How to solve difficult sudoku?

Question

Algorithms

The problem is that I can not understand the principles of solving the puzzle without using the enumeration method, because I try to solve the problem without making mistakes.

The screenshots show two different puzzles that led to a dead end:

Answer 1

It is necessary to look for the "convergence" (the exact position of any one digit) of two or more digits after the occurrence of uncertainty.
Step by step:
1. Put down the number until there is uncertainty.
2. Move on to another, and so on.
3. Repeat item 1.
I.e., as it were, "fold the discrepancies into a spiral."
Profit!

Answer 2

And who told you that difficult sudoku should be solved without busting?
A person in his mind can figure out "if this figure is here, then ..." a few steps ahead, keeping each of them in memory.
The machine does the same by overkill. This is fine.
Another thing is that if you are making a program for compiling Sudoku, you should rely on a human to solve it - which means that you still need to avoid the need for deep enumeration.

Answer 3

Depth search with mini-max. The same goes for chess and checkers and tic-tac-toe. Only the limiters on where you can put the next figure change. The main core of the search algorithm is the generic. A generalized algorithm, if I may say so.

Answer 4

There is a similar problem for the simpler 6 by 6 Sudoku.
I'd love to hear ideas for the next move.