13. (15 points) There are 60 students in the class, and their birthdays are recorded as a certain month and day. Ask each student the same two questions: How many students in the class have the same birth month as you? How many students in the class have the same birth day as you (for example, the birth day of January 12 and December 12 is the same). It is found that the answers obtained include all integers from 0 to 14. Then, what is the minimum number of students who have the same birthday?
【Analysis】The answers for the same month and the same day number cover from 0 to 14, meaning the number of people with the same month and the same day number ranges from 1 to 15, thus leading to the analysis and solution.

【Solution】The answers include all integers from 0 to 14, which means each answer contains a number of students ranging from 1 to 15.

Since $1+2+3+\cdots+15=120=2 \times 60$,
it follows that whether the answer is for the same month or the same day number, the number of people with the same month or the same day number will not repeat (for example, if there are 3 people born in a certain month, there will not be 3 people born on a certain day). Therefore, when counting the number of people with the same month or the same day number, each of the 15 numbers from 1 to 15 appears only once. To minimize the number of people with the same month and day, the distribution of months or day numbers should be as dispersed as possible. For example, 60 can be broken down as: $60=1+2+3+4+5+7+8+9+10+11$ for the number of people in the same month,

and another case: $60=6+12+13+14+15$ for the number of people with the same day number.
Analyzing the largest number 15, if 15 people with the same day number are distributed among the above 10 months, it is known that there will be at least two people with the same month and day.

Therefore: The number of people in the class with the same birthday is at least 2.