An interesting and twisted version of the twenty question game came across recently. I saw it in the 2009 ISIT paper on the error correction under Feedback with list decoding, by Ofer Shayevitz.  The problem goes like this (I am going by the nice narration of Ofer with the famous Alice and Bob duo).

The game is being played by Alice and Bob. Alice selects one of $M$ possible objects, and Bob can ask $n$  binary questions (where the answer can be either  yes or no only), in a quest to identify the object selected. If Alice is always truthful, then $n=\lceil \log M \rceil$ questions are obviously both necessary and sufficient. Now, suppose Alice is allowed to lie up to $t$ times. How many questions $n(M, t)$ does Bob need to get the correct object? Alternatively, given $n$ questions, what is the maximal number of objects $M(n, t)$ that Bob can separate? This version of the “twenty questions game” with lies is known as Ulam’s game.