TH-TMO 2011 Problem 4

There are $900$ students in an International School. There are $59$ international boys and $59$ international girls. The Students are partitioned into $30$ classrooms (each classrooms have equal number of student) and in each of the classrooms, the student will labelled number from $1$ to $30$ . The Partition must satisfy at least one follow condition: [list=i] [] Any Two international boys in same classroom can't have consecutive numbers. [] For every classroom, the student who is labelled $1$ must be a boy. [/list] Prove that there are $2$ classrooms, each of which has $2$ international boys with their labels difference equal.