The halflie problem

Joel Spencer, Catherine H. Yan

Research output: Contribution to journalArticle


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+k k!q-k + Θ(2q q-k-1/2).

Original languageEnglish (US)
Pages (from-to)69-89
Number of pages21
JournalJournal of Combinatorial Theory. Series A
Issue number1
StatePublished - Jul 2003


  • Asymmetric packing
  • Asymptotic formula
  • Liar's game
  • Ulam's problem

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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