[jacb]

It seems like a common misconception that humans have some secret power to solve undecidable problems that computers lack. But "this problem is undecidable in general" doesn't mean "computers cannot solve small instances of the problem", it means "there's no single algorithm that will correctly solve all instances of this problem". Typically undecidability results in language theory rely on embedding a Turing machine in the language and going "Turing machines halting is undecidable, therefore this is undecidable in general". But this only tells you that _some_ problem instances are undecidable (at least those that correspond to Turing machine embeddings, and probably many more). Smaller problems (that aren't big enough to be disguised Turing machines) can still be decidable, and I suspect that any problem simple enough to happen in an exam is decidable.

Another example of this: theorem-proving is undecidable, yet automated thoerem provers are definitely capable of solving simple problems. The undecidability result means that any given automated theorem provers isn't capable of proving the truth/falsity of all statements. But this isn't some crazy limitation - this is true of humans as well. You can solve some math problems, but if someone showed up with an exabyte-long statement about how a problem-solver-who-is-identical-to-you-in-every-capability solves problems and asked you to prove it, obviously you wouldn't be able to do that.

[yters]

What I said is compatible with what you say.