Problem Solving

Explore challenging math problems — from Putnam and GRE to interesting puzzles I’ve found along the way. This is where I collect the questions that sent me down a rabbit hole and the ideas that helped unlock them.

2025

11/21/2025

Subset sums, generating functions, and roots of unity

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

[combinatorics][number theory][generating functions]

11/11/2025

Putnam 2017 A1

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

[Putnam][Number Theory][Logic][Math Blog]

11/5/2025

Putnam 2016 A1

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

[Putnam][Number Theory][Polynomials][Divisibility]

10/7/2025

Five Points on a Sphere

[putnam problem][math reflections][geometry][combinatorics]

5/28/2025

GRE Group Theory Problem

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

[GRE][Series][Visualization]

5/20/2025

Minimum of a Parabola

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

[GRE][Algebra][Visualization]