Analysis of xx-mith-te3-00041536-base.sdk
Contents
Original Sudoku
level: hard
position: ..34.6..94.7.89..669.37......6.48...8........9.47.3...3.9...827.....796.......51. initial
Autosolve
position: ..34.6..94.7.89..669.37......6.48.9.8........9.47.36..3.9...827.....796.......51. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B4: 1,2,5 => CTR => B4: 3,7 * DIS # B4: 1,2,5 => CTR => B4: 3,7 * DIS # B9: 2,7 => CTR => B9: 4,6,8 * DIS # B9: 2,8 => CTR => B9: 4,6,7 * CNT 4 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B4: 1,2,5 => CTR => B4: 3,7 * DIS B4: 3,7 # B9: 2,8 => CTR => B9: 4,6 * STA B4: 3,7 + B9: 4,6 * CNT 2 HDP CHAINS / 59 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: ..34.6..94.7.89..669.37......6.48.9.8........9.47.36..3.9...827.....796.7.....51. pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Pair Reduction
Time used: 0:00:06.574856
The following important HDP chains were detected:
* PRF # H1: 5,8 # B1: 1,2 => SOL * STA # H1: 5,8 + B1: 1,2 * CNT 1 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..34.6..94.7.89..669.37......6.48...8........9.47.3...3.9...827.....796.......51. | initial |
| ..34.6..94.7.89..669.37......6.48.9.8........9.47.36..3.9...827.....796.......51. | autosolve |
| ..34.6..94.7.89..669.37......6.48.9.8........9.47.36..3.9...827.....796.7.....51. | pair_reduction |
| 123456789457189236698372145276548391835961472914723658349615827581237964762894513 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (12) H2: 3,5 I3: 5,8 B5: 3,7 D5: 6,9 E5: 6,9 G4: 3,7 H6: 5,8 A9: 2,7 C9: 2,8 F9: 2,4 I8: 3,4 I9: 3,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G2,H2: 3.. / G2 = 3 => 10 pairs (_) / H2 = 3 => 13 pairs (_) B4,B5: 3.. / B4 = 3 => 12 pairs (_) / B5 = 3 => 12 pairs (_) E8,E9: 3.. / E8 = 3 => 13 pairs (_) / E9 = 3 => 12 pairs (_) I8,I9: 3.. / I8 = 3 => 12 pairs (_) / I9 = 3 => 13 pairs (_) B4,G4: 3.. / B4 = 3 => 12 pairs (_) / G4 = 3 => 12 pairs (_) E8,I8: 3.. / E8 = 3 => 13 pairs (_) / I8 = 3 => 12 pairs (_) E9,I9: 3.. / E9 = 3 => 12 pairs (_) / I9 = 3 => 13 pairs (_) H2,H5: 3.. / H2 = 3 => 13 pairs (_) / H5 = 3 => 10 pairs (_) G3,H3: 4.. / G3 = 4 => 17 pairs (_) / H3 = 4 => 14 pairs (_) G5,H5: 4.. / G5 = 4 => 14 pairs (_) / H5 = 4 => 17 pairs (_) F7,F9: 4.. / F7 = 4 => 16 pairs (_) / F9 = 4 => 12 pairs (_) I8,I9: 4.. / I8 = 4 => 13 pairs (_) / I9 = 4 => 12 pairs (_) B7,F7: 4.. / B7 = 4 => 12 pairs (_) / F7 = 4 => 16 pairs (_) B8,I8: 4.. / B8 = 4 => 12 pairs (_) / I8 = 4 => 13 pairs (_) G3,G5: 4.. / G3 = 4 => 17 pairs (_) / G5 = 4 => 14 pairs (_) H3,H5: 4.. / H3 = 4 => 14 pairs (_) / H5 = 4 => 17 pairs (_) D5,E5: 6.. / D5 = 6 => 11 pairs (_) / E5 = 6 => 12 pairs (_) B7,B9: 6.. / B7 = 6 => 15 pairs (_) / B9 = 6 => 12 pairs (_) G1,H1: 7.. / G1 = 7 => 12 pairs (_) / H1 = 7 => 14 pairs (_) A9,B9: 7.. / A9 = 7 => 12 pairs (_) / B9 = 7 => 0 pairs (X) A4,A9: 7.. / A4 = 7 => 0 pairs (X) / A9 = 7 => 12 pairs (_) H1,H5: 7.. / H1 = 7 => 14 pairs (_) / H5 = 7 => 12 pairs (_) B1,C3: 8.. / B1 = 8 => 13 pairs (_) / C3 = 8 => 15 pairs (_) H6,I6: 8.. / H6 = 8 => 12 pairs (_) / I6 = 8 => 18 pairs (_) D8,D9: 8.. / D8 = 8 => 12 pairs (_) / D9 = 8 => 12 pairs (_) B1,H1: 8.. / B1 = 8 => 13 pairs (_) / H1 = 8 => 15 pairs (_) I3,I6: 8.. / I3 = 8 => 12 pairs (_) / I6 = 8 => 18 pairs (_) D5,E5: 9.. / D5 = 9 => 12 pairs (_) / E5 = 9 => 11 pairs (_) D9,E9: 9.. / D9 = 9 => 11 pairs (_) / E9 = 9 => 12 pairs (_) D5,D9: 9.. / D5 = 9 => 12 pairs (_) / D9 = 9 => 11 pairs (_) E5,E9: 9.. / E5 = 9 => 11 pairs (_) / E9 = 9 => 12 pairs (_) * DURATION: 0:00:10.118808 START: 13:48:40.201388 END: 13:48:50.320196 2025-04-04 * CP COUNT: (31) * CLUE FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:06.452679 START: 13:49:07.599432 END: 13:49:14.052111 2025-04-04 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00041536-base-pr-002.dot * REASONING * PRF # H1: 5,8 # B1: 1,2 => SOL * STA # H1: 5,8 + B1: 1,2 * CNT 1 HDP CHAINS / 29 HYP OPENED
Header Info
rating: 8613; r2: 333425; index: 41536
Solution
position: 123456789457189236698372145276548391835961472914723658349615827581237964762894513 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 # H1: 5,8 => UNS * INC # H3: 5,8 => UNS * INC # C3: 5,8 => UNS * INC # C3: 1,2 => UNS * INC # I6: 5,8 => UNS * INC # I6: 1,2 => UNS * INC # B4: 3,7 => UNS * DIS # B4: 1,2,5 => CTR => B4: 3,7 * INC # G5: 3,7 => UNS * INC # H5: 3,7 => UNS * INC # D9: 6,9 => UNS * INC # D9: 2,8 => UNS * INC # E9: 6,9 => UNS * INC # E9: 2,3 => UNS * INC # G5: 3,7 => UNS * INC # H5: 3,7 => UNS * INC # B4: 3,7 => UNS * DIS # B4: 1,2,5 => CTR => B4: 3,7 * INC # I6: 5,8 => UNS * INC # I6: 1,2 => UNS * INC # H1: 5,8 => UNS * INC # H3: 5,8 => UNS * DIS # B9: 2,7 => CTR => B9: 4,6,8 * INC # B9: 4,6,8 => UNS * INC # A4: 2,7 => UNS * INC # A4: 1,5 => UNS * INC # B8: 2,8 => UNS * INC # C8: 2,8 => UNS * DIS # B9: 2,8 => CTR => B9: 4,6,7 * INC # B9: 4,6,7 => UNS * INC # D9: 2,8 => UNS * INC # D9: 6,9 => UNS * INC # C3: 2,8 => UNS * INC # C3: 1,5 => UNS * INC # B9: 2,4 => UNS * INC # B9: 6,7,8 => UNS * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # H1: 5,8 => UNS * INC # H3: 5,8 => UNS * INC # C3: 5,8 => UNS * INC # C3: 1,2 => UNS * INC # I6: 5,8 => UNS * INC # I6: 1,2 => UNS * INC # B4: 3,7 => UNS * DIS # B4: 1,2,5 => CTR => B4: 3,7 * INC B4: 3,7 # G5: 3,7 => UNS * INC B4: 3,7 # H5: 3,7 => UNS * INC B4: 3,7 # D9: 6,9 => UNS * INC B4: 3,7 # D9: 2,8 => UNS * INC B4: 3,7 # E9: 6,9 => UNS * INC B4: 3,7 # E9: 2,3 => UNS * INC B4: 3,7 # G5: 3,7 => UNS * INC B4: 3,7 # H5: 3,7 => UNS * INC B4: 3,7 # I6: 5,8 => UNS * INC B4: 3,7 # I6: 1,2 => UNS * INC B4: 3,7 # H1: 5,8 => UNS * INC B4: 3,7 # H3: 5,8 => UNS * INC B4: 3,7 # B8: 2,8 => UNS * INC B4: 3,7 # C8: 2,8 => UNS * DIS B4: 3,7 # B9: 2,8 => CTR => B9: 4,6 * INC B4: 3,7 + B9: 4,6 # D9: 2,8 => UNS * INC B4: 3,7 + B9: 4,6 # D9: 6,9 => UNS * INC B4: 3,7 + B9: 4,6 # C3: 2,8 => UNS * INC B4: 3,7 + B9: 4,6 # C3: 1,5 => UNS * INC B4: 3,7 + B9: 4,6 # B8: 2,8 => UNS * INC B4: 3,7 + B9: 4,6 # C8: 2,8 => UNS * INC B4: 3,7 + B9: 4,6 # D9: 2,8 => UNS * INC B4: 3,7 + B9: 4,6 # D9: 6,9 => UNS * INC B4: 3,7 + B9: 4,6 # C3: 2,8 => UNS * INC B4: 3,7 + B9: 4,6 # C3: 1,5 => UNS * INC B4: 3,7 + B9: 4,6 # H1: 5,8 => UNS * INC B4: 3,7 + B9: 4,6 # H3: 5,8 => UNS * INC B4: 3,7 + B9: 4,6 # C3: 5,8 => UNS * INC B4: 3,7 + B9: 4,6 # C3: 1,2 => UNS * INC B4: 3,7 + B9: 4,6 # I6: 5,8 => UNS * INC B4: 3,7 + B9: 4,6 # I6: 1,2 => UNS * INC B4: 3,7 + B9: 4,6 # G5: 3,7 => UNS * INC B4: 3,7 + B9: 4,6 # H5: 3,7 => UNS * INC B4: 3,7 + B9: 4,6 # D9: 6,9 => UNS * INC B4: 3,7 + B9: 4,6 # D9: 2,8 => UNS * INC B4: 3,7 + B9: 4,6 # E9: 6,9 => UNS * INC B4: 3,7 + B9: 4,6 # E9: 2,3 => UNS * INC B4: 3,7 + B9: 4,6 # G5: 3,7 => UNS * INC B4: 3,7 + B9: 4,6 # H5: 3,7 => UNS * INC B4: 3,7 + B9: 4,6 # I6: 5,8 => UNS * INC B4: 3,7 + B9: 4,6 # I6: 1,2 => UNS * INC B4: 3,7 + B9: 4,6 # H1: 5,8 => UNS * INC B4: 3,7 + B9: 4,6 # H3: 5,8 => UNS * INC B4: 3,7 + B9: 4,6 # B7: 4,6 => UNS * INC B4: 3,7 + B9: 4,6 # B7: 1,5 => UNS * INC B4: 3,7 + B9: 4,6 # B8: 2,8 => UNS * INC B4: 3,7 + B9: 4,6 # C8: 2,8 => UNS * INC B4: 3,7 + B9: 4,6 # D9: 2,8 => UNS * INC B4: 3,7 + B9: 4,6 # D9: 6,9 => UNS * INC B4: 3,7 + B9: 4,6 # C3: 2,8 => UNS * INC B4: 3,7 + B9: 4,6 # C3: 1,5 => UNS * STA B4: 3,7 + B9: 4,6 * CNT 59 HDP CHAINS / 59 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # H1: 5,8 => UNS * INC # H3: 5,8 => UNS * INC # C3: 5,8 => UNS * INC # C3: 1,2 => UNS * INC # I6: 5,8 => UNS * INC # I6: 1,2 => UNS * INC # G5: 3,7 => UNS * INC # H5: 3,7 => UNS * INC # D9: 6,9 => UNS * INC # D9: 2,8 => UNS * INC # E9: 6,9 => UNS * INC # E9: 2,3 => UNS * INC # G5: 3,7 => UNS * INC # H5: 3,7 => UNS * INC # I6: 5,8 => UNS * INC # I6: 1,2 => UNS * INC # H1: 5,8 => UNS * INC # H3: 5,8 => UNS * INC # B7: 4,6 => UNS * INC # B7: 1,5 => UNS * INC # B8: 2,8 => UNS * INC # C8: 2,8 => UNS * INC # D9: 2,8 => UNS * INC # D9: 6,9 => UNS * INC # C3: 2,8 => UNS * INC # C3: 1,5 => UNS * INC # H1: 5,8 # B1: 5,8 => UNS * PRF # H1: 5,8 # B1: 1,2 => SOL * STA # H1: 5,8 + B1: 1,2 * CNT 28 HDP CHAINS / 29 HYP OPENED