“The puzzle. Three gods A, B, and C are called, in some order, ‘True’, ‘False’, and ‘Random’. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for ‘yes’ and ‘no’ are ‘da’ and ‘ja’, in some order. You do not know which word means which”.
A simple solution to the hardest logic puzzle ever, © Brian Rabern & Landon Rabern, Analysis 68 (2), April 2008, pp. 105–112.
Also, Why the hardest logic puzzle ever cannot be solved in less than three questions, Gregory Wheeler & Pedro Barahona
There’s one other referenced paper, How to solve the hardest logic puzzle ever in two questions, Gabriel Uzquiano, Analysis, 70 (1), 39-44, that’s behind paywalls but is anonymously posted here http://mesosyn.com/mental1-5b3.pdf
(oh, The apparent paradox is resolved I think.)