MathDB

Three schools have

200

students each. Every student has at least one friend in each school (if the student

a

is a friend of the student

b

then

b

is a friend of

a

). It is known that there exists a set

E

300

students (among the

600

) such that for any school

S

and any two students

x,y\in E

but not in

S

, the number of friends in

S

x

and

y

are different. Show that one can find a student in each school such that they are friends with each other.

Problem Statement