One of the great things about mathematics is that it’s always possible to look again at familiar things and discover something new. Sometimes these discoveries can happen when you combine well-known things in a new way. For example, you’re probably familiar with the four basic operations of addition, subtraction, multiplication, and division. And you may…

(Ian Stewart) Is it possible to number the edges of a cube using each of the numbers -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6 once, so that for every vertex, the sum of the numbers on the edges that meet there is zero…

In this classic dilemma, the director of a prison offers 100 prisoners, who have been assigned numbers from 1 to 100, a last chance at freedom. A room contains 100 boxes. The director randomly puts one prisoner’s number in each closed box. The prisoners enter the room, one after another. Each prisoner may open and…

One interesting thing about continued fractions is that every infinite continued fraction represents an irrational number. But in our first dilemma, we asked what happens when you have an infinite sequence of finite continued fractions with more and more terms…