Puzzled: Find the magic set
Peter M. Winkler · Communications of the ACM · 2012
Welcome to three new puzzles. Each involves a collection of items, and your job is to find a subset of them that is characterized by a particular property. Since solving the puzzles is not easy, here are a couple of hints: For the first, think about averages; for the other two, try constructing your sets sequentially, bearing in mind that if two partial sums are equal, the terms between them must add up to zero.