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Fall 2026 · 11 problems

If you can't solve a problem, then there is an easier problem you can solve: find it.

George Pólya

Five techniques worth owning: geometric series, complex numbers, Vieta's formulas, inclusion-exclusion, and counting the prime factors of a factorial. Then six harder problems, mostly past Putnam, built from the same ideas.

Download the problem set (PDF)

What is in it

Problems only — the club works these out together at meetings. Topic and attribution are listed as a starting point.

1. The Fly and the Trains Geometric Series / Lateral ThinkingEasy
2. A Geometric Series in Disguise Complex Numbers / Trigonometric SumsMedium
3. Roots You Never Have to Find Algebra / Vieta's FormulasEasy
4. Keep your primes close, and your coprimes closer Number Theory & Combinatorics / SievingEasy
5. Too many zeros!!! Plus: one-fourth of a mystery Number Theory & Combinatorics / Sieving and FactorialsEasy–Medium
6. Spreading a Fixed Total Analysis / SeriesMediumPutnam 2000 A1
7. Every Side and Every Diagonal Complex Numbers / Roots of UnityHard
8. Six Functions, One Minimum Trigonometry / Algebraic SubstitutionMediumPutnam 2003 A3
9. A Polynomial with Few Terms Algebra / Vieta's FormulasEasyPutnam 1985 B1
10. Unit Fractions Number Theory / DivisorsMediumPutnam 2018 A1
11. Three Sets, Ten Elements Combinatorics / CountingEasyPutnam 1985 A1