1.5 outta 7 ain't bad

This morning was the Virginia Tech Regional Mathematics Contest. For many, it's a preliminary for the Putnam.

I had two and a half hours to complete seven problems. The idea of these math contests is that any clever student with a few math undergrad courses under their belt can solve every problem. The catch is that you've got to be really freaking clever.

So how did I do? Well, I think I really nailed the second question. I looked at the third problem for a little while, writing out several of its cases, but I just couldn't really wrap my head around it. I worked for the remainder of the time on the fifth problem, a limit in three dimensions. I proved that if the limit exists, it must be zero, but I couldn't prove the existence of a limit.

The important thing to remember is this: If you're ever in need of a premutation (p(1),p(2),…,p(20)) of (1,2,…,20) such that k + p(k) is a power of 2 for k = 1,2,…,20, I'm your man. And I'll even prove its uniqueness for you.