The reason that it is impossible is that there is no possible set of answers that would require the test-giver to acknowledge that a test-taker passed the test. Anyone the test-taker does not like can be failed.
Most notably, pilot examinations for aviation and maritime certifications.
I think they use these types of questions to exclude rule memorisation and test the ability to reason about the intention or relevant effects of rules and principles of the art involved.
It seems like the intention is also to penalise the inability to reason about ambiguous situations, ensure that the subject can effectively divide attention (if you spend too much time focusing on these ambiguous situations trying to find a nonexistent perfect answer you will fail the test), and to filter out low cognitive ability in general.
I’m not a test design expert, however, so ymmv.