Vol. 15, No. 1, 2022

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 2, 183–362
Issue 1, 1–182

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
Editors' interests
ISSN (electronic): 1944-4184
ISSN (print): 1944-4176
Author index
To appear
Other MSP journals
Continuous guessing games with two secret numbers

David Clark and Nicholas Layman

Vol. 15 (2022), No. 1, 141–162

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.

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

Communicated by Kenneth S. Berenhaut
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