Three gods, three answers, and you don't even know their words for yes and no
Three gods, A, B and C, are called (in some order) True, False and Random — True always answers truthfully, False always answers falsely, and Random answers truthfully or falsely at random. You must identify which god is which by asking three yes/no questions, one at a time, to any god — but the gods answer in their own language, using the words 'da' and 'ja' for yes and no, and you don't know which word means which.
Reveal the answer
It's solvable, though the shortest known solutions use questions that predict what a god would answer to a different question, cancelling out both the randomness of Random and the unknown meaning of 'da' and 'ja' at once. Logician George Boolos published it in 1996, crediting the underlying idea to Raymond Smullyan's knights-and-knaves puzzles, and titled it — without much modesty — 'The Hardest Logic Puzzle Ever.'
— George Boolos, The Hardest Logic Puzzle Ever — The Harvard Review of Philosophy, 1996