Hmm. I actually wonder is such a question would be good to include in a human exam, since knowing the question is possible does somewhat impact your reasoning. And, often the answer works out to some nice round numbers…

Of course, it is also not unheard of for a question to be impossible because of an error by the test writer. Which can easily be cleared up. So it is probably best not to have impossible questions, because then students will be looking for reasons to declare the question impossible.