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May 2016 I'm Thinking of a Number $\ldots$
Adam Hammett, Greg Oman
Missouri J. Math. Sci. 28(1): 31-48 (May 2016). DOI: 10.35834/mjms/1474295354


Consider the following game: Player A chooses an integer $\alpha$ between $1$ and $n$ for some integer $n\geq1$, but does not reveal $\alpha$ 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 ($m\geq 1$), Player B must attempt to guess the number chosen by Player A. Player B wins if she guesses $\alpha$. The purpose of this note is to find, for every $m\geq 1$, 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).


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Adam Hammett. Greg Oman. "I'm Thinking of a Number $\ldots$." Missouri J. Math. Sci. 28 (1) 31 - 48, May 2016.


Published: May 2016
First available in Project Euclid: 19 September 2016

zbMATH: 06647877
MathSciNet: MR3549806
Digital Object Identifier: 10.35834/mjms/1474295354

Primary: 03B05
Secondary: 60B99

Keywords: conditional probability , event , Probability

Rights: Copyright © 2016 Central Missouri State University, Department of Mathematics and Computer Science


Vol.28 • No. 1 • May 2016
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