Intelligence is the ability to craft a more optimal solution than a brute force approach would take.

In the domain of data compression, Kolmogorov complexity https://en.wikipedia.org/wiki/Kolmogorov_complexity is one of the approaches to try to measure that amount.

Guess-and-check is not the same as brute force (nor exhaustive search). No one is sitting there with an empty sudoku grid, filling the whole thing in with guessed numbers, checking to see if the solution is valid, then erasing everything and starting over. Literally no one does that, not even software sudoku solvers (it takes way too long).

Guess-and-check is literally just another name for backtracking algorithms. These do not work (for humans) without an adequate suite of rules that can be use to prune the search space.