You are the math teacher at a high school and you are in charge of organizing Student Council for the whole school next year. Your boss, the Principal, read a research paper on Student Councils and made some crazy demands:
MORE OPPORTUNITY : There will no longer be one Student Council but instead we will have many of them over the course of the year
FAIR REPRESENTATION : No more elections. All students are assigned to Student Council by you. Each student must have equal time serving at the end of the year
GOOD PROPORTIONS : The only acceptable ratio of Total Students to the size of any Student Council is 17 to 1
EVEN MIXING : Each student council, when compared to any other student council, must have exactly 3 students in common. Pick any two Councils randomly from the year and they must share exactly 3 members
You think the Principal is taking the research too literally, but as luck would have it, all his demands are possible to satisfy
Question: How many students attend your school?
Bonus Question: Is that the only possible answer? You will need to do a good job explaining why