Keywords

mathematics, guessing games, combinatorics

Disciplines

Mathematics | Physical Sciences and Mathematics

Advisor

David Clark

Abstract

In an offline guessing game, there is a player called the Questioner and a player called the Responder. The Responder first picks two distinct numbers from the set {1, 2, 3, . . . , n}. The Questioner then creates a set of questions of the form “How many of your numbers are in the set qi ⊆ {1, 2, 3, . . . , n}?” and sends them to the Responder who answers them. The Questioner wins if they can guess the Responder’s numbers no matter which numbers the Responder chose. The Responder wins otherwise. We create a method of representing the game that makes computations simple. We show bounds for the minimum number of questions needed to ensure the Questioner wins any game. We also prove optimality for certain offline guessing games with a constant question length.

Included in

Mathematics Commons

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