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100 students from 2 clubs A,B in circle (HOMC 2018 ind. sen10)

Source:

February 2, 2020
combinatoricscircle

Problem Statement

There are 100100 school students from two clubs AA and BB standing in circle. Among them 6262 students stand next to at least one student from club AA, and 5454 students stand next to at least one student from club BB. 1) How many students stand side-by-side with one friend from club AA and one friend from club BB? 2) What is the number of students from club AA?