## Podium Presentations

#### Title

On a Multiple-Choice Guessing Game

#### Type of Submission

Podium Presentation

#### Keywords

Algorithm, event, probability, conditional probability

#### Abstract

We consider the following game (a generalization of a binary version explored by Hammett and Oman): the first player (“Ann”) chooses a (uniformly) random integer from the first n positive integers, which is not revealed to the second player (“Gus”). Then, Gus presents Ann with a k-option multiple choice question concerning the number she chose, to which Ann truthfully replies. After a predetermined number m of these questions have been asked, Gus attempts to guess the number chosen by Ann. Gus wins if he guesses Ann’s number. Our goal is to determine every m-question algorithm which maximizes the probability of Gus winning the game. A natural extension of this game is also discussed.

#### Campus Venue

Stevens Student Center, Room 241

Cedarville, OH

#### Start Date

4-20-2016 2:00 PM

#### End Date

4-20-2016 2:20 PM

#### Share

COinS

Apr 20th, 2:00 PM Apr 20th, 2:20 PM

On a Multiple-Choice Guessing Game

Cedarville, OH

We consider the following game (a generalization of a binary version explored by Hammett and Oman): the first player (“Ann”) chooses a (uniformly) random integer from the first n positive integers, which is not revealed to the second player (“Gus”). Then, Gus presents Ann with a k-option multiple choice question concerning the number she chose, to which Ann truthfully replies. After a predetermined number m of these questions have been asked, Gus attempts to guess the number chosen by Ann. Gus wins if he guesses Ann’s number. Our goal is to determine every m-question algorithm which maximizes the probability of Gus winning the game. A natural extension of this game is also discussed.