Squares and Squares and More Squares

Another quick one today, but still interesting. Let’s start by noting that $latex 2018=6^4+5^4+3^4+2^4=13^2+43^2=44^2+9^2+1^2$. It’s the sum of four fourth powers, two squares, or three squares. How many numbers can there be like that? As it turns out, there are an infinite number of them. Let’s start by noting that there are an infinite number … More Squares and Squares and More Squares

Magic!

We’ve all seen a magic square.  It looks like this: 8 1 6 3 5 7 4 9 2 The numbers in each row, column, and diagonal add up to .  What I want to do today is give you a formula for finding the magic constant for the normal magic square. What do those words mean?  … More Magic!

Slings and Arrows

Imagine you’re starting a country from scratch.  You’re given a couple of trillion pounds, a few billion people, a large plot of land somewhere, and told to get on with it.  In this admittedly unlikely scenario, what’s the first thing you do?  Setting up a voting system is probably fairly high on the list.  Today, … More Slings and Arrows