Vol. 15, No. 1, 2022

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Continuous guessing games with two secret numbers

David Clark and Nicholas Layman

Vol. 15 (2022), No. 1, 141–162
Abstract

A guessing game with two secret numbers is a game played between a questioner and a responder. The two players first agree upon the set, N, in which the game will be played, as well as the number of questions, Q, which will be asked by the questioner. The responder first chooses two distinct numbers from N. The questioner then asks questions of the form “How many of your chosen numbers are in the set A N?” to which the responder answers truthfully. The goal for the questioner is to determine the responder’s two numbers using at most Q questions. We study a continuous version of this game where N is the closed interval of real numbers from 0 to 1. We introduce tools to study this game and use them to examine strategies for the questioner using a geometric approach. We establish a condition that must be satisfied by optimal strategies and give a strategy that can be made arbitrarily close to optimal.

Keywords
guessing games, search, combinatorics
Mathematical Subject Classification
Primary: 68P10
Secondary: 94D99
Milestones
Received: 5 April 2021
Revised: 20 August 2021
Accepted: 21 August 2021
Published: 14 March 2022

Communicated by Kenneth S. Berenhaut
Authors
David Clark
Department of Mathematics
Grand Valley State University
Allendale, MI
United States
Nicholas Layman
Department of Mathematics
Grand Valley State University
Allendale, MI
United States