MathDB
Math Prize 2014 Problem 19

Source:

September 29, 2014
limitfunctionprobabilityexpected valueceiling function

Problem Statement

Let nn be a positive integer. Let (a,b,c)(a, b, c) be a random ordered triple of nonnegative integers such that a+b+c=na + b + c = n, chosen uniformly at random from among all such triples. Let MnM_n be the expected value (average value) of the largest of aa, bb, and cc. As nn approaches infinity, what value does Mnn\frac{M_n}{n} approach?
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