Finding a majority ball with majority answers

Suppose we are given a set of n balls {b1, . . . , bn} 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 {bi1 , bi2 , bi3}. 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 n2 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(n3) in the non-adaptive case.