Usually, the Collatz function is defined by $C(n)=3n+1$ if $n$ is odd and $C(n)=\frac{n}{2}$ if $n$ is even, and the famous conjecture states that some iterate of $C$ evaluated at $n$ is 1, for any positive integer $n$. I've spent a lot of time playing around with this problem, and one thing I've...

I have been reading a lot about TSP approximation algorithms recently, and I noticed that most of the algorithms tend to fall under two general categories: some that have a guaranteed approximation ratio for all possible graphs (most notably the Christofides algorithm), and some that perform very...