Answer:
49.
Step-by-step explanation:
Suppose we start with 12 people whose birth months are all different.
If there we add to make 13 people then we can say that at least 2 were born in the same month as there are 12 months in a year.
If we add another student then he could have the same month date as the other 2 but he is more likely to have another birth month.
So we could go on adding 1 student 11 times and get 12 pairs of students with the same birth month.
This is very unlikely but possible.
Now we could also add 12 more and end up with 12 sets of 3 with same birth month.
Then another 12 giving 12 sets of 4.
Then the next student must be 1 of 5 with same month.
So that makes 49 students.
