## Missouri Journal of Mathematical Sciences

### 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

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

#### 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.

#### References

• P. Billingsley, Probability and Measure, Wiley, Hoboken, 2012.
• H. Enderton, A Mathematical Introduction to Logic, Academic Press, New York - London, 1972.
• K. Rosen, Discrete Mathematics and Its Applications, seventh edition, McGraw-Hill, New York, 2012.