## Missouri Journal of Mathematical Sciences

- Missouri J. Math. Sci.
- Volume 28, Issue 1 (2016), 31-48.

### I'm Thinking of a Number $\ldots$

#### Abstract

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).

#### Article information

**Source**

Missouri J. Math. Sci. Volume 28, Issue 1 (2016), 31-48.

**Dates**

First available in Project Euclid: 19 September 2016

**Permanent link to this document**

http://projecteuclid.org/euclid.mjms/1474295354

**Mathematical Reviews number (MathSciNet)**

MR3549806

**Zentralblatt MATH identifier**

06647877

**Subjects**

Primary: 03B05: Classical propositional logic

Secondary: 60B99: None of the above, but in this section

**Keywords**

event conditional probability probability

#### Citation

Hammett, Adam; Oman, Greg. I'm Thinking of a Number $\ldots$. Missouri J. Math. Sci. 28 (2016), no. 1, 31--48. http://projecteuclid.org/euclid.mjms/1474295354.