Abstract
The plurality problem with three colors is a game between two participants: Paul and Carol. Suppose we are given n balls colored with three colors. At any step of the game, Paul chooses two balls and asks whether they are of the same color, whereupon Carol answers yes or no. The game ends when Paul either produces a ball a of the plurality color (meaning that the number of balls colored like a exceeds those of the other colors), or when Paul states that there is no plurality. How many questions L(n) does Paul have to ask in the worst case? We show that \(3\lfloor n/2 \rfloor - 2 \leq L(n) \leq \lfloor 5n/3 \rfloor - 2\)
Work supported in part by the European RTN Project under contract HPRN-CT-2002-00278, COMBSTRU.
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Aigner, M., De Marco, G., Montangero, M. (2004). The Plurality Problem with Three Colors. In: Diekert, V., Habib, M. (eds) STACS 2004. STACS 2004. Lecture Notes in Computer Science, vol 2996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24749-4_45
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DOI: https://doi.org/10.1007/978-3-540-24749-4_45
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