Analysis of xx-mith-te3-00081046-base.sdk
Contents
Original Sudoku
level: hard
position: 1.3.56....57.8....68...75...61....4.......192....13..5........1.16.38..787.5.1..6 initial
Autosolve
position: 1.3.56....57.8....68...75...61....4.......192....13..5........1.16.38..787.5.1..6 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A5: 3,4 => CTR => A5: 5,7 * CNT 1 HDP CHAINS / 24 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A5: 3,4 => CTR => A5: 5,7 * STA A5: 5,7 * CNT 1 HDP CHAINS / 43 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: 1.3.56....57.8....68...75...61....4..3....192....13..53.......1.16.38..787.5.1..6 pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Pair Reduction
Time used: 0:00:21.787133
The following important HDP chains were detected:
* DIS # H2: 2,6 # G4: 7 => CTR => G4: 3,8 * PRF # H2: 2,6 + G4: 3,8 # A4: 2,9 => SOL * STA # H2: 2,6 + G4: 3,8 + A4: 2,9 * CNT 2 HDP CHAINS / 80 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.3.56....57.8....68...75...61....4.......192....13..5........1.16.38..787.5.1..6 | initial |
| 1.3.56....57.8....68...75...61....4.......192....13..5........1.16.38..787.5.1..6 | autosolve |
| 1.3.56....57.8....68...75...61....4..3....192....13..53.......1.16.38..787.5.1..6 | pair_reduction |
| 123456789457189263689327514261795348735864192948213675394672851516938427872541936 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (9) D2: 1,3 D3: 1,3 B5: 3,4 F5: 4,5 I4: 3,8 D7: 6,7 E7: 6,7 H8: 2,5 H9: 2,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,D3: 1.. / D2 = 1 => 8 pairs (_) / D3 = 1 => 10 pairs (_) H2,H3: 1.. / H2 = 1 => 10 pairs (_) / H3 = 1 => 8 pairs (_) D2,H2: 1.. / D2 = 1 => 8 pairs (_) / H2 = 1 => 10 pairs (_) D3,H3: 1.. / D3 = 1 => 10 pairs (_) / H3 = 1 => 8 pairs (_) D2,D3: 3.. / D2 = 3 => 10 pairs (_) / D3 = 3 => 8 pairs (_) A5,B5: 3.. / A5 = 3 => 0 pairs (X) / B5 = 3 => 8 pairs (_) G4,I4: 3.. / G4 = 3 => 14 pairs (_) / I4 = 3 => 17 pairs (_) A7,B7: 3.. / A7 = 3 => 8 pairs (_) / B7 = 3 => 0 pairs (X) G9,H9: 3.. / G9 = 3 => 18 pairs (_) / H9 = 3 => 9 pairs (_) A5,A7: 3.. / A5 = 3 => 0 pairs (X) / A7 = 3 => 8 pairs (_) B5,B7: 3.. / B5 = 3 => 8 pairs (_) / B7 = 3 => 0 pairs (X) F4,F5: 5.. / F4 = 5 => 13 pairs (_) / F5 = 5 => 10 pairs (_) H7,H8: 5.. / H7 = 5 => 0 pairs (*) / H8 = 5 => 0 pairs (X) A4,F4: 5.. / A4 = 5 => 10 pairs (_) / F4 = 5 => 13 pairs (_) A8,H8: 5.. / A8 = 5 => 0 pairs (*) / H8 = 5 => 0 pairs (X) C5,C7: 5.. / C5 = 5 => 0 pairs (*) / C7 = 5 => 0 pairs (X) G2,H2: 6.. / G2 = 6 => 10 pairs (_) / H2 = 6 => 9 pairs (_) D5,E5: 6.. / D5 = 6 => 8 pairs (_) / E5 = 6 => 8 pairs (_) G6,H6: 6.. / G6 = 6 => 9 pairs (_) / H6 = 6 => 10 pairs (_) D7,E7: 6.. / D7 = 6 => 8 pairs (_) / E7 = 6 => 8 pairs (_) D5,D7: 6.. / D5 = 6 => 8 pairs (_) / D7 = 6 => 8 pairs (_) E5,E7: 6.. / E5 = 6 => 8 pairs (_) / E7 = 6 => 8 pairs (_) G2,G6: 6.. / G2 = 6 => 10 pairs (_) / G6 = 6 => 9 pairs (_) H2,H6: 6.. / H2 = 6 => 9 pairs (_) / H6 = 6 => 10 pairs (_) G1,H1: 7.. / G1 = 7 => 10 pairs (_) / H1 = 7 => 11 pairs (_) D7,E7: 7.. / D7 = 7 => 8 pairs (_) / E7 = 7 => 8 pairs (_) H1,H6: 7.. / H1 = 7 => 11 pairs (_) / H6 = 7 => 10 pairs (_) C5,C6: 8.. / C5 = 8 => 9 pairs (_) / C6 = 8 => 11 pairs (_) G7,H7: 8.. / G7 = 8 => 15 pairs (_) / H7 = 8 => 10 pairs (_) C5,D5: 8.. / C5 = 8 => 9 pairs (_) / D5 = 8 => 11 pairs (_) I1,I4: 8.. / I1 = 8 => 17 pairs (_) / I4 = 8 => 14 pairs (_) * DURATION: 0:00:09.239851 START: 11:33:19.518802 END: 11:33:28.758653 2025-04-06 * CP COUNT: (31) * SOLUTION FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:21.589998 START: 11:33:41.244098 END: 11:34:02.834096 2025-04-06 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00081046-base-pr-002.dot * REASONING * DIS # H2: 2,6 # G4: 7 => CTR => G4: 3,8 * PRF # H2: 2,6 + G4: 3,8 # A4: 2,9 => SOL * STA # H2: 2,6 + G4: 3,8 + A4: 2,9 * CNT 2 HDP CHAINS / 80 HYP OPENED
Header Info
rating: 19537; r2: 643373; index: 81046
Solution
position: 123456789457189263689327514261795348735864192948213675394672851516938427872541936 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 # H2: 1,3 => UNS * INC # H2: 2,6 => UNS * INC # H3: 1,3 => UNS * INC # H3: 2 => UNS * DIS # A5: 3,4 => CTR => A5: 5,7 * INC # A5: 5,7 => UNS * INC # B7: 3,4 => UNS * INC # B7: 2,9 => UNS * INC # A5: 4,5 => UNS * INC # C5: 4,5 => UNS * INC # G4: 3,8 => UNS * INC # G4: 7 => UNS * INC # D5: 6,7 => UNS * INC # D5: 4,8 => UNS * INC # E5: 6,7 => UNS * INC # E5: 4 => UNS * INC # H7: 2,5 => UNS * INC # H7: 8 => UNS * INC # A8: 2,5 => UNS * INC # A8: 4,9 => UNS * INC # G9: 2,3 => UNS * INC # G9: 4,9 => UNS * INC # H2: 2,3 => UNS * INC # H3: 2,3 => UNS * CNT 24 HDP CHAINS / 24 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # H2: 1,3 => UNS * INC # H2: 2,6 => UNS * INC # H3: 1,3 => UNS * INC # H3: 2 => UNS * DIS # A5: 3,4 => CTR => A5: 5,7 * INC A5: 5,7 # C5: 4,5 => UNS * INC A5: 5,7 # C5: 8 => UNS * INC A5: 5,7 # G4: 3,8 => UNS * INC A5: 5,7 # G4: 7 => UNS * INC A5: 5,7 # D5: 6,7 => UNS * INC A5: 5,7 # D5: 4,8 => UNS * INC A5: 5,7 # E5: 6,7 => UNS * INC A5: 5,7 # E5: 4 => UNS * INC A5: 5,7 # H7: 2,5 => UNS * INC A5: 5,7 # H7: 8 => UNS * INC A5: 5,7 # A8: 2,5 => UNS * INC A5: 5,7 # A8: 4,9 => UNS * INC A5: 5,7 # G9: 2,3 => UNS * INC A5: 5,7 # G9: 4,9 => UNS * INC A5: 5,7 # H2: 2,3 => UNS * INC A5: 5,7 # H3: 2,3 => UNS * INC A5: 5,7 # H2: 1,3 => UNS * INC A5: 5,7 # H2: 2,6 => UNS * INC A5: 5,7 # H3: 1,3 => UNS * INC A5: 5,7 # H3: 2 => UNS * INC A5: 5,7 # A4: 5,7 => UNS * INC A5: 5,7 # A4: 2,9 => UNS * INC A5: 5,7 # C5: 4,5 => UNS * INC A5: 5,7 # C5: 8 => UNS * INC A5: 5,7 # G4: 3,8 => UNS * INC A5: 5,7 # G4: 7 => UNS * INC A5: 5,7 # D5: 6,7 => UNS * INC A5: 5,7 # D5: 4,8 => UNS * INC A5: 5,7 # E5: 6,7 => UNS * INC A5: 5,7 # E5: 4 => UNS * INC A5: 5,7 # H7: 2,5 => UNS * INC A5: 5,7 # H7: 8 => UNS * INC A5: 5,7 # A8: 2,5 => UNS * INC A5: 5,7 # A8: 4,9 => UNS * INC A5: 5,7 # G9: 2,3 => UNS * INC A5: 5,7 # G9: 4,9 => UNS * INC A5: 5,7 # H2: 2,3 => UNS * INC A5: 5,7 # H3: 2,3 => UNS * STA A5: 5,7 * CNT 43 HDP CHAINS / 43 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # H2: 1,3 => UNS * INC # H2: 2,6 => UNS * INC # H3: 1,3 => UNS * INC # H3: 2 => UNS * INC # A4: 5,7 => UNS * INC # A4: 2,9 => UNS * INC # C5: 4,5 => UNS * INC # C5: 8 => UNS * INC # G4: 3,8 => UNS * INC # G4: 7 => UNS * INC # D5: 6,7 => UNS * INC # D5: 4,8 => UNS * INC # E5: 6,7 => UNS * INC # E5: 4 => UNS * INC # H7: 2,5 => UNS * INC # H7: 8 => UNS * INC # A8: 2,5 => UNS * INC # A8: 4,9 => UNS * INC # G9: 2,3 => UNS * INC # G9: 4,9 => UNS * INC # H2: 2,3 => UNS * INC # H3: 2,3 => UNS * INC # H2: 1,3 # H3: 1,3 => UNS * INC # H2: 1,3 # H3: 2 => UNS * INC # H2: 1,3 # H3: 1,3 => UNS * INC # H2: 1,3 # H3: 2 => UNS * INC # H2: 1,3 # I1: 4,9 => UNS * INC # H2: 1,3 # I3: 4,9 => UNS * INC # H2: 1,3 # A2: 4,9 => UNS * INC # H2: 1,3 # F2: 4,9 => UNS * INC # H2: 1,3 # A4: 5,7 => UNS * INC # H2: 1,3 # A4: 2,9 => UNS * INC # H2: 1,3 # C6: 4,8 => UNS * INC # H2: 1,3 # C6: 2,9 => UNS * INC # H2: 1,3 # D5: 4,8 => UNS * INC # H2: 1,3 # D5: 6,7 => UNS * INC # H2: 1,3 # G4: 3,8 => UNS * INC # H2: 1,3 # G4: 7 => UNS * INC # H2: 1,3 # G4: 7,8 => UNS * INC # H2: 1,3 # G4: 3 => UNS * INC # H2: 1,3 # D6: 7,8 => UNS * INC # H2: 1,3 # D6: 2,4,9 => UNS * INC # H2: 1,3 # D5: 6,7 => UNS * INC # H2: 1,3 # D5: 4,8 => UNS * INC # H2: 1,3 # E5: 6,7 => UNS * INC # H2: 1,3 # E5: 4 => UNS * INC # H2: 1,3 # G9: 2,3 => UNS * INC # H2: 1,3 # G9: 4,9 => UNS * INC # H2: 1,3 # H3: 2,3 => UNS * INC # H2: 1,3 # H3: 1 => UNS * INC # H2: 1,3 => UNS * INC # H2: 2,6 # G2: 2,6 => UNS * INC # H2: 2,6 # G2: 3 => UNS * INC # H2: 2,6 # I1: 4,9 => UNS * INC # H2: 2,6 # I2: 4,9 => UNS * INC # H2: 2,6 # C3: 4,9 => UNS * INC # H2: 2,6 # E3: 4,9 => UNS * INC # H2: 2,6 # A4: 5,7 => UNS * INC # H2: 2,6 # A4: 2,9 => UNS * INC # H2: 2,6 # C5: 4,5 => UNS * INC # H2: 2,6 # C5: 8 => UNS * INC # H2: 2,6 # G4: 3,8 => UNS * DIS # H2: 2,6 # G4: 7 => CTR => G4: 3,8 * INC # H2: 2,6 + G4: 3,8 # D5: 6,7 => UNS * INC # H2: 2,6 + G4: 3,8 # D5: 4,8 => UNS * INC # H2: 2,6 + G4: 3,8 # E5: 6,7 => UNS * INC # H2: 2,6 + G4: 3,8 # E5: 4 => UNS * INC # H2: 2,6 + G4: 3,8 # H7: 2,5 => UNS * INC # H2: 2,6 + G4: 3,8 # H7: 8 => UNS * INC # H2: 2,6 + G4: 3,8 # A8: 2,5 => UNS * INC # H2: 2,6 + G4: 3,8 # A8: 4,9 => UNS * INC # H2: 2,6 + G4: 3,8 # G2: 2,6 => UNS * INC # H2: 2,6 + G4: 3,8 # G2: 3 => UNS * INC # H2: 2,6 + G4: 3,8 # I1: 4,9 => UNS * INC # H2: 2,6 + G4: 3,8 # I2: 4,9 => UNS * INC # H2: 2,6 + G4: 3,8 # C3: 4,9 => UNS * INC # H2: 2,6 + G4: 3,8 # E3: 4,9 => UNS * INC # H2: 2,6 + G4: 3,8 # A4: 5,7 => UNS * PRF # H2: 2,6 + G4: 3,8 # A4: 2,9 => SOL * STA # H2: 2,6 + G4: 3,8 + A4: 2,9 * CNT 79 HDP CHAINS / 80 HYP OPENED