Problem sets
Everything the club has worked through, free to download.
Problems only. The club works them out together at meetings, so the sets carry topic and attribution as a starting point but no solutions. Every set is a PDF you can print and bring with you.
Fall 2026
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Optimization: Squares, Constraints, and Symmetry
Completing squares, dot products and symmetry find exact maxima and minima without multivariable calculus. Five warm-ups lead to three Putnam problems, ending with the largest circle that fits inside a four-dimensional cube (Putnam 2008 B3).
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Calculus: Look Before You Integrate
Reflection, reciprocal changes of variables, and geometry reveal the structure of definite integrals. Five warm-ups lead to competition problems, including an integral of an unknown function from Putnam 2016 A3.
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Invariants
Find the quantity that never changes, then use it to show something is forced or outright impossible: a chocolate bar whose game is decided before anyone moves, chameleons that can never agree on a colour, a knight that cannot cross the board, and the fifteen puzzle.
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Counting
Combinatorics from a standing start: pigeonhole, counting the complement, counting one thing two ways, and counting up to a symmetry. Ends with the Mad Teacups, where the riders of a spinning theme-park ride have to be counted up to every rotation at once.
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Learn by Doing: Number Sense
Magnitudes, digits and decimals, worked by hand: how many digits a sum of powers up to a googolplex has, the pattern hiding in 1/9899, and iterated digit sums. Then six competition problems in the same vein.
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The Toolkit
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.
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Opening Set
The set the club opened Fall 2026 with. Chosen to be inviting rather than hard: the McNugget numbers, a fair coin from a biased one, the two-envelopes paradox, ants on a stick, and the Josephus circle.
Spring 2026
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Geometry
Thirty problems in three parts: the basic facts, training exercises, and competition-level geometry. The most developed set in the archive.
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Assorted Classic Problems
Well-travelled problems that reward a second look.
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Linear Algebra
Matrix and linear-algebra problems in the competition style.
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Five-Minute Gems
Short problems with a clean idea at the centre. Each is meant to be stated, attacked, and resolved inside one sitting.
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Games and Strategy
Combinatorial games, invariants, and winning strategies.
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Opening Set
The set the club opened Spring 2026 with — the round table, the monk on the mountain, the pigeonholes, the broken stick.
Since 2022
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All-Time Favorites
Problems the club keeps coming back to.