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Counting

Fall 2026 · 12 problems

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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What is in it

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

1. Everybody Knows Somebody PigeonholeEasy
2. Cutting Up the Plane Counting / RecursionEasy
3. Even Parity Counting / BijectionsEasy
4. Count the Opposite Complementary CountingEasy
5. Routes Across Town Counting PathsEasy
6. Forty-Three Visits PigeonholeMedium
7. OPTIMIZATION Counting with RepetitionEasy
8. Around a Round Table Counting up to SymmetryEasy
9. Nobody Waits for Change Counting PathsHard
10. Thirty-Nine on an Icosahedron Double CountingMediumPutnam 2013 A1
11. Sliding Coins Bijections / Lattice PathsHardPutnam 2023 B1
12. The Mad Teacups Counting up to SymmetryHard