2003 AIME I Problem 3

Each element is written on the list once for every smaller element in the set

Sort the set as $1, 2, 3, 5, 8, 13, 21, 34$ and multiply each element by the count of smaller elements

An element $x$ is the greater element of a two-element subset exactly once for each smaller element of the set, so $x$ contributes to the sum once per element below it. Sorting the set as $1, 2, 3, 5, 8, 13, 21, 34,$ the sum of the list is $$\begin{aligned} &0(1) + 1(2) + 2(3) + 3(5) \\ &\quad {}+ 4(8) + 5(13) + 6(21) \\ &\quad {}+ 7(34) \\ &= 2 + 6 + 15 + 32 \\ &\quad {}+ 65 + 126 + 238 = 484. \end{aligned}$$