Puzzle
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The Farmer’s Impossible-Looking Receipt
A farmer buys 10,000 young animals at market: calves, lambs, and piglets. The receipt totals $505,000, the lambs outnumber calves three-to-one, and the piglets arrive in tidy hundreds. Can you reconstruct the herd?
Ride-sharing: What the Wait Time Tells You
An 8-minute wait sounds like evidence of surge pricing. The math says otherwise: it barely shifts your estimate from the prior. Using exponential wait-time distributions, Bayes' theorem, and simple cost-benefit analysis, this puzzle explores why observed data can be surprisingly uninformative.
How Big Is Half a Lottery?
A $1 billion jackpot. Seven numbers, drawn with replacement from 1–19. You want a 50% chance of winning. How many $1 tickets must you buy — and will it ever be worth it?
Where’s the Best Seat in the Theater?
Movie screens are designed to feel immersive — but not overwhelming. If you wanted the mathematically perfect seat, how far back should you sit to see the screen at exactly a 60° viewing angle?
The Geometry of a Coffee Splash
When you set your mug down too hard, the liquid forms a near-perfect annular wave. Can you derive the radius of the first ring using surface tension and your mug's diameter?
Elevator Probability
You enter a building with 12 floors and press your floor at random. What is the expected number of stops if 3 other passengers do the same?
Traffic Light Sequences
A city grid has lights timed on a 90-second cycle. Model the optimal path across 6 intersections to minimize expected wait time.