My solution for the 2018 International Mathematical Olympiad first combinatorics question: "Let n ≥ 3 be an integer. Prove that there exists a set S of 2n positive integers satisfying the following property: For every m = 2, 3, . . . , n the set S can be partitioned into two subsets with equal sums of elements, with one of subsets of cardinality m."

I must apologise for my poor explanations, especially from 22:00 onward. I was going to remake that bit, but I'm apparently too lazy and freaked out by the bushfires to get anything done.