Question: Let a and b be positive integers, with a ≤ b. A certain class has b students, and among any a of them there is always one that is friends with the other a − 1. Find all values of a and b for which there must necessarily be a student who is friends with everyone else in the class.
My thoughts are that a can be any integer greater than 1 because a student in a class of one cannot have friends, and that b must equal a, as one student must be friends with everyone and a-1 equals maximum number of friendships. Therefore there are infinites values for a and b, provided that a is greater than 1.
Is my solution correct and logical? If it isn't please explain why, thanks.