ABSTRACT
This chapter studies those basic objects of mathematics called numbers. In most cases it uses only the basic fact that every positive integer is uniquely expressible as a product of primes, that is, numbers with no factors other than 1 and themselves. Numbers are the stars in eleven puzzles and a theorem. The puzzles ask the reader to deal with a broken ATM, find maximal number sets with certain properties, construct a card trick, predict the status of locker doors, and deal with a product of factorials. One puzzle merely presents an expression for a number, and asks: is it prime? It turns out that the number does not have any small factors, but a clever trick shows that is has a large one. The theorem confirms a fact that many people know, but few can explain: that the square root of a whole number is either another whole number, or it's irrational.
