Denoting by X(1) <= X(2) <= · · · <= X(n) the order statistic based on a random sample X1, X2, ..., Xn drawn from a distribution F, it is shown that the property "E(X1X(1), X(n)) = (X(1) + X(n)), almost surely" holds for some n >= 3 if and only if F is either a uniform distribution on an interval or a discrete uniform distribution supported on a set of equispaced points. The heart of our proof is the interesting observation that the above equation involving conditional expectations completely determines...</=>