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
Location
Cedarville, OH
Start Date
4-20-2016 2:00 PM
End Date
4-20-2016 2:20 PM
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
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Included in
Discrete Mathematics and Combinatorics Commons, Logic and Foundations Commons, Probability Commons, Theory and Algorithms Commons
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.
