2018 AIME I Problem 9

Find the number of four-element subsets of \{1,2,3,4,\ldots , 20\} with the property that two distinct elements of a subset have a sum of 16, and two distinct elements of a subset have a sum of 24. For example, \{3,5,13,19\} and \{6,10,20,18\} are two such subsets.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.