Analysis of xx-mith-te3-00001046-base.sdk
Contents
Original Sudoku
level: hard
position: ......7.9456....23...2..64.2.56.8...38...4.6..64......5.8..23.664.5.3..8......... initial
Autosolve
position: ......7.9456....23...2..64.2.56.8...38...4.6..64......5.8..23.664.5.3..8......... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D1: 3,8 => CTR => D1: 4 * CNT 1 HDP CHAINS / 18 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D1: 3,8 => CTR => D1: 4 * STA D1: 4 * CNT 1 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: ...4..7.9456....23...2..64.2.56.8.3.38...4.6..643.....5.8.423.664.5.3..8......... pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Pair Reduction
Time used: 0:00:04.578932
The following important HDP chains were detected:
* PRF # E1: 5,6 # C9: 1,7,9 => SOL * STA # E1: 5,6 + C9: 1,7,9 * CNT 1 HDP CHAINS / 20 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ......7.9456....23...2..64.2.56.8...38...4.6..64......5.8..23.664.5.3..8......... | initial |
| ......7.9456....23...2..64.2.56.8...38...4.6..64......5.8..23.664.5.3..8......... | autosolve |
| ...4..7.9456....23...2..64.2.56.8.3.38...4.6..643.....5.8.423.664.5.3..8......... | pair_reduction |
| 123456789456789123897231645215698437389174562764325891578942316642513978931867254 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (7) A1: 1,8 F1: 5,6 E3: 3,8 F3: 1,5 H1: 5,8 G2: 1,8 I3: 1,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G2,I3: 1.. / G2 = 1 => 12 pairs (_) / I3 = 1 => 10 pairs (_) F3,I3: 1.. / F3 = 1 => 12 pairs (_) / I3 = 1 => 10 pairs (_) B1,C1: 2.. / B1 = 2 => 8 pairs (_) / C1 = 2 => 9 pairs (_) E5,E6: 2.. / E5 = 2 => 7 pairs (_) / E6 = 2 => 7 pairs (_) C8,G8: 2.. / C8 = 2 => 0 pairs (*) / G8 = 2 => 0 pairs (X) B1,B9: 2.. / B1 = 2 => 8 pairs (_) / B9 = 2 => 9 pairs (_) H4,H6: 3.. / H4 = 3 => 7 pairs (_) / H6 = 3 => 0 pairs (X) B9,C9: 3.. / B9 = 3 => 9 pairs (_) / C9 = 3 => 9 pairs (_) E4,H4: 3.. / E4 = 3 => 0 pairs (X) / H4 = 3 => 7 pairs (_) D1,D6: 3.. / D1 = 3 => 0 pairs (X) / D6 = 3 => 8 pairs (_) D1,E1: 4.. / D1 = 4 => 7 pairs (_) / E1 = 4 => 0 pairs (X) G4,I4: 4.. / G4 = 4 => 8 pairs (_) / I4 = 4 => 8 pairs (_) D7,E7: 4.. / D7 = 4 => 0 pairs (X) / E7 = 4 => 7 pairs (_) G9,I9: 4.. / G9 = 4 => 8 pairs (_) / I9 = 4 => 8 pairs (_) D1,D7: 4.. / D1 = 4 => 7 pairs (_) / D7 = 4 => 0 pairs (X) E1,E7: 4.. / E1 = 4 => 0 pairs (X) / E7 = 4 => 7 pairs (_) G4,G9: 4.. / G4 = 4 => 8 pairs (_) / G9 = 4 => 8 pairs (_) I4,I9: 4.. / I4 = 4 => 8 pairs (_) / I9 = 4 => 8 pairs (_) H1,I3: 5.. / H1 = 5 => 10 pairs (_) / I3 = 5 => 12 pairs (_) F3,I3: 5.. / F3 = 5 => 10 pairs (_) / I3 = 5 => 12 pairs (_) E1,F1: 6.. / E1 = 6 => 20 pairs (_) / F1 = 6 => 7 pairs (_) E9,F9: 6.. / E9 = 6 => 7 pairs (_) / F9 = 6 => 20 pairs (_) E1,E9: 6.. / E1 = 6 => 20 pairs (_) / E9 = 6 => 7 pairs (_) F1,F9: 6.. / F1 = 6 => 7 pairs (_) / F9 = 6 => 20 pairs (_) A1,A3: 8.. / A1 = 8 => 10 pairs (_) / A3 = 8 => 13 pairs (_) H1,G2: 8.. / H1 = 8 => 12 pairs (_) / G2 = 8 => 10 pairs (_) G6,H6: 8.. / G6 = 8 => 12 pairs (_) / H6 = 8 => 10 pairs (_) D9,E9: 8.. / D9 = 8 => 8 pairs (_) / E9 = 8 => 21 pairs (_) A3,E3: 8.. / A3 = 8 => 13 pairs (_) / E3 = 8 => 10 pairs (_) G2,G6: 8.. / G2 = 8 => 10 pairs (_) / G6 = 8 => 12 pairs (_) H1,H6: 8.. / H1 = 8 => 12 pairs (_) / H6 = 8 => 10 pairs (_) * DURATION: 0:00:09.134263 START: 02:15:42.410931 END: 02:15:51.545194 2025-04-06 * CP COUNT: (31) * SOLUTION FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:04.457560 START: 02:16:01.308724 END: 02:16:05.766284 2025-04-06 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00001046-base-pr-002.dot * REASONING * PRF # E1: 5,6 # C9: 1,7,9 => SOL * STA # E1: 5,6 + C9: 1,7,9 * CNT 1 HDP CHAINS / 20 HYP OPENED
Header Info
rating: 224; r2: 23631; index: 1046
Solution
position: 123456789456789123897231645215698437389174562764325891578942316642513978931867254 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 # E1: 5,6 => UNS * INC # E1: 3,4,8 => UNS * DIS # D1: 3,8 => CTR => D1: 4 * INC # D1: 4 => UNS * INC # E1: 3,8 => UNS * INC # F6: 1,5 => UNS * INC # F6: 7,9 => UNS * INC # E1: 5,8 => UNS * INC # E1: 3,4,6 => UNS * INC # H6: 5,8 => UNS * INC # H6: 1,3,7,9 => UNS * INC # D2: 1,8 => UNS * INC # E2: 1,8 => UNS * INC # G6: 1,8 => UNS * INC # G6: 2,5,9 => UNS * INC # I5: 1,5 => UNS * INC # I6: 1,5 => UNS * INC # I9: 1,5 => UNS * CNT 18 HDP CHAINS / 18 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E1: 5,6 => UNS * INC # E1: 3,4,8 => UNS * DIS # D1: 3,8 => CTR => D1: 4 * INC D1: 4 # E1: 3,8 => UNS * INC D1: 4 # E1: 3,8 => UNS * INC D1: 4 # E1: 5,6 => UNS * INC D1: 4 # F6: 1,5 => UNS * INC D1: 4 # F6: 7,9 => UNS * INC D1: 4 # E1: 5,8 => UNS * INC D1: 4 # E1: 3,6 => UNS * INC D1: 4 # H6: 5,8 => UNS * INC D1: 4 # H6: 1,7,9 => UNS * INC D1: 4 # D2: 1,8 => UNS * INC D1: 4 # E2: 1,8 => UNS * INC D1: 4 # G6: 1,8 => UNS * INC D1: 4 # G6: 2,5,9 => UNS * INC D1: 4 # I5: 1,5 => UNS * INC D1: 4 # I6: 1,5 => UNS * INC D1: 4 # I9: 1,5 => UNS * INC D1: 4 # E1: 5,6 => UNS * INC D1: 4 # E1: 3,8 => UNS * INC D1: 4 # E1: 3,8 => UNS * INC D1: 4 # E1: 5,6 => UNS * INC D1: 4 # F6: 1,5 => UNS * INC D1: 4 # F6: 7,9 => UNS * INC D1: 4 # E1: 5,8 => UNS * INC D1: 4 # E1: 3,6 => UNS * INC D1: 4 # H6: 5,8 => UNS * INC D1: 4 # H6: 1,7,9 => UNS * INC D1: 4 # D2: 1,8 => UNS * INC D1: 4 # E2: 1,8 => UNS * INC D1: 4 # G6: 1,8 => UNS * INC D1: 4 # G6: 2,5,9 => UNS * INC D1: 4 # I5: 1,5 => UNS * INC D1: 4 # I6: 1,5 => UNS * INC D1: 4 # I9: 1,5 => UNS * STA D1: 4 * CNT 36 HDP CHAINS / 36 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # E1: 5,6 => UNS * INC # E1: 3,8 => UNS * INC # E1: 3,8 => UNS * INC # E1: 5,6 => UNS * INC # F6: 1,5 => UNS * INC # F6: 7,9 => UNS * INC # E1: 5,8 => UNS * INC # E1: 3,6 => UNS * INC # H6: 5,8 => UNS * INC # H6: 1,7,9 => UNS * INC # D2: 1,8 => UNS * INC # E2: 1,8 => UNS * INC # G6: 1,8 => UNS * INC # G6: 2,5,9 => UNS * INC # I5: 1,5 => UNS * INC # I6: 1,5 => UNS * INC # I9: 1,5 => UNS * INC # E1: 5,6 # C9: 2,3 => UNS * PRF # E1: 5,6 # C9: 1,7,9 => SOL * STA # E1: 5,6 + C9: 1,7,9 * CNT 19 HDP CHAINS / 20 HYP OPENED