Analysis of xx-mith-te3-00107127-base.sdk
Contents
Original Sudoku
level: hard
position: 12..5.7...571..2..6.927.5.......16.8.16...92....6...4......7....719.2.5.96.5..... initial
Autosolve
position: 12..5.7...571..2..6.927.5.......16.8.16...92....6...4......7....719.2.5.96.5..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H9: 1 => CTR => H9: 3,7 * DIS # H7: 3,6 => CTR => H7: 1,9 * DIS # I7: 3,6 => CTR => I7: 1,2,9 * CNT 3 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 # H9: 1 => CTR => H9: 3,7 * STA H9: 3,7 * CNT 1 HDP CHAINS / 18 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: 12..5.7...571..2..6.927.5.......16.8.16...92....6...4.....67....719.2.5696.51.... pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Pair Reduction
Time used: 0:00:09.805011
The following important HDP chains were detected:
* DIS # A4: 3,7 # C1: 3,8 => CTR => C1: 4 * DIS # A4: 3,7 + C1: 4 # H2: 8 => CTR => H2: 6,9 * DIS # A4: 3,7 + C1: 4 + H2: 6,9 # E8: 3,8 => CTR => E8: 4 * DIS # A4: 3,7 + C1: 4 + H2: 6,9 + E8: 4 # H1: 6,9 => CTR => H1: 8 * DIS # A4: 3,7 + C1: 4 + H2: 6,9 + E8: 4 + H1: 8 => CTR => A4: 2,4,5 * PRF A4: 2,4,5 # D4: 3,7 # I6: 1 => SOL * STA A4: 2,4,5 # D4: 3,7 + I6: 1 * CNT 6 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 12..5.7...571..2..6.927.5.......16.8.16...92....6...4......7....719.2.5.96.5..... | initial |
| 12..5.7...571..2..6.927.5.......16.8.16...92....6...4......7....719.2.5.96.5..... | autosolve |
| 12..5.7...571..2..6.927.5.......16.8.16...92....6...4.....67....719.2.5696.51.... | pair_reduction |
| 123456789457189263689273514245391678316748925798625341534867192871932456962514837 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (3) H4: 3,7 G6: 1,3 I8: 3,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H3,I3: 1.. / H3 = 1 => 9 pairs (_) / I3 = 1 => 13 pairs (_) G6,I6: 1.. / G6 = 1 => 9 pairs (_) / I6 = 1 => 13 pairs (_) E7,E9: 1.. / E7 = 1 => 0 pairs (X) / E9 = 1 => 7 pairs (_) E4,E6: 2.. / E4 = 2 => 4 pairs (_) / E6 = 2 => 7 pairs (_) I7,I9: 2.. / I7 = 2 => 13 pairs (_) / I9 = 2 => 9 pairs (_) C9,I9: 2.. / C9 = 2 => 13 pairs (_) / I9 = 2 => 9 pairs (_) A4,C4: 5.. / A4 = 5 => 3 pairs (_) / C4 = 5 => 4 pairs (_) F5,F6: 5.. / F5 = 5 => 7 pairs (_) / F6 = 5 => 7 pairs (_) I5,I6: 5.. / I5 = 5 => 7 pairs (_) / I6 = 5 => 7 pairs (_) A7,C7: 5.. / A7 = 5 => 4 pairs (_) / C7 = 5 => 3 pairs (_) F5,I5: 5.. / F5 = 5 => 7 pairs (_) / I5 = 5 => 7 pairs (_) F6,I6: 5.. / F6 = 5 => 7 pairs (_) / I6 = 5 => 7 pairs (_) A4,A7: 5.. / A4 = 5 => 3 pairs (_) / A7 = 5 => 4 pairs (_) C4,C7: 5.. / C4 = 5 => 4 pairs (_) / C7 = 5 => 3 pairs (_) F1,F2: 6.. / F1 = 6 => 3 pairs (_) / F2 = 6 => 3 pairs (_) E7,E8: 6.. / E7 = 6 => 7 pairs (_) / E8 = 6 => 0 pairs (X) E8,I8: 6.. / E8 = 6 => 0 pairs (X) / I8 = 6 => 7 pairs (_) D4,D5: 7.. / D4 = 7 => 8 pairs (_) / D5 = 7 => 7 pairs (_) H9,I9: 7.. / H9 = 7 => 9 pairs (_) / I9 = 7 => 13 pairs (_) A6,I6: 7.. / A6 = 7 => 5 pairs (_) / I6 = 7 => 12 pairs (_) H4,H9: 7.. / H4 = 7 => 13 pairs (_) / H9 = 7 => 9 pairs (_) B4,B6: 9.. / B4 = 9 => 4 pairs (_) / B6 = 9 => 10 pairs (_) H7,I7: 9.. / H7 = 9 => 3 pairs (_) / I7 = 9 => 13 pairs (_) B4,E4: 9.. / B4 = 9 => 4 pairs (_) / E4 = 9 => 10 pairs (_) * DURATION: 0:00:06.532945 START: 02:35:46.020109 END: 02:35:52.553054 2025-04-05 * CP COUNT: (24) * CLUE FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:09.654242 START: 02:35:59.009215 END: 02:36:08.663457 2025-04-05 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00107127-base-pr-002.dot * REASONING * DIS # A4: 3,7 # C1: 3,8 => CTR => C1: 4 * DIS # A4: 3,7 + C1: 4 # H2: 8 => CTR => H2: 6,9 * DIS # A4: 3,7 + C1: 4 + H2: 6,9 # E8: 3,8 => CTR => E8: 4 * DIS # A4: 3,7 + C1: 4 + H2: 6,9 + E8: 4 # H1: 6,9 => CTR => H1: 8 * DIS # A4: 3,7 + C1: 4 + H2: 6,9 + E8: 4 + H1: 8 => CTR => A4: 2,4,5 * PRF A4: 2,4,5 # D4: 3,7 # I6: 1 => SOL * STA A4: 2,4,5 # D4: 3,7 + I6: 1 * CNT 6 HDP CHAINS / 36 HYP OPENED
Header Info
rating: 26893; r2: 724815; index: 107127
Solution
position: 123456789457189263689273514245391678316748925798625341534867192871932456962514837 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 # I5: 3,7 => UNS * INC # I6: 3,7 => UNS * INC # A4: 3,7 => UNS * INC # D4: 3,7 => UNS * INC # H9: 3,7 => UNS * DIS # H9: 1 => CTR => H9: 3,7 * INC # I6: 1,3 => UNS * INC # I6: 5,7 => UNS * INC # G7: 1,3 => UNS * INC # G9: 1,3 => UNS * DIS # H7: 3,6 => CTR => H7: 1,9 * INC # H7: 1,9 => UNS * DIS # I7: 3,6 => CTR => I7: 1,2,9 * INC # I7: 1,2,9 => UNS * INC # E8: 3,6 => UNS * INC # E8: 4,8 => UNS * INC # I1: 3,6 => UNS * INC # I2: 3,6 => UNS * CNT 18 HDP CHAINS / 18 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # I5: 3,7 => UNS * INC # I6: 3,7 => UNS * INC # A4: 3,7 => UNS * INC # D4: 3,7 => UNS * INC # H9: 3,7 => UNS * DIS # H9: 1 => CTR => H9: 3,7 * INC H9: 3,7 # A4: 3,7 => UNS * INC H9: 3,7 # D4: 3,7 => UNS * INC H9: 3,7 # G7: 1,3 => UNS * INC H9: 3,7 # G7: 4,8 => UNS * INC H9: 3,7 # A4: 3,7 => UNS * INC H9: 3,7 # D4: 3,7 => UNS * INC H9: 3,7 # I6: 5,7 => UNS * INC H9: 3,7 # I6: 1 => UNS * INC H9: 3,7 # G7: 1,3 => UNS * INC H9: 3,7 # G7: 4,8 => UNS * INC H9: 3,7 # I7: 1,9 => UNS * INC H9: 3,7 # I7: 2 => UNS * STA H9: 3,7 * CNT 18 HDP CHAINS / 18 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # A4: 3,7 => UNS * INC # D4: 3,7 => UNS * INC # I6: 5,7 => UNS * INC # I6: 1 => UNS * INC # G7: 1,3 => UNS * INC # G7: 4,8 => UNS * INC # I7: 1,9 => UNS * INC # I7: 2 => UNS * DIS # A4: 3,7 # C1: 3,8 => CTR => C1: 4 * INC # A4: 3,7 + C1: 4 # E2: 3,8 => UNS * INC # A4: 3,7 + C1: 4 # E2: 4 => UNS * INC # A4: 3,7 + C1: 4 # E2: 3,8 => UNS * INC # A4: 3,7 + C1: 4 # F3: 3,8 => UNS * INC # A4: 3,7 + C1: 4 # H1: 6,9 => UNS * INC # A4: 3,7 + C1: 4 # H1: 8 => UNS * INC # A4: 3,7 + C1: 4 # H2: 6,9 => UNS * DIS # A4: 3,7 + C1: 4 # H2: 8 => CTR => H2: 6,9 * INC # A4: 3,7 + C1: 4 + H2: 6,9 # E2: 3,8 => UNS * DIS # A4: 3,7 + C1: 4 + H2: 6,9 # E8: 3,8 => CTR => E8: 4 * DIS # A4: 3,7 + C1: 4 + H2: 6,9 + E8: 4 # H1: 6,9 => CTR => H1: 8 * DIS # A4: 3,7 + C1: 4 + H2: 6,9 + E8: 4 + H1: 8 => CTR => A4: 2,4,5 * INC A4: 2,4,5 # D4: 3,7 => UNS * INC A4: 2,4,5 # D4: 4 => UNS * INC A4: 2,4,5 # I6: 5,7 => UNS * INC A4: 2,4,5 # I6: 1 => UNS * INC A4: 2,4,5 # G7: 1,3 => UNS * INC A4: 2,4,5 # G7: 4,8 => UNS * INC A4: 2,4,5 # I7: 1,9 => UNS * INC A4: 2,4,5 # I7: 2 => UNS * INC A4: 2,4,5 # D4: 3,7 # E4: 4,9 => UNS * INC A4: 2,4,5 # D4: 3,7 # E4: 2 => UNS * INC A4: 2,4,5 # D4: 3,7 # D5: 3,7 => UNS * INC A4: 2,4,5 # D4: 3,7 # D5: 4,8 => UNS * INC A4: 2,4,5 # D4: 3,7 # I6: 5,7 => UNS * PRF A4: 2,4,5 # D4: 3,7 # I6: 1 => SOL * STA A4: 2,4,5 # D4: 3,7 + I6: 1 * CNT 35 HDP CHAINS / 36 HYP OPENED