# The Prisoner's Dilemma

• ### D6. Rectangle Pinwheel

The outermost polygon shown in figure 2 as the region shaded in pink consists of 16 congruent rectangles placed so that their edges align (and vertices of four of the rectangles coincide at the center of the polygon). We call this polygon a 28-gon because it has 28 edges: the line segments that make up […]

Posted: 2022 May 26   Solutions will be accepted through 2022 Sep 1
• ### D5. Triple Fever

Caught up in the excitement of the Derby and the Preakness, a buddy of yours heads to the track, and discovers that today is the running of the Medium-Rare Stakes. Only three horses have been entered: Tee Bone, New York Strip, and Rib Eye. Your buddy then notices the posted odds: Tee Bone is paying […]

Posted: 2022 May 23   Solutions will be accepted through 2022 Sep 1
• ### D4. Four Operations Revisited

One of the great things about mathematics is that it’s always possible to look again at familiar things and discover something new. Sometimes this 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 have […]

Posted: 2022 Jan 30   Solutions will be accepted through 2022 Sep 1
• ### D3. Zero Sum Game

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, and 6 once, so that for every vertex, the sum of the numbers on the edges that meet there is zero? (See figure 1 for a diagram of the […]

Posted: 2022 Jan 29
• ### D2. Find Yourselves

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 […]

Posted: 2022 Jan 28
• ### D1. Continuing Irrationality

One interesting thing about continued fractions is that every infinite continued fraction represents an irrational number. But in our first dilemma, we ask what happens when you have an infinite sequence of finite continued fractions with more and more terms. Recall that the binomial coefficient $a\choose b$ has the formula $\frac{a!}{b!(a-b)!}$. Now for any integer […]

Posted: 2022 Jan 27