Analysis of xx-mith-te3-00086122-base.sdk
Contents
Original Sudoku
level: hard
position: .2..56.8..5678..2...8..........75..6.7....3...81...475.6..17......62...1.125.8..7 initial
Autosolve
position: 12..5678..5678.12.7.8..........75..6.7....3...81...475.6..17.....762...1.125.8..7 autosolve
Pair Reduction Variants
Deep Pair Reduction
Time used: 0:00:09.965109
The following important HDP chains were detected:
* PRF # D4: 1,2 # A7: 3,4 => SOL * STA # D4: 1,2 + A7: 3,4 * CNT 1 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2..56.8..5678..2...8..........75..6.7....3...81...475.6..17......62...1.125.8..7 | initial |
| 12..5678..5678.12.7.8..........75..6.7....3...81...475.6..17.....762...1.125.8..7 | autosolve |
| 123456789456789123798231564234175896579864312681392475365917248847623951912548637 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (10) D3: 1,2 F3: 1,2 G3: 5,6 H3: 5,6 G4: 2,8 H4: 1,9 H5: 1,9 I5: 2,8 I7: 2,8 G9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D3,F3: 1.. / D3 = 1 => 9 pairs (_) / F3 = 1 => 12 pairs (_) H4,H5: 1.. / H4 = 1 => 10 pairs (_) / H5 = 1 => 11 pairs (_) D4,H4: 1.. / D4 = 1 => 11 pairs (_) / H4 = 1 => 10 pairs (_) F3,F5: 1.. / F3 = 1 => 12 pairs (_) / F5 = 1 => 9 pairs (_) D3,F3: 2.. / D3 = 2 => 12 pairs (_) / F3 = 2 => 9 pairs (_) G4,I5: 2.. / G4 = 2 => 10 pairs (_) / I5 = 2 => 9 pairs (_) G7,I7: 2.. / G7 = 2 => 9 pairs (_) / I7 = 2 => 10 pairs (_) G4,G7: 2.. / G4 = 2 => 10 pairs (_) / G7 = 2 => 9 pairs (_) I5,I7: 2.. / I5 = 2 => 9 pairs (_) / I7 = 2 => 10 pairs (_) G3,H3: 5.. / G3 = 5 => 9 pairs (_) / H3 = 5 => 13 pairs (_) A5,C5: 5.. / A5 = 5 => 13 pairs (_) / C5 = 5 => 12 pairs (_) C5,C7: 5.. / C5 = 5 => 12 pairs (_) / C7 = 5 => 13 pairs (_) G3,H3: 6.. / G3 = 6 => 13 pairs (_) / H3 = 6 => 9 pairs (_) A5,A6: 6.. / A5 = 6 => 13 pairs (_) / A6 = 6 => 12 pairs (_) E5,E6: 6.. / E5 = 6 => 12 pairs (_) / E6 = 6 => 13 pairs (_) G9,H9: 6.. / G9 = 6 => 9 pairs (_) / H9 = 6 => 13 pairs (_) A5,E5: 6.. / A5 = 6 => 13 pairs (_) / E5 = 6 => 12 pairs (_) A6,E6: 6.. / A6 = 6 => 12 pairs (_) / E6 = 6 => 13 pairs (_) G3,G9: 6.. / G3 = 6 => 13 pairs (_) / G9 = 6 => 9 pairs (_) H3,H9: 6.. / H3 = 6 => 9 pairs (_) / H9 = 6 => 13 pairs (_) D4,D5: 8.. / D4 = 8 => 10 pairs (_) / D5 = 8 => 9 pairs (_) G4,I5: 8.. / G4 = 8 => 9 pairs (_) / I5 = 8 => 10 pairs (_) A7,A8: 8.. / A7 = 8 => 10 pairs (_) / A8 = 8 => 13 pairs (_) D4,G4: 8.. / D4 = 8 => 10 pairs (_) / G4 = 8 => 9 pairs (_) D5,I5: 8.. / D5 = 8 => 9 pairs (_) / I5 = 8 => 10 pairs (_) A8,G8: 8.. / A8 = 8 => 13 pairs (_) / G8 = 8 => 10 pairs (_) I5,I7: 8.. / I5 = 8 => 10 pairs (_) / I7 = 8 => 9 pairs (_) H4,H5: 9.. / H4 = 9 => 11 pairs (_) / H5 = 9 => 10 pairs (_) * DURATION: 0:00:10.255111 START: 22:14:42.666175 END: 22:14:52.921286 2025-04-04 * CP COUNT: (28) * INCONCLUSIVE * DEEP PAIR REDUCTION * DURATION: 0:00:09.839773 START: 22:14:59.704480 END: 22:15:09.544253 2025-04-04 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00086122-base-pr-002.dot * REASONING * PRF # D4: 1,2 # A7: 3,4 => SOL * STA # D4: 1,2 + A7: 3,4 * CNT 1 HDP CHAINS / 30 HYP OPENED
Header Info
rating: 21532; r2: 472228; index: 86122
Solution
position: 123456789456789123798231564234175896579864312681392475365917248847623951912548637 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 # D4: 1,2 => UNS * INC # D5: 1,2 => UNS * INC # F5: 1,2 => UNS * INC # F5: 4,9 => UNS * INC # D4: 2,8 => UNS * INC # D4: 1,3,4,9 => UNS * INC # G7: 2,8 => UNS * INC # G7: 5,9 => UNS * INC # D4: 1,9 => UNS * INC # D4: 2,3,4,8 => UNS * INC # D5: 1,9 => UNS * INC # F5: 1,9 => UNS * INC # D5: 2,8 => UNS * INC # D5: 1,4,9 => UNS * INC # G7: 2,8 => UNS * INC # G7: 5,9 => UNS * CNT 16 HDP CHAINS / 16 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D4: 1,2 => UNS * INC # D5: 1,2 => UNS * INC # F5: 1,2 => UNS * INC # F5: 4,9 => UNS * INC # D4: 2,8 => UNS * INC # D4: 1,3,4,9 => UNS * INC # G7: 2,8 => UNS * INC # G7: 5,9 => UNS * INC # D4: 1,9 => UNS * INC # D4: 2,3,4,8 => UNS * INC # D5: 1,9 => UNS * INC # F5: 1,9 => UNS * INC # D5: 2,8 => UNS * INC # D5: 1,4,9 => UNS * INC # G7: 2,8 => UNS * INC # G7: 5,9 => UNS * CNT 16 HDP CHAINS / 16 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # D4: 1,2 => UNS * INC # D5: 1,2 => UNS * INC # F5: 1,2 => UNS * INC # F5: 4,9 => UNS * INC # D4: 2,8 => UNS * INC # D4: 1,3,4,9 => UNS * INC # G7: 2,8 => UNS * INC # G7: 5,9 => UNS * INC # D4: 1,9 => UNS * INC # D4: 2,3,4,8 => UNS * INC # D5: 1,9 => UNS * INC # F5: 1,9 => UNS * INC # D5: 2,8 => UNS * INC # D5: 1,4,9 => UNS * INC # G7: 2,8 => UNS * INC # G7: 5,9 => UNS * INC # D4: 1,2 # A5: 5,9 => UNS * INC # D4: 1,2 # A5: 6 => UNS * INC # D4: 1,2 # C7: 5,9 => UNS * INC # D4: 1,2 # C7: 3,4 => UNS * INC # D4: 1,2 # E6: 3,9 => UNS * INC # D4: 1,2 # F6: 3,9 => UNS * INC # D4: 1,2 # D1: 3,9 => UNS * INC # D4: 1,2 # D7: 3,9 => UNS * INC # D4: 1,2 # F5: 1,9 => UNS * INC # D4: 1,2 # F5: 4 => UNS * INC # D4: 1,2 # H8: 3,4 => UNS * INC # D4: 1,2 # H9: 3,4 => UNS * PRF # D4: 1,2 # A7: 3,4 => SOL * STA # D4: 1,2 + A7: 3,4 * CNT 29 HDP CHAINS / 30 HYP OPENED