Puzzles
How many cereal boxes before you've collected every prize?
A cereal company hides one of 50 different collectible toys at random in every box. Assuming each of the 50 is equally likely and you buy boxes one at a time, roughly how many boxes should you expect to buy before you've collected all 50?
Reveal the answer
About 225 boxes — far more than 50. The expected number of draws grows roughly as n times the natural log of n, and the last few items are disproportionately expensive to find because you're increasingly likely to draw duplicates you already have. It's a classical result in probability theory with real applications in software testing and ecology.