Analysis of xx-mith-te3-00002144-base.sdk
Contents
Original Sudoku
level: hard
position: .23......4..789...78....6....819..76..1.7.9.4............96...86..8.1.9.8...47.61 initial
Autosolve
position: .23......4..789...78....6....819..76..1.7.9.4............96...86..8.1.9.8...47.61 autosolve
Pair Reduction Variants
Deep Pair Reduction
Time used: 0:00:03.969472
The following important HDP chains were detected:
* DIS # B2: 5,6 # B5: 3 => CTR => B5: 5,6 * DIS # B2: 5,6 + B5: 5,6 # C6: 5,6 => CTR => C6: 4 * PRF # B2: 5,6 + B5: 5,6 + C6: 4 => SOL * STA B2: 5,6 * CNT 3 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .23......4..789...78....6....819..76..1.7.9.4............96...86..8.1.9.8...47.61 | initial |
| .23......4..789...78....6....819..76..1.7.9.4............96...86..8.1.9.8...47.61 | autosolve |
| 123456789456789132789213645238194576561378924974625813317962458645831297892547361 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (7) A1: 1,9 C2: 5,6 C3: 5,9 E1: 1,5 I1: 7,9 H3: 1,4 I3: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,B2: 1.. / A1 = 1 => 13 pairs (_) / B2 = 1 => 12 pairs (_) E1,E3: 1.. / E1 = 1 => 10 pairs (_) / E3 = 1 => 12 pairs (_) G6,H6: 1.. / G6 = 1 => 10 pairs (_) / H6 = 1 => 12 pairs (_) A7,B7: 1.. / A7 = 1 => 12 pairs (_) / B7 = 1 => 13 pairs (_) E3,H3: 1.. / E3 = 1 => 12 pairs (_) / H3 = 1 => 10 pairs (_) A1,A7: 1.. / A1 = 1 => 13 pairs (_) / A7 = 1 => 12 pairs (_) B2,B7: 1.. / B2 = 1 => 12 pairs (_) / B7 = 1 => 13 pairs (_) B4,F4: 4.. / B4 = 4 => 7 pairs (_) / F4 = 4 => 0 pairs (*) C3,I3: 5.. / C3 = 5 => 12 pairs (_) / I3 = 5 => 13 pairs (_) B2,C2: 6.. / B2 = 6 => 0 pairs (X) / C2 = 6 => 7 pairs (_) D1,F1: 6.. / D1 = 6 => 10 pairs (_) / F1 = 6 => 8 pairs (_) C2,C6: 6.. / C2 = 6 => 7 pairs (_) / C6 = 6 => 0 pairs (X) G1,I1: 7.. / G1 = 7 => 13 pairs (_) / I1 = 7 => 12 pairs (_) B6,C6: 7.. / B6 = 7 => 8 pairs (_) / C6 = 7 => 7 pairs (_) I1,I8: 7.. / I1 = 7 => 12 pairs (_) / I8 = 7 => 13 pairs (_) G1,H1: 8.. / G1 = 8 => 10 pairs (_) / H1 = 8 => 12 pairs (_) F5,F6: 8.. / F5 = 8 => 9 pairs (_) / F6 = 8 => 0 pairs (X) F5,H5: 8.. / F5 = 8 => 9 pairs (_) / H5 = 8 => 0 pairs (X) G1,G6: 8.. / G1 = 8 => 10 pairs (_) / G6 = 8 => 12 pairs (_) A1,C3: 9.. / A1 = 9 => 12 pairs (_) / C3 = 9 => 13 pairs (_) I1,I3: 9.. / I1 = 9 => 13 pairs (_) / I3 = 9 => 12 pairs (_) B9,C9: 9.. / B9 = 9 => 8 pairs (_) / C9 = 9 => 12 pairs (_) A1,I1: 9.. / A1 = 9 => 12 pairs (_) / I1 = 9 => 13 pairs (_) C3,I3: 9.. / C3 = 9 => 13 pairs (_) / I3 = 9 => 12 pairs (_) A1,A6: 9.. / A1 = 9 => 12 pairs (_) / A6 = 9 => 13 pairs (_) B6,B9: 9.. / B6 = 9 => 12 pairs (_) / B9 = 9 => 8 pairs (_) * DURATION: 0:00:08.168139 START: 04:37:25.520880 END: 04:37:33.689019 2025-04-04 * CP COUNT: (26) * SOLUTION FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:03.863362 START: 04:37:36.711781 END: 04:37:40.575143 2025-04-04 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00002144-base-pr-002.dot * REASONING * DIS # B2: 5,6 # B5: 3 => CTR => B5: 5,6 * DIS # B2: 5,6 + B5: 5,6 # C6: 5,6 => CTR => C6: 4 * PRF # B2: 5,6 + B5: 5,6 + C6: 4 => SOL * STA B2: 5,6 * CNT 3 HDP CHAINS / 12 HYP OPENED
Header Info
rating: 359; r2: 83107; index: 2144
Solution
position: 123456789456789132789213645238194576561378924974625813317962458645831297892547361 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 # B2: 5,6 => UNS * INC # B2: 1 => UNS * INC # C6: 5,6 => UNS * INC # C6: 2,4,7,9 => UNS * INC # C6: 5,9 => UNS * INC # C9: 5,9 => UNS * INC # G1: 1,4 => UNS * INC # H1: 1,4 => UNS * CNT 8 HDP CHAINS / 8 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 5,6 => UNS * INC # B2: 1 => UNS * INC # C6: 5,6 => UNS * INC # C6: 2,4,7,9 => UNS * INC # C6: 5,9 => UNS * INC # C9: 5,9 => UNS * INC # G1: 1,4 => UNS * INC # H1: 1,4 => UNS * CNT 8 HDP CHAINS / 8 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 5,6 => UNS * INC # B2: 1 => UNS * INC # C6: 5,6 => UNS * INC # C6: 2,4,7,9 => UNS * INC # C6: 5,9 => UNS * INC # C9: 5,9 => UNS * INC # G1: 1,4 => UNS * INC # H1: 1,4 => UNS * INC # B2: 5,6 # B5: 5,6 => UNS * DIS # B2: 5,6 # B5: 3 => CTR => B5: 5,6 * DIS # B2: 5,6 + B5: 5,6 # C6: 5,6 => CTR => C6: 4 * PRF # B2: 5,6 + B5: 5,6 + C6: 4 => SOL * STA B2: 5,6 * CNT 12 HDP CHAINS / 12 HYP OPENED