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So, what does it mean exactly when they say that these kinds of problems are in the same class as Sudoku?


Simulated annealing and similar techniques such as Tabu Search are good for problems that have large search spaces due to combinatorial explosion (https://en.wikipedia.org/wiki/Combinatorial_explosion) and can be expressed as a state and an associated cost/fitness function.


This is true provided your cost function is "continuous" w.r.t. distance. Roughly what this means is that if you make a small change - e.g. one edit in this example - then your cost function shouldn't change a lot.

If you don't have some form of continuity condition you are actually just doing random search.



both problems have constraints and you solve the puzzle by finding the right configuration of data that meets the constraints.


They're both examples of an exact cover problem: https://en.wikipedia.org/wiki/Exact_cover




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