Reciprocity

In 2006, Math Horizons challenged its readers to pose a problem in such a way that it contained its own answer. Rheta Rubenstein of the University of Michigan-Dearborn offered a pair of questions that answer one another:

  1. What fraction of the letters in three-eighths are vowels?
  2. What fraction of the letters in one-third are vowels?

(“Self-Answering Problems,” Math Horizons 13:4 [April 2006], 19.)