How to guess an n-digit number

Zilin Jiang, Nikita Polyanskii

Research output: Contribution to conferencePaperpeer-review

Abstract

In a deductive game for two players, SF and PGOM, SF conceals an n-digit number x = x1, . . ., xn in base q, and PGOM, who knows n and q, tries to identify x by asking a number of questions, which are answered by SF. Each question is an n-digit number y = y1, . . ., yn in base q; each answer is the number of subscripts i such that xi = yi. Moreover, we require PGOM send all the questions at once. We show that the minimum number of questions required to determine x is (2+oq(1))n/logq n. Our result closes the gap between the lower bound attributed to Erdos and Rényi and the upper bounds developed subsequently by Lindström, Chvátal, Kabatianski, Lebedev and Thorpe. A more general problem is to determine the asymptotic formula of the metric dimension of Cartesian powers of a graph. We state the class of graphs for which the formula can be determined, and the smallest graphs for which we did not manage to settle.

Original languageEnglish (US)
Pages1215-1220
Number of pages6
DOIs
StatePublished - 2019
Externally publishedYes
Event30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019 - San Diego, United States
Duration: Jan 6 2019Jan 9 2019

Conference

Conference30th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019
CountryUnited States
CitySan Diego
Period1/6/191/9/19

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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