USAMO 1979 Problem 3

$a_{1}, a_{2}, \ldots, a_{n}$ is an arbitrary sequence of positive integers. A member of the sequence is picked at random. Its value is a. Another member is picked at random, independently of the first. Its value is $b$. Then a third, value c. Show that the probability that $\mathrm{a}+\mathrm{b}+\mathrm{c}$ is divisible by 3 is at least $1 / 4$.