It's like that math problem of "how many people need to be in a room before the odds are >50% that 2 people share the same birthday" -- the answer is much smaller than you expect.
In a typical classroom of 20-30 this doesn't happen, so intuitively I'd guess 60-90.
Let's see.. 1 person = 0 2 people = 1/365 3 people = 1/365 + 2/365 4 people = 1/365 + 2/365 + 3/365.. N people = 1/365 + 2/365... N-1/365 = (n-1)(n)/2 > 182.5 (n-1)(n)/2 > 365/2 => (n^2 - n) / 2 > 365/2 => (n^2-n) > 365 => n=20
Wow! I oversimplified the math so this is an estimate, but it takes ~20 people. Interesting.