☕ Tuesday’s Puzzles: October Edition
Test your math instincts: Three puzzles for sharp minds
Three puzzles, three sips of math: Are you ready for your mid-October brain brew?
Welcome to this second edition of The Math Cafe!
I’m so glad to see you here.
A bit more about me: I’m Sybille, a mathematician specialised in Algebraic and Enumerative Geometry. I believe studying and doing math can be genuinely fun and stimulating when approached with curiosity; and my goal here is to share that spirit with you. I aim to make math friendlier and more approachable, and I’d love your feedback: what caught your attention, what felt too dry, or what could be clearer? You can contact me here, or by writing in the comments.
For today’s edition, I selected three puzzles from algebra, geometry and probability, each one trickier than the last. You’ll find the estimated difficulty marked with coffee cups ☕, a hint of how many cups you might need to tackle the problem (just a warning, not a recommendation!).
Note:
Puzzles 1 and 2 only require high-school algebra and geometry, and a touch of creativity.
Puzzle 3 calls for some probability basics, and sharper problem-solving instincts.
🧩 The Puzzles
Puzzle 1 — ☕
Can you spot the error in this ‘proof’?
A good warm-up for spotting logical slips: can you pinpoint the exact flaw?
Puzzle 2 — ☕☕
The diagram below was found in the writings of Indian mathematician Bhāskara II (12th century). It hides the proof of a famous theorem. Can you discover which one?
Hint: You probably learned the theorem in junior high school.
Note that Bhāskara’s elegant diagram offers a wordless proof: a perfect example of how geometry can speak for itself.
Puzzle 3 — ☕☕☕☕☕
Determine how many times, on average, one must toss a fair coin (independently and successively) until obtaining a sequence of an odd number of heads followed by a tail.
This problem appeared in the 2019 entrance exam for the elite mathematics program at ENS Ulm, Paris.
Candidates had only a blackboard, a piece of chalk, and 25 minutes to make decent progress on it.
So... would you get in? 🤓
🔹 Suggested approach: Try the puzzles in order of difficulty, and, most importantly, have fun!
That’s all for this week’s brew of puzzles! How did you find them: Too easy, too tricky, or just right? I’d love to hear from you!
🗓️ Next week teaser
Next Tuesday, The Café will serve a freshly brewed selection of recent news in the fields of Mathematics and AI.
I look forward to seeing you next Tuesday.
Until then, have a wonderful week!
With love and curiosity,
Sybille ☕
P.S.: Solutions will appear in next week’s edition of The Café.
In the meantime, paid subscribers are very welcome to share their solving process and tentative answers using this form: I’ll send back personal feedback, tips, and good coffee vibes ☕💡.