Finding a majority ball with majority answers

Abstract Suppose we are given a set of n balls { b 1 , … , b n } each colored either red or blue in some way unknown to us. To find out some information about the colors, we can query any triple of balls { b i 1 , b i 2 , b i 3 } . As an answer to such a query we obtain (the index of) a majority ball, that is, a ball whose color is the same as the color of another ball from the triple. Our goal is to find a non-minority ball, that is, a ball whose color occurs at least n 2 times among the n balls. We show that the minimum number of queries needed to solve this problem is Θ ( n ) in the adaptive case and Θ ( n 3 ) in the non-adaptive case.

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