The halflie problem

Authors:
Joel Spencer;Catherine H. Yan
Affiliations:
Courant Institute of Mathematical Sciences, New York University, New York;Department of Mathematics, Texas A&M University, College Station, TX
Venue:
Journal of Combinatorial Theory Series A
Year:
2003

Citing 5
Cited 0

Enumerative combinatorics

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A Halfliar's game

Theoretical Computer Science - Algorithmic combinatorial game theory

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Abstract

In Ulam's game Paul tries to find one of n possibilities with q Yes-No questions, while responder Carole is allowed to lie a fixed number k of times. We consider an asymmetric variant in which Carole must say yes when that is the correct answer (whence the halflie). We show that the maximal Ak(q) for which Paul wins has the asymptotic form Ak(q) = 2q+kk!q-k + Θ(2qq-k-1/2).