Question 186
There are $n \ge 2$ classes organized $m \ge 1$ learning groups for students. Every class has students participating in at least one group. Every group has exactly $a$ classes that the students in this group participate in. For any two groups, there are no more than $b$ classes with students participating in both groups simultaneously.
a) Find $m$ when $n = 8, a = 4, b = 1$.
b) Prove that $n \ge 20$ when $m = 6, a = 10, b = 4$.
c) Find the minimum value of $n$ when $m = 20, a = 4, b = 1$.
a) Find $m$ when $n = 8, a = 4, b = 1$.
b) Prove that $n \ge 20$ when $m = 6, a = 10, b = 4$.
c) Find the minimum value of $n$ when $m = 20, a = 4, b = 1$.