Problem Solving

Explore challenging math problems — from Putnam and GRE to interesting puzzles I’ve found along the way.

• Subset sums, generating functions, and roots of unity

  11/21/2025

  From a small example to a slick root-of-unity trick.

• Putnam 2017 A1

  11/11/2025

  Our exploration of the 2017 Putnam A1 problem with Dr. Pragel — and how a simple modular idea connects everything beautifully.

• Putnam 2016 A1

  11/5/2025

  My handwritten exploration, Dr. Pragel’s explanation, and the reasoning behind why the smallest integer j is 8.

• Five Points on a Sphere

  10/7/2025

  Five Points on a Sphere

• GRE Group Theory Problem

  5/28/2025

  Step-by-step solution and visual explanation of a basic GRE series problem

• Minimum of a Parabola

  5/20/2025

  Step-by-step solution and visual explanation of a basic GRE algebra problem