Question 22
Let $n \gt 1$ and $m$ be natural numbers. A parliament consists of $m n$ deputies who have formed $2 n$ committees such that the following holds:
(i) Each committee consists of $m$ deputies.
(ii) Each deputy is a member of exactly $2$ committees.
(iii) Any two committees have at most one common member.
Determine, as a function of $n$, the largest possible value of $m$ for which this is possible.
(i) Each committee consists of $m$ deputies.
(ii) Each deputy is a member of exactly $2$ committees.
(iii) Any two committees have at most one common member.
Determine, as a function of $n$, the largest possible value of $m$ for which this is possible.