Analysis of xx-mith-te3-00109977-base.sdk
Contents
Original Sudoku
level: hard
position: ..3.....945...9...7.92.3.4.....7.35.3...2..94......2..53.897.......4297.97.6.1... initial
Autosolve
position: .23.....945...9...7.92.3.4.2...7.35.3.7.2..94..5...2.753.897.......4297.97.6.1... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D1: 1,7 => CTR => D1: 4,5 * 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: 1,7 => CTR => D1: 4,5 * STA D1: 4,5 * CNT 1 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: .23...7.945.7.9...7.92.3.4.2...7.35.3.7.2..94..5...2.753.897.......4297.97.6.1... pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Pair Reduction
Time used: 0:00:12.054461
The following important HDP chains were detected:
* DIS # F1: 6,8 # A1: 6,8 => CTR => A1: 1 * PRF # F1: 6,8 + A1: 1 # G3: 6,8 => SOL * STA # F1: 6,8 + A1: 1 + G3: 6,8 * CNT 2 HDP CHAINS / 33 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..3.....945...9...7.92.3.4.....7.35.3...2..94......2..53.897.......4297.97.6.1... | initial |
| .23.....945...9...7.92.3.4.2...7.35.3.7.2..94..5...2.753.897.......4297.97.6.1... | autosolve |
| .23...7.945.7.9...7.92.3.4.2...7.35.3.7.2..94..5...2.753.897.......4297.97.6.1... | pair_reduction |
| 123456789456789132789213645241978356367125894895364217532897461618542973974631528 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (11) D2: 1,7 H2: 2,3 I2: 2,3 B4: 4,9 B6: 4,9 D5: 1,5 C7: 2,4 C9: 2,4 D8: 3,5 E9: 3,5 I8: 3,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H2,I2: 2.. / H2 = 2 => 10 pairs (_) / I2 = 2 => 11 pairs (_) C7,C9: 2.. / C7 = 2 => 13 pairs (_) / C9 = 2 => 11 pairs (_) H2,I2: 3.. / H2 = 3 => 11 pairs (_) / I2 = 3 => 10 pairs (_) D6,E6: 3.. / D6 = 3 => 10 pairs (_) / E6 = 3 => 10 pairs (_) D8,E9: 3.. / D8 = 3 => 10 pairs (_) / E9 = 3 => 10 pairs (_) D8,I8: 3.. / D8 = 3 => 10 pairs (_) / I8 = 3 => 10 pairs (_) D6,D8: 3.. / D6 = 3 => 10 pairs (_) / D8 = 3 => 10 pairs (_) E6,E9: 3.. / E6 = 3 => 10 pairs (_) / E9 = 3 => 10 pairs (_) H2,H9: 3.. / H2 = 3 => 11 pairs (_) / H9 = 3 => 10 pairs (_) D1,F1: 4.. / D1 = 4 => 11 pairs (_) / F1 = 4 => 13 pairs (_) B4,B6: 4.. / B4 = 4 => 10 pairs (_) / B6 = 4 => 10 pairs (_) C7,C9: 4.. / C7 = 4 => 11 pairs (_) / C9 = 4 => 13 pairs (_) G7,G9: 4.. / G7 = 4 => 13 pairs (_) / G9 = 4 => 11 pairs (_) C7,G7: 4.. / C7 = 4 => 11 pairs (_) / G7 = 4 => 13 pairs (_) C9,G9: 4.. / C9 = 4 => 13 pairs (_) / G9 = 4 => 11 pairs (_) D5,F5: 5.. / D5 = 5 => 10 pairs (_) / F5 = 5 => 14 pairs (_) D8,E9: 5.. / D8 = 5 => 10 pairs (_) / E9 = 5 => 10 pairs (_) D8,I8: 5.. / D8 = 5 => 10 pairs (_) / I8 = 5 => 10 pairs (_) F1,F5: 5.. / F1 = 5 => 10 pairs (_) / F5 = 5 => 14 pairs (_) D1,D2: 7.. / D1 = 7 => 0 pairs (X) / D2 = 7 => 10 pairs (_) G1,G2: 7.. / G1 = 7 => 10 pairs (_) / G2 = 7 => 0 pairs (X) D1,G1: 7.. / D1 = 7 => 0 pairs (X) / G1 = 7 => 10 pairs (_) D2,G2: 7.. / D2 = 7 => 10 pairs (_) / G2 = 7 => 0 pairs (X) B4,B6: 9.. / B4 = 9 => 10 pairs (_) / B6 = 9 => 10 pairs (_) D4,D6: 9.. / D4 = 9 => 10 pairs (_) / D6 = 9 => 10 pairs (_) B4,D4: 9.. / B4 = 9 => 10 pairs (_) / D4 = 9 => 10 pairs (_) B6,D6: 9.. / B6 = 9 => 10 pairs (_) / D6 = 9 => 10 pairs (_) * DURATION: 0:00:11.371138 START: 17:11:34.336768 END: 17:11:45.707906 2025-04-06 * CP COUNT: (27) * CLUE FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:11.894210 START: 17:11:56.866370 END: 17:12:08.760580 2025-04-06 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00109977-base-pr-002.dot * REASONING * DIS # F1: 6,8 # A1: 6,8 => CTR => A1: 1 * PRF # F1: 6,8 + A1: 1 # G3: 6,8 => SOL * STA # F1: 6,8 + A1: 1 + G3: 6,8 * CNT 2 HDP CHAINS / 33 HYP OPENED
Header Info
rating: 27813; r2: 738771; index: 109977
Solution
position: 123456789456789132789213645241978356367125894895364217532897461618542973974631528 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:
* DIS # D1: 1,7 => CTR => D1: 4,5 * INC # D1: 4,5 => UNS * INC # G2: 1,7 => UNS * INC # G2: 6,8 => UNS * INC # H9: 2,3 => UNS * INC # H9: 8 => UNS * INC # I9: 2,3 => UNS * INC # I9: 5,8 => UNS * INC # D4: 4,9 => UNS * INC # D4: 1 => UNS * INC # D6: 4,9 => UNS * INC # D6: 1,3 => UNS * INC # D1: 1,5 => UNS * INC # D1: 4,7 => UNS * INC # I9: 3,5 => UNS * INC # I9: 2,8 => UNS * INC # I9: 3,5 => UNS * INC # I9: 2,8 => UNS * CNT 18 HDP CHAINS / 18 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D1: 1,7 => CTR => D1: 4,5 * INC D1: 4,5 # H9: 2,3 => UNS * INC D1: 4,5 # H9: 8 => UNS * INC D1: 4,5 # I9: 2,3 => UNS * INC D1: 4,5 # I9: 5,8 => UNS * INC D1: 4,5 # D4: 4,9 => UNS * INC D1: 4,5 # D4: 1 => UNS * INC D1: 4,5 # D6: 4,9 => UNS * INC D1: 4,5 # D6: 1,3 => UNS * INC D1: 4,5 # I9: 3,5 => UNS * INC D1: 4,5 # I9: 2,8 => UNS * INC D1: 4,5 # I9: 3,5 => UNS * INC D1: 4,5 # I9: 2,8 => UNS * INC D1: 4,5 # F1: 4,5 => UNS * INC D1: 4,5 # F1: 6,8 => UNS * INC D1: 4,5 # H9: 2,3 => UNS * INC D1: 4,5 # H9: 8 => UNS * INC D1: 4,5 # I9: 2,3 => UNS * INC D1: 4,5 # I9: 5,8 => UNS * INC D1: 4,5 # D4: 4,9 => UNS * INC D1: 4,5 # D4: 1 => UNS * INC D1: 4,5 # D6: 4,9 => UNS * INC D1: 4,5 # D6: 1,3 => UNS * INC D1: 4,5 # I9: 3,5 => UNS * INC D1: 4,5 # I9: 2,8 => UNS * INC D1: 4,5 # I9: 3,5 => UNS * INC D1: 4,5 # I9: 2,8 => UNS * STA D1: 4,5 * CNT 27 HDP CHAINS / 27 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # F1: 4,5 => UNS * INC # F1: 6,8 => UNS * INC # H9: 2,3 => UNS * INC # H9: 8 => UNS * INC # I9: 2,3 => UNS * INC # I9: 5,8 => UNS * INC # D4: 4,9 => UNS * INC # D4: 1 => UNS * INC # D6: 4,9 => UNS * INC # D6: 1,3 => UNS * INC # I9: 3,5 => UNS * INC # I9: 2,8 => UNS * INC # I9: 3,5 => UNS * INC # I9: 2,8 => UNS * INC # F1: 4,5 # H9: 2,3 => UNS * INC # F1: 4,5 # H9: 8 => UNS * INC # F1: 4,5 # I9: 2,3 => UNS * INC # F1: 4,5 # I9: 8 => UNS * INC # F1: 4,5 # D4: 4,9 => UNS * INC # F1: 4,5 # D4: 1 => UNS * INC # F1: 4,5 # D6: 4,9 => UNS * INC # F1: 4,5 # D6: 1 => UNS * INC # F1: 4,5 => UNS * INC # F1: 6,8 # E2: 6,8 => UNS * INC # F1: 6,8 # E3: 6,8 => UNS * DIS # F1: 6,8 # A1: 6,8 => CTR => A1: 1 * INC # F1: 6,8 + A1: 1 # E2: 6,8 => UNS * INC # F1: 6,8 + A1: 1 # E3: 6,8 => UNS * INC # F1: 6,8 + A1: 1 # E2: 6,8 => UNS * INC # F1: 6,8 + A1: 1 # E3: 6,8 => UNS * INC # F1: 6,8 + A1: 1 # G2: 6,8 => UNS * PRF # F1: 6,8 + A1: 1 # G3: 6,8 => SOL * STA # F1: 6,8 + A1: 1 + G3: 6,8 * CNT 32 HDP CHAINS / 33 HYP OPENED