Kazuki silently observed the goings on from the back of the auditorium, taking notes on his fellow students. Still unable to find a common denominator. Still no clue as to why 20 or so students who have nearly nothing in common. Still he was wracking his brain until the incredibly moronic one said something interesting. He was just invited, no application or anything, in fact he said he was something of a dropout. That was a connection, Kazuki was just invited himself without any rhyme or reason, sure he had good grades but he was far from a remarkable student. 

hmm, so then it is entirely possible that every student here was specifically invited out of the blue without any application at all. The question then becomes why? Why gather so many people who have nearly nothing in common at all? Just from a cursory glance the only person he even had a chance of having something in common with was the girl who seemed to be doing the same as him, hanging in the back and studying. He adjusted his tie and waited, as that was the only thing he really could do.