Puzzle
Archive
Too Even to Be Random
A teacher catches the students who faked their coin flips with one rule. Real randomness is lumpier than you think.
The Cards That Count for Nothing... Or Do They?
Card counting squeezes a whole shoe into one number — and the famous Hi-Lo system scores three of the thirteen ranks as a flat zero. Wasteful? We test whether folding the 7, 8 and 9 back in builds a sharper count, and find that doing *less* wins.
The Pen That Cried Wolf
A counterfeit-detector pen is 99% accurate at catching fakes and almost never misfires. It just flagged a customer's $100 bill. So why is the bill still almost certainly real?
Up Like a Rocket, Down Like a Feather
Five price signals, five right triangles, one angle that tells you when the (asset) rocket is too vertical to stay aloft. A trader's intuition expressed in tangents.
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.