Key idea. There are fewer months than people.

1. Group the 13 people according to their birth month. There are 12 possible groups.

2. If every group contained at most one person, there would be at most 12 people.

3. There are 13 people, so at least one group must contain two or more. Those people were born in the same month, possibly in different years.

Remember. If more objects than boxes are placed in the boxes, some box contains at least two objects.