Analysis of xx-mith-te3-00109964-base.sdk
Contents
Original Sudoku
level: hard
position: 12.....89..7.8....6.......4...8.4.95....75......93...753..97.48...54.9.394.3.8... initial
Autosolve
position: 12.....89..7.8....6.......4...8.4.95....75......93...753..97.48...54.9.394.3.8... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 5 => CTR => C1: 3,4 * CNT 1 HDP CHAINS / 20 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 5 => CTR => C1: 3,4 * STA C1: 3,4 * CNT 1 HDP CHAINS / 40 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: 12.....89..7.8....6.......4...8.4.95....75......93...753..97.48...54.9.394.3.8... pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Pair Reduction
Time used: 0:00:09.191069
The following important HDP chains were detected:
* DIS # C5: 3,4 # G1: 5,6 => CTR => G1: 3,7 * DIS # C5: 3,4 + G1: 3,7 # G3: 5,7 => CTR => G3: 1,2,3 * DIS # C5: 3,4 + G1: 3,7 + G3: 1,2,3 # A5: 4,8 => CTR => A5: 2,3 * DIS # C5: 3,4 + G1: 3,7 + G3: 1,2,3 + A5: 2,3 # B4: 1,6 => CTR => B4: 7 * PRF # C5: 3,4 + G1: 3,7 + G3: 1,2,3 + A5: 2,3 + B4: 7 # H6: 1,6 => SOL * STA # C5: 3,4 + G1: 3,7 + G3: 1,2,3 + A5: 2,3 + B4: 7 + H6: 1,6 * CNT 5 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 12.....89..7.8....6.......4...8.4.95....75......93...753..97.48...54.9.394.3.8... | initial |
| 12.....89..7.8....6.......4...8.4.95....75......93...753..97.48...54.9.394.3.8... | autosolve |
| 12.....89..7.8....6.......4...8.4.95....75......93...753..97.48...54.9.394.3.8... | pair_reduction |
| 123456789457189236689723154276814395394675812815932467531297648768541923942368571 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (8) A2: 3,4 B2: 5,9 E1: 5,6 F1: 3,6 G5: 4,8 G6: 4,8 G9: 5,7 H9: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G4,H5: 3.. / G4 = 3 => 9 pairs (_) / H5 = 3 => 8 pairs (_) C1,A2: 4.. / C1 = 4 => 9 pairs (_) / A2 = 4 => 11 pairs (_) D1,D2: 4.. / D1 = 4 => 11 pairs (_) / D2 = 4 => 9 pairs (_) G5,G6: 4.. / G5 = 4 => 7 pairs (_) / G6 = 4 => 7 pairs (_) C1,D1: 4.. / C1 = 4 => 9 pairs (_) / D1 = 4 => 11 pairs (_) A2,D2: 4.. / A2 = 4 => 11 pairs (_) / D2 = 4 => 9 pairs (_) E1,E3: 5.. / E1 = 5 => 9 pairs (_) / E3 = 5 => 12 pairs (_) B6,C6: 5.. / B6 = 5 => 10 pairs (_) / C6 = 5 => 10 pairs (_) G9,H9: 5.. / G9 = 5 => 6 pairs (_) / H9 = 5 => 7 pairs (_) D1,D3: 7.. / D1 = 7 => 9 pairs (_) / D3 = 7 => 7 pairs (_) A4,B4: 7.. / A4 = 7 => 11 pairs (_) / B4 = 7 => 9 pairs (_) A8,B8: 7.. / A8 = 7 => 9 pairs (_) / B8 = 7 => 11 pairs (_) G9,H9: 7.. / G9 = 7 => 7 pairs (_) / H9 = 7 => 6 pairs (_) D1,G1: 7.. / D1 = 7 => 9 pairs (_) / G1 = 7 => 7 pairs (_) A4,A8: 7.. / A4 = 7 => 11 pairs (_) / A8 = 7 => 9 pairs (_) B4,B8: 7.. / B4 = 7 => 9 pairs (_) / B8 = 7 => 11 pairs (_) H3,H9: 7.. / H3 = 7 => 7 pairs (_) / H9 = 7 => 6 pairs (_) B3,C3: 8.. / B3 = 8 => 8 pairs (_) / C3 = 8 => 12 pairs (_) G5,G6: 8.. / G5 = 8 => 7 pairs (_) / G6 = 8 => 7 pairs (_) F2,F3: 9.. / F2 = 9 => 11 pairs (_) / F3 = 9 => 8 pairs (_) B5,C5: 9.. / B5 = 9 => 11 pairs (_) / C5 = 9 => 8 pairs (_) B2,F2: 9.. / B2 = 9 => 8 pairs (_) / F2 = 9 => 11 pairs (_) C3,C5: 9.. / C3 = 9 => 11 pairs (_) / C5 = 9 => 8 pairs (_) * DURATION: 0:00:05.977923 START: 02:54:46.658132 END: 02:54:52.636055 2025-04-05 * CP COUNT: (23) * INCONCLUSIVE * DEEP PAIR REDUCTION * DURATION: 0:00:09.057816 START: 02:55:02.136552 END: 02:55:11.194368 2025-04-05 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00109964-base-pr-002.dot * REASONING * DIS # C5: 3,4 # G1: 5,6 => CTR => G1: 3,7 * DIS # C5: 3,4 + G1: 3,7 # G3: 5,7 => CTR => G3: 1,2,3 * DIS # C5: 3,4 + G1: 3,7 + G3: 1,2,3 # A5: 4,8 => CTR => A5: 2,3 * DIS # C5: 3,4 + G1: 3,7 + G3: 1,2,3 + A5: 2,3 # B4: 1,6 => CTR => B4: 7 * PRF # C5: 3,4 + G1: 3,7 + G3: 1,2,3 + A5: 2,3 + B4: 7 # H6: 1,6 => SOL * STA # C5: 3,4 + G1: 3,7 + G3: 1,2,3 + A5: 2,3 + B4: 7 + H6: 1,6 * CNT 5 HDP CHAINS / 30 HYP OPENED
Header Info
rating: 27811; r2: 526610; index: 109964
Solution
position: 123456789457189236689723154276814395394675812815932467531297648768541923942368571 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 # C1: 3,4 => UNS * DIS # C1: 5 => CTR => C1: 3,4 * INC # A5: 3,4 => UNS * INC # A5: 2,8 => UNS * INC # B3: 5,9 => UNS * INC # C3: 5,9 => UNS * INC # G1: 5,6 => UNS * INC # G1: 3,7 => UNS * INC # F2: 3,6 => UNS * INC # F2: 1,2,9 => UNS * INC # G1: 3,6 => UNS * INC # G1: 5,7 => UNS * INC # A5: 4,8 => UNS * INC # C5: 4,8 => UNS * INC # A6: 4,8 => UNS * INC # C6: 4,8 => UNS * INC # G1: 5,7 => UNS * INC # G3: 5,7 => UNS * INC # H3: 5,7 => UNS * INC # H3: 1,2,3 => UNS * CNT 20 HDP CHAINS / 20 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 3,4 => UNS * DIS # C1: 5 => CTR => C1: 3,4 * INC C1: 3,4 # A5: 3,4 => UNS * INC C1: 3,4 # A5: 2,8 => UNS * INC C1: 3,4 # B3: 5,9 => UNS * INC C1: 3,4 # C3: 5,9 => UNS * INC C1: 3,4 # G1: 5,6 => UNS * INC C1: 3,4 # G1: 3,7 => UNS * INC C1: 3,4 # F2: 3,6 => UNS * INC C1: 3,4 # F2: 1,2,9 => UNS * INC C1: 3,4 # G1: 3,6 => UNS * INC C1: 3,4 # G1: 5,7 => UNS * INC C1: 3,4 # A5: 4,8 => UNS * INC C1: 3,4 # C5: 4,8 => UNS * INC C1: 3,4 # A6: 4,8 => UNS * INC C1: 3,4 # C6: 4,8 => UNS * INC C1: 3,4 # G1: 5,7 => UNS * INC C1: 3,4 # G3: 5,7 => UNS * INC C1: 3,4 # H3: 5,7 => UNS * INC C1: 3,4 # H3: 1,2,3 => UNS * INC C1: 3,4 # C5: 3,4 => UNS * INC C1: 3,4 # C5: 1,2,6,8,9 => UNS * INC C1: 3,4 # A5: 3,4 => UNS * INC C1: 3,4 # A5: 2,8 => UNS * INC C1: 3,4 # B3: 5,9 => UNS * INC C1: 3,4 # C3: 5,9 => UNS * INC C1: 3,4 # G1: 5,6 => UNS * INC C1: 3,4 # G1: 3,7 => UNS * INC C1: 3,4 # F2: 3,6 => UNS * INC C1: 3,4 # F2: 1,2,9 => UNS * INC C1: 3,4 # G1: 3,6 => UNS * INC C1: 3,4 # G1: 5,7 => UNS * INC C1: 3,4 # A5: 4,8 => UNS * INC C1: 3,4 # C5: 4,8 => UNS * INC C1: 3,4 # A6: 4,8 => UNS * INC C1: 3,4 # C6: 4,8 => UNS * INC C1: 3,4 # G1: 5,7 => UNS * INC C1: 3,4 # G3: 5,7 => UNS * INC C1: 3,4 # H3: 5,7 => UNS * INC C1: 3,4 # H3: 1,2,3 => UNS * STA C1: 3,4 * CNT 40 HDP CHAINS / 40 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # C5: 3,4 => UNS * INC # C5: 1,2,6,8,9 => UNS * INC # A5: 3,4 => UNS * INC # A5: 2,8 => UNS * INC # B3: 5,9 => UNS * INC # C3: 5,9 => UNS * INC # G1: 5,6 => UNS * INC # G1: 3,7 => UNS * INC # F2: 3,6 => UNS * INC # F2: 1,2,9 => UNS * INC # G1: 3,6 => UNS * INC # G1: 5,7 => UNS * INC # A5: 4,8 => UNS * INC # C5: 4,8 => UNS * INC # A6: 4,8 => UNS * INC # C6: 4,8 => UNS * INC # G1: 5,7 => UNS * INC # G3: 5,7 => UNS * INC # H3: 5,7 => UNS * INC # H3: 1,2,3 => UNS * INC # C5: 3,4 # A5: 3,4 => UNS * INC # C5: 3,4 # A5: 2,8 => UNS * DIS # C5: 3,4 # G1: 5,6 => CTR => G1: 3,7 * DIS # C5: 3,4 + G1: 3,7 # G3: 5,7 => CTR => G3: 1,2,3 * INC # C5: 3,4 + G1: 3,7 + G3: 1,2,3 # A5: 3,4 => UNS * INC # C5: 3,4 + G1: 3,7 + G3: 1,2,3 # A5: 2,8 => UNS * DIS # C5: 3,4 + G1: 3,7 + G3: 1,2,3 # A5: 4,8 => CTR => A5: 2,3 * DIS # C5: 3,4 + G1: 3,7 + G3: 1,2,3 + A5: 2,3 # B4: 1,6 => CTR => B4: 7 * PRF # C5: 3,4 + G1: 3,7 + G3: 1,2,3 + A5: 2,3 + B4: 7 # H6: 1,6 => SOL * STA # C5: 3,4 + G1: 3,7 + G3: 1,2,3 + A5: 2,3 + B4: 7 + H6: 1,6 * CNT 29 HDP CHAINS / 30 HYP OPENED