Analysis of xx-mith-te3-00137162-base.sdk
Contents
Original Sudoku
level: hard
position: 12....78...718.2.3.......15...83.......9615.2...5.21.858...3.21.3....8.77....835. initial
Autosolve
position: 12....78...718.2.3.......152..83.......9615.2...5.21.858...3.21.3....8.77....835. autosolve
Pair Reduction Variants
Deep Pair Reduction
Time used: 0:00:03.705272
The following important HDP chains were detected:
* PRF # B6: 4,7 # C3: 4,6,9 => SOL * STA # B6: 4,7 + C3: 4,6,9 * CNT 1 HDP CHAINS / 15 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 12....78...718.2.3.......15...83.......9615.2...5.21.858...3.21.3....8.77....835. | initial |
| 12....78...718.2.3.......152..83.......9615.2...5.21.858...3.21.3....8.77....835. | autosolve |
| 123456789457189263869327415215834976378961542946572138584793621631245897792618354 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (5) B4: 1,5 C4: 1,5 B5: 4,7 F4: 4,7 E6: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B4,C4: 1.. / B4 = 1 => 5 pairs (_) / C4 = 1 => 0 pairs (X) E8,E9: 1.. / E8 = 1 => 5 pairs (_) / E9 = 1 => 4 pairs (_) C8,E8: 1.. / C8 = 1 => 4 pairs (_) / E8 = 1 => 5 pairs (_) B4,B9: 1.. / B4 = 1 => 5 pairs (_) / B9 = 1 => 0 pairs (X) D3,E3: 2.. / D3 = 2 => 14 pairs (_) / E3 = 2 => 5 pairs (_) C8,C9: 2.. / C8 = 2 => 5 pairs (_) / C9 = 2 => 6 pairs (_) D1,D3: 3.. / D1 = 3 => 7 pairs (_) / D3 = 3 => 0 pairs (*) H5,H6: 3.. / H5 = 3 => 8 pairs (_) / H6 = 3 => 9 pairs (_) C1,D1: 3.. / C1 = 3 => 0 pairs (*) / D1 = 3 => 0 pairs (X) F4,E6: 4.. / F4 = 4 => 10 pairs (_) / E6 = 4 => 12 pairs (_) C1,B2: 5.. / C1 = 5 => 0 pairs (X) / B2 = 5 => 5 pairs (_) B4,C4: 5.. / B4 = 5 => 0 pairs (X) / C4 = 5 => 5 pairs (_) E8,F8: 5.. / E8 = 5 => 5 pairs (_) / F8 = 5 => 6 pairs (_) B2,F2: 5.. / B2 = 5 => 5 pairs (_) / F2 = 5 => 0 pairs (X) B2,B4: 5.. / B2 = 5 => 5 pairs (_) / B4 = 5 => 0 pairs (X) C1,C4: 5.. / C1 = 5 => 0 pairs (X) / C4 = 5 => 5 pairs (_) E1,E8: 5.. / E1 = 5 => 6 pairs (_) / E8 = 5 => 5 pairs (_) B5,B6: 7.. / B5 = 7 => 5 pairs (_) / B6 = 7 => 14 pairs (_) F4,E6: 7.. / F4 = 7 => 12 pairs (_) / E6 = 7 => 10 pairs (_) D7,E7: 7.. / D7 = 7 => 6 pairs (_) / E7 = 7 => 11 pairs (_) F4,H4: 7.. / F4 = 7 => 12 pairs (_) / H4 = 7 => 10 pairs (_) B5,H5: 7.. / B5 = 7 => 5 pairs (_) / H5 = 7 => 14 pairs (_) D3,D7: 7.. / D3 = 7 => 11 pairs (_) / D7 = 7 => 6 pairs (_) F3,F4: 7.. / F3 = 7 => 10 pairs (_) / F4 = 7 => 12 pairs (_) A3,C3: 8.. / A3 = 8 => 6 pairs (_) / C3 = 8 => 6 pairs (_) A5,C5: 8.. / A5 = 8 => 6 pairs (_) / C5 = 8 => 6 pairs (_) A3,A5: 8.. / A3 = 8 => 6 pairs (_) / A5 = 8 => 6 pairs (_) C3,C5: 8.. / C3 = 8 => 6 pairs (_) / C5 = 8 => 6 pairs (_) * DURATION: 0:00:08.539529 START: 21:27:39.285314 END: 21:27:47.824843 2025-04-06 * CP COUNT: (28) * SOLUTION FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:03.585778 START: 21:27:51.871379 END: 21:27:55.457157 2025-04-06 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00137162-base-pr-002.dot * REASONING * PRF # B6: 4,7 # C3: 4,6,9 => SOL * STA # B6: 4,7 + C3: 4,6,9 * CNT 1 HDP CHAINS / 15 HYP OPENED
Header Info
rating: 36485; r2: 676704; index: 137162
Solution
position: 123456789457189263869327415215834976378961542946572138584793621631245897792618354 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 # B6: 4,7 => UNS * INC # B6: 6,9 => UNS * INC # H5: 4,7 => UNS * INC # H5: 3 => UNS * INC # H4: 4,7 => UNS * INC # H4: 6,9 => UNS * INC # F3: 4,7 => UNS * INC # F3: 6,9 => UNS * INC # B6: 4,7 => UNS * INC # H6: 4,7 => UNS * INC # E3: 4,7 => UNS * INC # E7: 4,7 => UNS * CNT 12 HDP CHAINS / 12 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B6: 4,7 => UNS * INC # B6: 6,9 => UNS * INC # H5: 4,7 => UNS * INC # H5: 3 => UNS * INC # H4: 4,7 => UNS * INC # H4: 6,9 => UNS * INC # F3: 4,7 => UNS * INC # F3: 6,9 => UNS * INC # B6: 4,7 => UNS * INC # H6: 4,7 => UNS * INC # E3: 4,7 => UNS * INC # E7: 4,7 => UNS * CNT 12 HDP CHAINS / 12 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # B6: 4,7 => UNS * INC # B6: 6,9 => UNS * INC # H5: 4,7 => UNS * INC # H5: 3 => UNS * INC # H4: 4,7 => UNS * INC # H4: 6,9 => UNS * INC # F3: 4,7 => UNS * INC # F3: 6,9 => UNS * INC # B6: 4,7 => UNS * INC # H6: 4,7 => UNS * INC # E3: 4,7 => UNS * INC # E7: 4,7 => UNS * INC # B6: 4,7 # C3: 3,8 => UNS * PRF # B6: 4,7 # C3: 4,6,9 => SOL * STA # B6: 4,7 + C3: 4,6,9 * CNT 14 HDP CHAINS / 15 HYP OPENED