## Happy 3*11*61

It’s common for the Putnam exam to include problems that involve the number of the current year in some way. (There weren’t any such problems on the past exam, but in 2011 there were two, A1 and B4.) Usually these problems don’t rely on any specific property of the number, but they simply use the number as a stand-in for “n”, so as to make the problem a little bit more concrete; for example, for either of the 2011 problems, you could replace the number 2011 with any other number without changing the nature of the problem.

## On 2012 Putnam problem B2

This post continues my effort to write up solutions (aimed at students) to the problems on this year’s Putnam exam. Here is problem B2:

## On 2012 Putnam Problem B1

This post continues my effort to write solutions, aimed at students, to the problems on this year’s Putnam exam. Here is problem B1:

## On 2012 Putnam Problem A3

This post continues my effort to write detailed solutions to the problems on this year’s Putnam exam (previous solutions are here and here). More than the actual solutions, I hope that students will find my commentary valuable. When writing these, I try to emphasize the thought processes and the strategies that were used to solve the problem, so that a reader might feel empowered to solve similar problems. I feel like some of the solutions in the MAA’s Putnam Directory are too slick and might reinforce a student’s feeling that they never would have come up with a solution on their own. These solutions attempt to counter that feeling.

## On 2012 Putnam Problem A2

This post continues my effort to write solutions to the problems on this year’s Putnam competition. I previously posted a solution to problem A1. Problem A2 seems like it should have been reasonable for students familiar with abstract algebra, but it could have been tricky for students without much exposure to axiomatic theories.

## On 2012 Putnam problem A1

The Putnam competition was last weekend, on December 1. I was coaching Smith’s team this year, so I’d like to go through solutions to each of the problems (or as many as I can solve), with my students being the intended audience. But I’ll post the solutions on this blog, since I’m sure they’ll be of interest to a wider audience.

I’ll start with the first one, Problem A1. It’s often the case that Putnam problems can be solved in several different ways, but sometimes you discover a solution that is clearly the most elegant of all possible approaches. That’s the case with this one, although I will include greater-than-necessary detail for pedagogical purposes.