In the distributional Twenty Questions game, Bob chooses a number x from 1 to n according to a distribution µ, and Alice (who knows µ) attempts to identify x using Yes/No questions, which Bob answers truthfully. Her goal is to minimize the expected number of questions.The optimal strategy for the Twenty Questions game corresponds to a Huffman code for µ, yet this strategy could potentially uses all 2 n possible questions. Dagan et al. constructed a set of 1.25 n+o(n) questions which suffice to construct an optimal strategy for all µ, and showed that this number is optimal (up to sub-exponential factors) for infinitely many n.We determine the optimal size of such a set of questions for all n (up to sub-exponential factors), answering an open question of Dagan et al. In addition, we generalize the results of Dagan et al. to the d-ary setting, obtaining similar results with 1.25 replaced by 1 + (d − 1)/d d/(d−1) .