Analysis of xx-ph-02237081-2019_01_07-base.sdk
Contents
Original Sudoku
level: hard
position: 9876.....5...4.8.........6.84..3...6..6...53....2..4..63..8..5..5...9.....1.....8 initial
Autosolve
position: 9876.....56..4.8.........6.84..3...6..6...53....2..48.63..8..5..58..9.....1.....8 autosolve
Pair Reduction Variants
Deep Pair Reduction
Time used: 0:00:38.007390
The following important HDP chains were detected:
* DIS # C3: 2,3 # G4: 7,9 => CTR => G4: 1,2 * DIS # C3: 2,3 + G4: 1,2 # H4: 1,2 => CTR => H4: 7,9 * DIS # C3: 2,3 + G4: 1,2 + H4: 7,9 # I2: 7,9 => CTR => I2: 2,3 * DIS # C3: 2,3 + G4: 1,2 + H4: 7,9 + I2: 2,3 # I3: 7,9 => CTR => I3: 2,3,5 * PRF # C3: 2,3 + G4: 1,2 + H4: 7,9 + I2: 2,3 + I3: 2,3,5 => SOL * STA C3: 2,3 * CNT 5 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 9876.....5...4.8.........6.84..3...6..6...53....2..4..63..8..5..5...9.....1.....8 | initial |
| 9876.....56..4.8.........6.84..3...6..6...53....2..48.63..8..5..58..9.....1.....8 | autosolve |
| 987625314563941872412378965845137296126894537379256481634782159758419623291563748 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (4) C2: 2,3 B3: 1,2 D5: 4,8 F5: 4,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A3,B3: 1.. / A3 = 1 => 6 pairs (_) / B3 = 1 => 4 pairs (_) A6,C6: 3.. / A6 = 3 => 5 pairs (_) / C6 = 3 => 8 pairs (_) A3,A6: 3.. / A3 = 3 => 8 pairs (_) / A6 = 3 => 5 pairs (_) A3,C3: 4.. / A3 = 4 => 12 pairs (_) / C3 = 4 => 5 pairs (_) H1,I1: 4.. / H1 = 4 => 4 pairs (_) / I1 = 4 => 5 pairs (_) D5,F5: 4.. / D5 = 4 => 3 pairs (_) / F5 = 4 => 2 pairs (_) C3,C7: 4.. / C3 = 4 => 5 pairs (_) / C7 = 4 => 12 pairs (_) I1,I3: 5.. / I1 = 5 => 5 pairs (_) / I3 = 5 => 4 pairs (_) C4,C6: 5.. / C4 = 5 => 8 pairs (_) / C6 = 5 => 5 pairs (_) E6,F6: 6.. / E6 = 6 => 4 pairs (_) / F6 = 6 => 4 pairs (_) G8,G9: 6.. / G8 = 6 => 4 pairs (_) / G9 = 6 => 4 pairs (_) E8,G8: 6.. / E8 = 6 => 4 pairs (_) / G8 = 6 => 4 pairs (_) F6,F9: 6.. / F6 = 6 => 4 pairs (_) / F9 = 6 => 4 pairs (_) D3,F3: 8.. / D3 = 8 => 3 pairs (_) / F3 = 8 => 2 pairs (_) D5,F5: 8.. / D5 = 8 => 2 pairs (_) / F5 = 8 => 3 pairs (_) D3,D5: 8.. / D3 = 8 => 3 pairs (_) / D5 = 8 => 2 pairs (_) F3,F5: 8.. / F3 = 8 => 2 pairs (_) / F5 = 8 => 3 pairs (_) C7,B9: 9.. / C7 = 9 => 7 pairs (_) / B9 = 9 => 9 pairs (_) * DURATION: 0:00:15.614801 START: 16:30:06.618414 END: 16:30:22.233215 2020-10-10 * CP COUNT: (18) * INCONCLUSIVE * DEEP PAIR REDUCTION * DURATION: 0:00:37.703349 START: 16:30:30.483591 END: 16:31:08.186940 2020-10-10 * SOLUTION FOUND * SAVE PR GRAPH xx-ph-02237081-2019_01_07-base-pr-002.dot * REASONING * DIS # C3: 2,3 # G4: 7,9 => CTR => G4: 1,2 * DIS # C3: 2,3 + G4: 1,2 # H4: 1,2 => CTR => H4: 7,9 * DIS # C3: 2,3 + G4: 1,2 + H4: 7,9 # I2: 7,9 => CTR => I2: 2,3 * DIS # C3: 2,3 + G4: 1,2 + H4: 7,9 + I2: 2,3 # I3: 7,9 => CTR => I3: 2,3,5 * PRF # C3: 2,3 + G4: 1,2 + H4: 7,9 + I2: 2,3 + I3: 2,3,5 => SOL * STA C3: 2,3 * CNT 5 HDP CHAINS / 46 HYP OPENED
Header Info
2237081;2019_01_07;PAQ;25;11.50;1.20;1.20
Solution
position: 987625314563941872412378965845137296126894537379256481634782159758419623291563748 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 # A3: 2,3 => UNS * INC # C3: 2,3 => UNS * INC # F2: 2,3 => UNS * INC # I2: 2,3 => UNS * INC # A3: 1,2 => UNS * INC # A3: 3,4 => UNS * INC # B5: 1,2 => UNS * INC # B5: 7,9 => UNS * CNT 8 HDP CHAINS / 8 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 2,3 => UNS * INC # C3: 2,3 => UNS * INC # F2: 2,3 => UNS * INC # I2: 2,3 => UNS * INC # A3: 1,2 => UNS * INC # A3: 3,4 => UNS * INC # B5: 1,2 => UNS * INC # B5: 7,9 => UNS * CNT 8 HDP CHAINS / 8 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 2,3 => UNS * INC # C3: 2,3 => UNS * INC # F2: 2,3 => UNS * INC # I2: 2,3 => UNS * INC # A3: 1,2 => UNS * INC # A3: 3,4 => UNS * INC # B5: 1,2 => UNS * INC # B5: 7,9 => UNS * INC # A3: 2,3 # F2: 2,3 => UNS * INC # A3: 2,3 # I2: 2,3 => UNS * INC # A3: 2,3 # F3: 2,3 => UNS * INC # A3: 2,3 # G3: 2,3 => UNS * INC # A3: 2,3 # I3: 2,3 => UNS * INC # A3: 2,3 # B5: 7,9 => UNS * INC # A3: 2,3 # B5: 2 => UNS * INC # A3: 2,3 # E6: 7,9 => UNS * INC # A3: 2,3 # I6: 7,9 => UNS * INC # A3: 2,3 # B9: 7,9 => UNS * INC # A3: 2,3 # B9: 2 => UNS * INC # A3: 2,3 # B9: 2,9 => UNS * INC # A3: 2,3 # B9: 7 => UNS * INC # A3: 2,3 # G7: 2,9 => UNS * INC # A3: 2,3 # I7: 2,9 => UNS * INC # A3: 2,3 # C4: 2,9 => UNS * INC # A3: 2,3 # C4: 5 => UNS * INC # A3: 2,3 => UNS * INC # C3: 2,3 # F2: 2,3 => UNS * INC # C3: 2,3 # I2: 2,3 => UNS * INC # C3: 2,3 # F3: 2,3 => UNS * INC # C3: 2,3 # G3: 2,3 => UNS * INC # C3: 2,3 # I3: 2,3 => UNS * INC # C3: 2,3 # D4: 5,9 => UNS * INC # C3: 2,3 # D4: 1,7 => UNS * INC # C3: 2,3 # E6: 5,9 => UNS * INC # C3: 2,3 # E6: 1,6 => UNS * INC # C3: 2,3 # D4: 7,9 => UNS * INC # C3: 2,3 # D4: 1,5 => UNS * INC # C3: 2,3 # E3: 7,9 => UNS * INC # C3: 2,3 # E3: 2,5 => UNS * DIS # C3: 2,3 # G4: 7,9 => CTR => G4: 1,2 * INC # C3: 2,3 + G4: 1,2 # H4: 7,9 => UNS * INC # C3: 2,3 + G4: 1,2 # H4: 7,9 => UNS * DIS # C3: 2,3 + G4: 1,2 # H4: 1,2 => CTR => H4: 7,9 * DIS # C3: 2,3 + G4: 1,2 + H4: 7,9 # I2: 7,9 => CTR => I2: 2,3 * DIS # C3: 2,3 + G4: 1,2 + H4: 7,9 + I2: 2,3 # I3: 7,9 => CTR => I3: 2,3,5 * PRF # C3: 2,3 + G4: 1,2 + H4: 7,9 + I2: 2,3 + I3: 2,3,5 => SOL * STA C3: 2,3 * CNT 46 HDP CHAINS / 46 HYP OPENED