MathDB

There are

32

students in the class with

10

interesting group. Each group contains exactly

16

students. For each couple of students, the square of the number of the groups which are only involved by just one of the two students is defined as their

interests-disparity

. Define

S

as the sum of the

interests-disparity

of all the couples,

\binom{32}{2}\left ( =\: 496 \right )

ones in total. Determine the minimal possible value of

S

Problem Statement