The Birthday Problem
How many people must be in a room before two of them probably share a birthday? The answer is far smaller than you expect.
1939 (first published), circulating from the 1920s14 min read
Domain
Probability
Puzzles where the correct answer feels obviously wrong.
12 entriesFilter these further →
Beginner
Ages 8+, no background needed.
The Monty Hall Problem
Three doors, one car. The host opens a losing door and offers you the swap. Does it make any difference whether you take it?
1975 (posed), 1990 (made famous)9 min read
Bertrand's Box Paradox
You reach into one of three boxes and pull out a gold coin. The chance the other coin in that box is gold is not one half.
188910 min read
Intermediate
Curious teenagers and general adult readers.
Simpson's Paradox
A treatment does better for men, and better for women, and worse for people. None of the arithmetic is wrong.
1903 (Yule), 1951 (Simpson), 1972 (named)20 min read
The Fermi Paradox
The universe is ancient, enormous, and full of ordinary stars much like ours. So where is everybody?
1950 (Fermi's remark), 1975 (Hart's argument)22 min read
The Boy or Girl Paradox
A family has two children and one of them is a boy. What are the odds the other is a girl? It depends on how you found out.
1959 (posed), 1961 (retracted in part)13 min read
The Ellsberg Paradox
You know exactly how many red balls there are, and nothing about how many are black. Does knowing more make a bet more attractive?
19617 min read
Zipf's Law
The most common English word is twice as frequent as the second. Why does language obey the same mathematical law as city populations?
19357 min read
Berkson's Paradox
Two things with nothing whatever to do with each other can look strongly related — purely because of who ended up in the study.
194615 min read
Advanced
Undergraduate level in the relevant field.
The Sleeping Beauty Problem
Woken with no memory of having been woken before, how confident should you be that the coin came up heads?
1997 (posed), 2000 (named and popularised)24 min read
The St. Petersburg Paradox
A coin-flipping game whose average winnings are infinite. How much of your own money would you actually pay to play?
1713 (posed by Nicolaus Bernoulli), 1738 (published by Daniel Bernoulli)19 min read
The Two Envelopes Problem
One envelope holds twice as much money as the other. The arithmetic says swap — then says swap back, forever.
1953 (Littlewood, crediting Schrödinger), 1989 (envelope form)19 min read