## Three Circles in a Triangle: A Solution

In my last post, I posed the problem of showing that if triangles $ABC$ and $PQR$ (as shown in the diagram below) are similar, then $\Delta ABC$ is equilateral. We will solve this problem in two steps: Show that the… Continue Reading

## Maximizing the Product: A Solution

In my last post, I asked What is the largest possible product you can make with a group of positive integers if the sum of those integers is 2017? Before we rush to the numerical answer, let’s follow my usual… Continue Reading

My last post put forward the challenge to find numbers whose binary representations end with their decimal representations, like how $11 = 1011_2.$ It turns out that there are lots of them. Infinity of them, in fact. If we’re going to… Continue Reading