Backtracking with conditions (narrow the results)

Hi all!
I have a question, (I don’t know how to do something)
How do I make bactracking with conditions, like I want to make a large number backtracking (more dimensions) but with conditions so I narrow the results (something like sudoku solving), for reaching faster desired result.
I see I have

Permutations[]

What any other functions related to combinatorics with parameters and arguments are there?