There are some problems for which the number of possible outcomes is not that big, so it makes sense to try all of them, one by one, till the correct outcome is reached. Even if you skipped combinations that were not grammatical, or made no sense, you would still be faced with a stupendously large number of possible combinations. So if the strategy for solving a problem is combinatorial, trying out all the possibilities one by one, you can be pretty sure that's not the way the mind does it.
Mental models are possible for other problems too, for example, logical ones.
Well there are several, but few of them are interesting. One conclusion is that no acrobat is a botanist. Another is that no botanist is an acrobat. Another is that no one is both a acrobat and a botanist. You see how it works, though.