Problem:
Let the set . Susan makes a list as follows: for each two-element subset of , she writes on her list the greater of the set's two elements. Find the sum of the numbers on the list.
Solution:
Since each element of is paired exactly once with every other element in the set, the number of times contributes to the sum is the number of other elements in the set that are smaller than . For example, the first number, , will contribute four times to the sum because the greater elements of the subsets , and are all . Since the order of listing the elements in the set is not significant, it is helpful to first sort the elements of the set in increasing order. Thus, since , the sum of the numbers on the list is .
The problems on this page are the property of the MAA's American Mathematics Competitions