6,9 => UNS * INC # C3: 6,9 => UNS * INC # F3: 6,9 => UNS * INC # F3: 2,3,5 => UNS * INC # E3: 1,5 => UNS * INC # E3: 2,3 => UNS * INC # G1: 1,5 => UNS * INC # G1: 7 => UNS * INC # C2: 6,9 => UNS * INC # C3: 6,9 => UNS * INC # B5: 3,7 => UNS * INC # B5: 8 => UNS * CNT 14 HDP CHAINS / 14 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C3: 1,8 => UNS * INC # C3: 6,9 => UNS * INC # C2: 6,9 => UNS * INC # C3: 6,9 => UNS * INC # F3: 6,9 => UNS * INC # F3: 2,3,5 => UNS * INC # E3: 1,5 => UNS * INC # E3: 2,3 => UNS * INC # G1: 1,5 => UNS * INC # G1: 7 => UNS * INC # C2: 6,9 => UNS * INC # C3: 6,9 => UNS * INC # B5: 3,7 => UNS * INC # B5: 8 => UNS * CNT 14 HDP CHAINS / 14 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # C3: 1,8 => UNS * INC # C3: 6,9 => UNS * INC # C2: 6,9 => UNS * INC # C3: 6,9 => UNS * INC # F3: 6,9 => UNS * INC # F3: 2,3,5 => UNS * INC # E3: 1,5 => UNS * INC # E3: 2,3 => UNS * INC # G1: 1,5 => UNS * INC # G1: 7 => UNS * INC # C2: 6,9 => UNS * INC # C3: 6,9 => UNS * INC # B5: 3,7 => UNS * INC # B5: 8 => UNS * INC # C3: 1,8 # F2: 6,9 => UNS * INC # C3: 1,8 # F2: 2,3 => UNS * INC # C3: 1,8 # F3: 6,9 => UNS * INC # C3: 1,8 # F3: 2,3,5 => UNS * INC # C3: 1,8 # E3: 1,5 => UNS * INC # C3: 1,8 # E3: 2,3 => UNS * INC # C3: 1,8 # I1: 5,7 => UNS * INC # C3: 1,8 # I1: 9 => UNS * INC # C3: 1,8 # B5: 3,7 => UNS * INC # C3: 1,8 # B5: 8 => UNS * INC # C3: 1,8 => UNS * INC # C3: 6,9 # E3: 1,5 => UNS * INC # C3: 6,9 # E3: 2,3 => UNS * INC # C3: 6,9 # H2: 2,3 => UNS * INC # C3: 6,9 # I2: 2,3 => UNS * INC # C3: 6,9 # G4: 2,3 => UNS * INC # C3: 6,9 # G9: 2,3 => UNS * INC # C3: 6,9 # B8: 4,8 => UNS * INC # C3: 6,9 # B8: 3 => UNS * INC # C3: 6,9 # B9: 4,8 => UNS * INC # C3: 6,9 # B9: 3 => UNS * INC # C3: 6,9 => UNS * INC # C2: 6,9 # F2: 6,9 => UNS * INC # C2: 6,9 # F2: 2,3 => UNS * INC # C2: 6,9 # F3: 6,9 => UNS * INC # C2: 6,9 # F3: 2,3,5 => UNS * INC # C2: 6,9 # E3: 1,5 => UNS * INC # C2: 6,9 # E3: 2,3 => UNS * INC # C2: 6,9 # I1: 5,7 => UNS * INC # C2: 6,9 # I1: 9 => UNS * INC # C2: 6,9 # B5: 3,7 => UNS * INC # C2: 6,9 # B5: 8 => UNS * INC # C2: 6,9 => UNS * INC # C3: 6,9 # E3: 1,5 => UNS * INC # C3: 6,9 # E3: 2,3 => UNS * INC # C3: 6,9 # H2: 2,3 => UNS * INC # C3: 6,9 # I2: 2,3 => UNS * INC # C3: 6,9 # G4: 2,3 => UNS * INC # C3: 6,9 # G9: 2,3 => UNS * INC # C3: 6,9 # B8: 4,8 => UNS * INC # C3: 6,9 # B8: 3 => UNS * INC # C3: 6,9 # B9: 4,8 => UNS * INC # C3: 6,9 # B9: 3 => UNS * INC # C3: 6,9 => UNS * INC # F3: 6,9 # F2: 6,9 => UNS * INC # F3: 6,9 # F2: 2,3 => UNS * INC # F3: 6,9 # E3: 1,5 => UNS * INC # F3: 6,9 # E3: 2,3 => UNS * INC # F3: 6,9 # F1: 6,9 => UNS * INC # F3: 6,9 # F2: 6,9 => UNS * INC # F3: 6,9 # I1: 5,7 => UNS * INC # F3: 6,9 # I1: 9 => UNS * INC # F3: 6,9 # B5: 3,7 => UNS * INC # F3: 6,9 # B5: 8 => UNS * INC # F3: 6,9 => UNS * INC # F3: 2,3,5 # C3: 1,8 => UNS * INC # F3: 2,3,5 # C3: 6,9 => UNS * INC # F3: 2,3,5 # C2: 6,9 => UNS * INC # F3: 2,3,5 # C3: 6,9 => UNS * INC # F3: 2,3,5 # E3: 1,5 => UNS * INC # F3: 2,3,5 # E3: 2,3 => UNS * INC # F3: 2,3,5 # G1: 1,5 => UNS * INC # F3: 2,3,5 # G1: 7 => UNS * INC # F3: 2,3,5 # C2: 6,9 => UNS * INC # F3: 2,3,5 # C2: 1 => UNS * INC # F3: 2,3,5 # C2: 6,9 => UNS * INC # F3: 2,3,5 # C3: 6,9 => UNS * INC # F3: 2,3,5 # B5: 3,7 => UNS * INC # F3: 2,3,5 # B5: 8 => UNS * INC # F3: 2,3,5 => UNS * INC # E3: 1,5 # C3: 1,8 => UNS * INC # E3: 1,5 # C3: 6,9 => UNS * INC # E3: 1,5 # C2: 6,9 => UNS * INC # E3: 1,5 # C3: 6,9 => UNS * INC # E3: 1,5 # F3: 6,9 => UNS * INC # E3: 1,5 # F3: 2,3 => UNS * INC # E3: 1,5 # G1: 1,5 => UNS * INC # E3: 1,5 # G1: 7 => UNS * INC # E3: 1,5 # F2: 6,9 => UNS * INC # E3: 1,5 # F3: 6,9 => UNS * INC # E3: 1,5 # F2: 2,3 => UNS * INC # E3: 1,5 # F3: 2,3 => UNS * INC # E3: 1,5 # G3: 2,3 => UNS * DIS # E3: 1,5 # H3: 2,3 => CTR => H3: 5,6,8 * INC # E3: 1,5 + H3: 5,6,8 # I3: 2,3 => UNS * INC # E3: 1,5 + H3: 5,6,8 # D4: 2,3 => UNS * PRF # E3: 1,5 + H3: 5,6,8 # D6: 2,3 => SOL * STA # E3: 1,5 + H3: 5,6,8 + D6: 2,3 * CNT 101 HDP CHAINS / 102 HYP OPENED