1979 USAMO Problems/Problem 3

Problem

$a_1, a_2, \ldots, a_n$ 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 $a \plus{ } b \plus{ } c$ (Error compiling LaTeX. Unknown error_msg) is divisible by $3$ is at least $\frac14$ .

1979 USAMO (Problems • Resources)
Preceded by Problem 2	Followed by Problem 4
1 • 2 • 3 • 4 • 5
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1979 USAMO Problems/Problem 3

Problem