Here's my take: Let n be the number of people needed. Probability that a person's birthday is not today: 364/365 Prob. that no one's birthday is today: (364/3

Here's my take: Let n be the number of people needed. Probability that a person's birthday is not today: 364/365 Prob. that no one's birthday is today: (364/365)^n Prob. that someone's birthday is today: 1 - (364/365)^n Prob. that someone's birthday covers every day: (1 - (364/365)^n)^365 Setting equal to 0.5 and solving, I get n==2284, which is close to metaphyze's brute force number.