I found Wntrmute's tactics quite similiar to what's going on in my troubled head solving the damn sudoku of the day, but I noticed one thing missing... The tactic I usually leave to the super-duper complicated puzzles, just before the guessing part of "proof by contradiction".
I call it by its lame title:
A row's safe value
It goes like this. Suppose we've tried all the other tactics over and over again. Now we have, in some box, a value that can only populate two or three cells, which happen to be on the same row or column.
I'll demonstrate:
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|(1,4,6): 3 : (1,7,9) |
| 2 : (4,6,8) : (7,9) |
|(1,4,8): (4,5,8) : (1,5,7) |
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You can see here that 5 could only exist in the two right cells of the bottom row. This could happen for many reasons, but what's important right now is that you can conclude that no 5s could exist in the same row... Eliminate the options of the other cells in this row and it might be the trick to finding your next number.
The same goes for 7 and 9 in my almost-impossible example.
This one tactic helped me solve some serious sudoku puzzles without having to take guesses. So there you go. Off with your Sudoku.