A growing library of 90–120 minute sessions, each built around a single compelling challenge explored from multiple mathematical perspectives.
Modular arithmetic Chinese Remainder Theorem GCD
Combination-lock rings that advance at different speeds — when (if ever) do they align?
Perfect squares Digit splitting Enumeration
Find all perfect squares under 2000 that split into two parts which are themselves perfect squares.
Area bisection Similar triangles Law of Cosines Integration
Cut a scalene triangle in half with a single line perpendicular to its base — where exactly does it go?
Cryptarithms Carry analysis Modular arithmetic Place-value algebra
Crack the code: GRAND + BRAVO = XXXXX. Each letter is a unique digit — what's the largest GRAND can be?
Divisibility Factoring Egyptian fractions SFFT Unit fractions
Two ink-stained denominators hide in Matilda's grandfather's notebook: 2/85 = 1/? + 1/?. Find every possibility.
Chinese Remainder Theorem Digit splitting Divisibility Triangular numbers
Among the running sums 0, 1, 3, 6, 10, 15, 21, … find all six-digit numbers whose halves satisfy "first = twice second."
Champagne fountain Geometric series Recurrence relations Symmetry
A 5-storey square pyramid of 55 flutes — pour champagne into the top until all are full. How much is wasted? (Spoiler: a LOT.)
Binary encoding ASCII Error correction Hamming codes QR codes
From zeros and ones to scannable squares — build a QR code by hand and discover why mathematics protects your data from damage.
Modular arithmetic One-way functions Diffie-Hellman RSA Post-quantum crypto Lattices
Send a secret to someone you've never met, on a postcard everyone can read — then ask: what happens when quantum computers arrive?
Image representation Huffman coding DCT JPEG Shannon entropy Human perception
A raw photo is 24 million bytes. The JPEG is 2 million. Where did the other 22 million go — and why does it still look perfect?
SHA-256 Merkle trees Proof of work Game theory Bitcoin protocol Ethereum
Build a system where nobody is in charge yet nobody can cheat — from hash functions to mining to the $690 M pizza.
| File | Purpose |
|---|---|
| .copilot-instructions.md | Agentic rules — attach as context for every new challenge |
| _TEMPLATE-Lecture.md | Skeleton for new lectures — copy and fill in |
| math-circle.css | Shared stylesheet for all HTML outputs |
| README.md | This same index in Markdown (for GitHub / VS Code preview) |
| Future-Lecture-Ideas.md | Backlog of cool lecture ideas — Shazam, JPEG, Birthday Paradox, Four Colours… |