Subset sums, generating functions, and roots of unity
11/21/2025
From a small example to a slick root-of-unity trick.
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.
Below is a rotating glimpse of some of the tactics I like to use — from modular tricks to symmetry arguments and clever transformations. You’ll see these show up throughout the problems that follow.
problem-solving tactics
Euler’s identity
The most beautiful formula: $$e^{i\pi} + 1 = 0.$$
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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.
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Putnam 2016 A1
11/5/2025
My handwritten exploration, Dr. Pragel’s explanation, and the reasoning behind why the smallest integer j is 8.
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Five Points on a Sphere
10/7/2025
Five Points on a Sphere
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GRE Group Theory Problem
5/28/2025
Step-by-step solution and visual explanation of a basic GRE series problem
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Minimum of a Parabola
5/20/2025
Step-by-step solution and visual explanation of a basic GRE algebra problem