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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The number hides game
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by V. J. Baston, F. A. Bostock and T. S. Ferguson PDF
Proc. Amer. Math. Soc. 107 (1989), 437-447 Request permission

Abstract:

We solve the following two-person zero-sum game, introduced by Ruckle. Players I and II simultaneously choose sequences of $m$ and $n$ consecutive integers respectively from the integers 1 to $p$ inclusive. The payoff to I is the number of integers in the intersection of the two sequences. A continuous version of this game is also solved as well as the variations in which one of the players need not choose his integers consecutively.
References
    W. H. Ruckle, Technical Report #384, Department of Mathematical Sciences, Clemson University, 1982.
  • William H. Ruckle, Geometric games and their applications, Research Notes in Mathematics, vol. 82, Pitman (Advanced Publishing Program), Boston, MA, 1983. MR 704355
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 107 (1989), 437-447
  • MSC: Primary 90D05
  • DOI: https://doi.org/10.1090/S0002-9939-1989-0972227-7
  • MathSciNet review: 972227