2026 AIME II Problem 13

Call finite sets of integers S and T cousins if

- S and T have the same number of elements,

- S and T are disjoint, and

- the elements of S can be paired with the elements of T so that the elements in each pair differ by exactly 1.

For example, \{1,2,5\} and \{0,3,4\} are cousins. Suppose that the set S has exactly 4040 cousins. Find the least number of elements the set S can have.

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.