It is true that newer models that have ingested more training data are better at this kind of thing, but it is not because they are using logic, but because they are copying and following examples they already learnt, if that makes sense. I got the question from a test passed to kids ages 12-13, so arguably it wasn’t really that challenging. If you want to you can try out the more advanced problems from the same place I got it from, although it’s in Spanish, so pass it through Google Translate first.
If you turn to programmers they’ll tell you that AI usually makes mistakes no human would normally make such as inventing variables that don’t exist and that kind of thing. It is because in the examples it learnt from they have mostly existed.
What I mean to say is, if you give an AI a problem that is not in its training data and can only be solved using logic (so, you can’t apply what is used in other problems) it will be incapable of solving it. The Internet is so vast that almost everything has been written about so AIs will seem to know how to solve any problem, but it is no more than an illusion.
HOWEVER, if we manage to integrate AIs and normal, mathematical computation really closely so that they function as one, that problem might be solved. It will probably also have its caveats, though.