Question 58
The teacher has $2013$ candies of $11$ different types. She distributes the candies to her students such that no student obtains more than one candy of each type. She then asks each pair of students to write down on the board the number of candy types that they have in common. Let $M$ be the sum of written numbers.
a)
Find the minimum value of $M$.
b)
What happens if the teacher has only $9$ different types of candy?
a)
Find the minimum value of $M$.
b)
What happens if the teacher has only $9$ different types of candy?