Science and Mathematics Faculty Publications

Document Type

Article

Publication Date

2-6-2018

Journal Title

Minnesota Journal of Undergraduate Mathematics

ISSN

2378-5810

Volume

3

Issue

1

Abstract

We consider the following guessing game: fix positive integers k, m, and n. Player A ("Ann") chooses a (uniformly) random integer from the set {1,2,3,...,n}, but does not reveal it to Player B ("Gus"). Gus then presents Ann with a k-option multiple choice question about which number she chose, to which Ann responds truthfully. After m such questions have been asked, Gus must attempt to guess the number chosen by Ann. Gus wins if he guesses Ann's number. The purpose of this note is to find all canonical m-question algorithms which maximize the probability of Gus winning the game. An analysis of a natural extension of this game is also presented.

Keywords

Guessing games, mathematics

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