Putnam Competition

Yesterday was the nationwide 71st William Newell Putnam Mathematical competition.  (More info here).  It started at 8:30 am here in the Rocky Mountains, and it was off to a riveting start:  opening the manilla envelope with the first set of six questions, and then reading…rereading, stopping for a minute for a breather, then reading again.  Then drawing some pictures to try and see if we were understanding…

So the problems were pretty hard, I expected that.  Somewhere around half of the participants actually don’t score a single point.  I did feel like I understood and gave a good effort at a few of the problems.  A1, B2, and B3 specifically.  We’ll see what they tell us in March though. 

I’m excited for the time being to see what the solutions are, they should be posting them tonight. 

Intermediate Value theorem

I was fascinated the other day by my teacher's description of the fixed point theorem:

By taking two identical pieces of paper, crumpling up one and placing it anywhere on the second piece of paper you are guaranteed to have some point in the crumpled up mess that is over the same point on the flat piece of paper if you unfolded it again. Another explanation is here.

So I wanted to post my findings on the intermediate value theorem! You have to scroll down a little bit, but I found really interesting the part about the world having two antipodal points exactly the same temperature.