If P(n) is the probability that no 2 people (out of n people) share the same birthday, then 1 - P(n) is the probability that at least 2 people (out of n people) share the same birthday.

Now, the 'real' problem is finding P(n).

The probability that the second person does not have the same birthday as the first person is . The probability that the third person does not have the same birthday as either the first person or second person is . The probability that the nth person does not have the same birthday as any of the people before that person is . Therefore, .

It follows that . The question asks for what n is the probability greater than 1/2 = 0.5. Therefore, solve the inequality for n to answer the question. (In my opinion, it's easier to plug in different values for n until 1 - P(n) exceeds 1/2.)