Answer:
Hence to get same number of students in each classroom,the sufficient condition is that assign 13n students to each classroom.
Explanation:
Given:
There are m classrooms and n be the students
3<m<13<n.
To Find:
Whether it is possible to assign each of n students to one of m classrooms with same no.of students.
Solution:
This problem is related to p/q form has to be integer in order to get same no of students assigned to the classroom.
As similar as ,n/m ratio
So 1st condition is that,
If it is possible to assign the n/m must be integer and n should be multiple of m,
when we assign 3n students to m classrooms ,we cannot say that 3n/m= integer so that n is greater than 13 i.e n=14 and m=6
hence they are not multiple of each other so they will not make same students in each classrooms.
Otherwise,n=14 and m=7 they will give same number but this condition is not sufficient condition to assign the student.
So 2nd condition is that ,
When we assign 13n students to m classrooms, as 13 is prime number and
3<m<13 which implies the 13n/m to be integer so n and m must be multiple of each other.
Suppose n=20 and m=5 classrooms
then 13*20=260 ,
260/5=52 students in each classroom,