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Five-Minute Gems

Spring 2026 · 13 problems

It is not enough to have a good mind; the main thing is to use it well.

René Descartes

Short problems with a clean idea at the centre. Each is meant to be stated, attacked, and resolved inside one sitting.

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 Handshake Lemma Graph Theory
2. The Mutilated Chessboard Logic / Invariants
3. The Boy or Girl Paradox Probability
4. Values without Solving Algebra / Manipulation
5. The Burning Ropes Logic / Lateral Thinking
6. The Fly and the Trains Logic / Series
7. A Symmetric Integral Calculus / Symmetry
8. The Infinite Radical Algebra / Limits
9. Trailing Zeros Number Theory / Factors
10. The River Crossing Measurement / Optimization
11. Powers of 2 Number Theory / Modulo Arithmetic
12. Telescoping Series Algebra / Series
13. The largest slice Logic / Lateral Thinking