Gems in the Field of Bounded Queries

Let A be a set. Given {x₁,…,x _n }, I may want to know (1) which elements of {x₁,…,x _n }, are in A, (2) how many elements of {x₁,…,x _n } are in A, or (3) is |{x₁,…,x _n }∩A| even. All of these can be determined with n queries to A. For which A, n can we get by with fewer queries? Other questions involving ‘how many queries do you need to…’ have been posed and (some) answered. This article is a survey of the gems in the field—the results that both answer an interesting question and have a nice proof.