I'm Thinking of a Number …
Missouri Journal of Mathematical Sciences
Consider the following game: Player A chooses an integer α between 1 and n for some integer n≥1, but does not reveal α to Player B. Player B then asks Player A a yes/no question about which number Player A chose, after which Player A responds truthfully with either ``yes'' or ``no.'' After a predetermined number m of questions have been asked (m≥1), Player B must attempt to guess the number chosen by Player A. Player B wins if she guesses α. The purpose of this note is to find, for every m≥1, all canonical m-question algorithms which maximize the probability of Player B winning the game (the notion of ``canonical algorithm'' will be made precise in Section 3).
Hammett, Adam J. and Oman, Greg, "I'm Thinking of a Number …" (2016). Science and Mathematics Faculty Publications. 332.