On the lottery problem

Authors

  • Zoltán Füredi,

    Corresponding author
    1. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801-2917
    2. Mathematical Institute of the Hungarian Academy of Sciences, Budapest 1364 Hungary
    • Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801-2917
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  • Gábor J. Székely,

    1. Department of Mathematics, Technical University, 1521 Budapest, Hungary
    2. Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403-0221
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  • Zoltán Zubor

    1. Department of Mathematics, Technical University, 1521 Budapest, Hungary
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Abstract

Let L(n,k,k,t) denote the minimum number of k-subsets of an n-set such that all the (nk) k-sets are intersected by one of them in at least t elements. In this article L(n,k,k,2) is calculated for infinite sets of n's. We obtain L(90,5,5,2) = 100, i.e., 100 tickets needed to guarantee 2 correct matches in the Hungarian Lottery. The main tool of proofs is a version of Turán's theorem due to Erdös. © 1996 John Wiley & Sons, Inc.

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