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Combinatorica

, Volume 3, Issue 3–4, pp 325–329 | Cite as

Mastermind

  • V. Chvátal
Article

Abstract

LetV(n, k) denote the set of vectors of lengthn whose components are integersj with 1≦jk. For every two vectorsx, y inV(n, k), leta(x, y) stand for the number of subscriptsi withx i =y i . We prove that for every positive ε there is ann(ε) with the following property: ifn>n(ε) andk<n 1−ε then there is a setQ of at most (6+ε)(n logk)/(logn−logk) vectors inV(n, k) such that for every two distinct vectorsx, y inV(n, k) someq inQ hasa(q, x) ≠a(q, y).

AMS subject classification (1980)

05 B 99 94 A 50, 90 D 99 

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Reference

  1. [1]
    D. E. Knuth, The computer as a Master Mind,Journal of Recreational Mathematics 9 (1976–77), 1–6.MathSciNetGoogle Scholar

Copyright information

© Akadémiai Kiadó 1983

Authors and Affiliations

  • V. Chvátal
    • 1
  1. 1.School of Computer Science McGill UniversityMontrealCanada

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