# Putnam Mathematical Competition

A guest series of articles by **Pat Lachapelle**, physics major at the University of Washington.

## 1. Introduction

Over the last 9 months, I have been studying for the **William Lowell Putnam Mathematical Competition**, an annual exam that has gained quite a reputation.

A top 5 score will earn you:

- The title of Putnam Fellow;
- $2500;
- A chance at a full scholarship to Harvard’s graduate Math program

Solving a problem from this exam may seem daunting or even impossible, a reasonable sentiment given its nature. The median score on the exam is often 0 out of 120 possible points. In 2018, a score of 23 would have been good enough to place you in the top 10 percent of students.

However, I assure you that I possess a remarkably average intellect and a tendency to be drawn to undertakings far beyond my ability. But upon studying for the Putnam, I was surprised at the deceptive simplicity of some of the problems. My surprise hatched an idea, which then grew into the following series.

Over the course of the next 7 articles, we will solve a problem from the notorious Putnam Competition. This series will break the problem into bite-sized sections, so simple that anyone with a 3rd grade education can understand. I invite you to embark on this journey with an open mind and full heart, for we will be traveling through what may be a foreign land. Don’t like math? Don’t worry! This series is for everyone, and perhaps upon its conclusion, you will have a newfound appreciation (maybe even fondness?) for the subject.

1985 Putnam Question A-2: Solution Part 1 - statement of the problem; vocabulary and overview

1985 Putnam Question A-2: Solution Part 2 - generalization

1985 Putnam Question A-2: Solution Part 3 - required background on triangles

1985 Putnam Question A-2: Solution Part 4 - tying together generalization, geometry and some required algebra, including summation notation

1985 Putnam Question A-2: Solution Part 5 - using similar triangles to simplify our problem

1985 Putnam Question A-2: Solution Part 6 - the Cauchy-Schwarz Inequality

1985 Putnam Question A-2: Solution Part 7 - tying it all together to solve the problem