Analysis of xx-mith-te3-00045517-base.sdk
Contents
Original Sudoku
level: hard
position: 1.3.567...57.8....68...75...68.71..3.........5.183.........389.......1.4.16....75 initial
Autosolve
position: 1.3.567...57.8....68...75...68.71.53.........5.183...7....1389.......1.4.16....75 autosolve
Pair Reduction Variants
Deep Pair Reduction
Time used: 0:00:10.912221
The following important HDP chains were detected:
* PRF # H2: 1,3 # E8: 9 => SOL * STA # H2: 1,3 + E8: 9 * CNT 1 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.3.567...57.8....68...75...68.71..3.........5.183.........389.......1.4.16....75 | initial |
| 1.3.567...57.8....68...75...68.71.53.........5.183...7....1389.......1.4.16....75 | autosolve |
| 123456789457189236689327541268971453374562918591834627745613892832795164916248375 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (9) D2: 1,3 D3: 1,3 A5: 3,7 B5: 3,7 D5: 5,6 H5: 1,8 I5: 1,8 I7: 2,6 G9: 2,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,D3: 1.. / D2 = 1 => 7 pairs (_) / D3 = 1 => 8 pairs (_) H5,I5: 1.. / H5 = 1 => 8 pairs (_) / I5 = 1 => 10 pairs (_) D2,D3: 3.. / D2 = 3 => 8 pairs (_) / D3 = 3 => 7 pairs (_) A5,B5: 3.. / A5 = 3 => 8 pairs (_) / B5 = 3 => 11 pairs (_) H8,G9: 3.. / H8 = 3 => 18 pairs (_) / G9 = 3 => 9 pairs (_) D3,H3: 3.. / D3 = 3 => 7 pairs (_) / H3 = 3 => 8 pairs (_) A9,G9: 3.. / A9 = 3 => 18 pairs (_) / G9 = 3 => 9 pairs (_) B5,B8: 3.. / B5 = 3 => 11 pairs (_) / B8 = 3 => 8 pairs (_) G2,G9: 3.. / G2 = 3 => 18 pairs (_) / G9 = 3 => 9 pairs (_) D5,F5: 5.. / D5 = 5 => 15 pairs (_) / F5 = 5 => 12 pairs (_) C7,C8: 5.. / C7 = 5 => 11 pairs (_) / C8 = 5 => 11 pairs (_) C7,D7: 5.. / C7 = 5 => 11 pairs (_) / D7 = 5 => 11 pairs (_) F5,F8: 5.. / F5 = 5 => 12 pairs (_) / F8 = 5 => 15 pairs (_) D5,E5: 6.. / D5 = 6 => 12 pairs (_) / E5 = 6 => 15 pairs (_) G6,H6: 6.. / G6 = 6 => 10 pairs (_) / H6 = 6 => 12 pairs (_) I7,H8: 6.. / I7 = 6 => 12 pairs (_) / H8 = 6 => 14 pairs (_) D7,I7: 6.. / D7 = 6 => 14 pairs (_) / I7 = 6 => 12 pairs (_) E5,E8: 6.. / E5 = 6 => 15 pairs (_) / E8 = 6 => 12 pairs (_) G2,G6: 6.. / G2 = 6 => 12 pairs (_) / G6 = 6 => 10 pairs (_) I2,I7: 6.. / I2 = 6 => 14 pairs (_) / I7 = 6 => 12 pairs (_) A5,B5: 7.. / A5 = 7 => 11 pairs (_) / B5 = 7 => 8 pairs (_) D7,D8: 7.. / D7 = 7 => 18 pairs (_) / D8 = 7 => 10 pairs (_) H1,I1: 8.. / H1 = 8 => 8 pairs (_) / I1 = 8 => 10 pairs (_) H5,I5: 8.. / H5 = 8 => 10 pairs (_) / I5 = 8 => 8 pairs (_) A8,A9: 8.. / A8 = 8 => 9 pairs (_) / A9 = 8 => 12 pairs (_) F8,F9: 8.. / F8 = 8 => 12 pairs (_) / F9 = 8 => 9 pairs (_) A8,F8: 8.. / A8 = 8 => 9 pairs (_) / F8 = 8 => 12 pairs (_) A9,F9: 8.. / A9 = 8 => 12 pairs (_) / F9 = 8 => 9 pairs (_) H1,H5: 8.. / H1 = 8 => 8 pairs (_) / H5 = 8 => 10 pairs (_) I1,I5: 8.. / I1 = 8 => 10 pairs (_) / I5 = 8 => 8 pairs (_) * DURATION: 0:00:11.441921 START: 08:18:23.426009 END: 08:18:34.867930 2025-04-06 * CP COUNT: (30) * INCONCLUSIVE * DEEP PAIR REDUCTION * DURATION: 0:00:10.756633 START: 08:18:43.257172 END: 08:18:54.013805 2025-04-06 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00045517-base-pr-002.dot * REASONING * PRF # H2: 1,3 # E8: 9 => SOL * STA # H2: 1,3 + E8: 9 * CNT 1 HDP CHAINS / 35 HYP OPENED
Header Info
rating: 9458; r2: 191936; index: 45517
Solution
position: 123456789457189236689327541268971453374562918591834627745613892832795164916248375 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: 2,4,6 => UNS * INC # H3: 1,3 => UNS * INC # H3: 2,4 => UNS * INC # A8: 3,7 => UNS * INC # A8: 2,8,9 => UNS * INC # B8: 3,7 => UNS * INC # B8: 2,9 => UNS * INC # D7: 5,6 => UNS * INC # D8: 5,6 => UNS * INC # H8: 2,6 => UNS * INC # H8: 3 => UNS * INC # I2: 2,6 => UNS * INC # I2: 1,9 => UNS * INC # H8: 2,3 => UNS * INC # H8: 6 => UNS * INC # A9: 2,3 => UNS * INC # A9: 8,9 => UNS * INC # G2: 2,3 => UNS * INC # G2: 4,6 => UNS * CNT 20 HDP CHAINS / 20 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # H2: 1,3 => UNS * INC # H2: 2,4,6 => UNS * INC # H3: 1,3 => UNS * INC # H3: 2,4 => UNS * INC # A8: 3,7 => UNS * INC # A8: 2,8,9 => UNS * INC # B8: 3,7 => UNS * INC # B8: 2,9 => UNS * INC # D7: 5,6 => UNS * INC # D8: 5,6 => UNS * INC # H8: 2,6 => UNS * INC # H8: 3 => UNS * INC # I2: 2,6 => UNS * INC # I2: 1,9 => UNS * INC # H8: 2,3 => UNS * INC # H8: 6 => UNS * INC # A9: 2,3 => UNS * INC # A9: 8,9 => UNS * INC # G2: 2,3 => UNS * INC # G2: 4,6 => UNS * CNT 20 HDP CHAINS / 20 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # H2: 1,3 => UNS * INC # H2: 2,4,6 => UNS * INC # H3: 1,3 => UNS * INC # H3: 2,4 => UNS * INC # A8: 3,7 => UNS * INC # A8: 2,8,9 => UNS * INC # B8: 3,7 => UNS * INC # B8: 2,9 => UNS * INC # D7: 5,6 => UNS * INC # D8: 5,6 => UNS * INC # H8: 2,6 => UNS * INC # H8: 3 => UNS * INC # I2: 2,6 => UNS * INC # I2: 1,9 => UNS * INC # H8: 2,3 => UNS * INC # H8: 6 => UNS * INC # A9: 2,3 => UNS * INC # A9: 8,9 => UNS * INC # G2: 2,3 => UNS * INC # G2: 4,6 => UNS * INC # H2: 1,3 # H3: 1,3 => UNS * INC # H2: 1,3 # H3: 2,4 => UNS * INC # H2: 1,3 # H3: 1,3 => UNS * INC # H2: 1,3 # H3: 2,4 => UNS * INC # H2: 1,3 # A8: 3,7 => UNS * INC # H2: 1,3 # A8: 2,8,9 => UNS * INC # H2: 1,3 # B8: 3,7 => UNS * INC # H2: 1,3 # B8: 2,9 => UNS * INC # H2: 1,3 # D7: 5,6 => UNS * INC # H2: 1,3 # D8: 5,6 => UNS * INC # H2: 1,3 # I2: 2,6 => UNS * INC # H2: 1,3 # I2: 9 => UNS * INC # H2: 1,3 # E8: 2,6 => UNS * PRF # H2: 1,3 # E8: 9 => SOL * STA # H2: 1,3 + E8: 9 * CNT 34 HDP CHAINS / 35 HYP OPENED