Keywords

mathematics, guessing games, combinatorics

Disciplines

Mathematics | Physical Sciences and Mathematics

Advisor

David Clark

Abstract

A guessing game is a two-player game between a Responder and a Questioner. In a guessing game, the Responder is thinking of x ≥ 1 secret numbers in a set S of size n. The Questioner is tasked with asking questions of the form: “How many numbers are in Q ⊆ S?” until the Questioner knows at least 1 of the Responder’s secret numbers. We find a game-winning strategy for the Questioner with minimal possible questions for games with x = 2. We also find lower-bounds for x = 2 and x = 3.

Included in

Mathematics Commons

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