number theory

Nov 04 2025

Circular Sorting

Anurag Bishnoi

How many swaps do you need to sort objects on a circle in clockwise order? This fairly simple and natural question quickly leads to some deep mathematics that I would like share. Let’s start with an example for : After swapping 2 with 6, 1 with 4, and then 4 with 5, we get the...

mathematics math combinatorics number theory polynomials circular sorting strong complete mappings wreath products orthomorphisms finite fields

Dec 13 2017

Polygonal Number Last Digits

Alaric Stephen

I want this article to be an extensive to one of the problems we analysed in Odds and Evenings episode 1. However you don't have to listen to episode to understand this. In the episode we had a think about the possible last digits of triangle numbers when you write them out normally (base 10). We...

mathematics number theory