On Some Planet,there are \(2^n\) Countries (\(n \geq 4 \) ).
Each Country Has a Flag \(n\) units wide and one unit high composed of \(n\) Fields of size \(1 \times 1\),each field being either yellow or blue.No two countries have the same flag.
We say that a set of \(n\) flags is diverse if these flags can be Arranged in \(n \times n\) square so that all \(n\) fields on its Main Diagonal will have the same colour.
Determine the Smallest Possible integer \(m\) such that among any \(m\) distinct flags,there exist \(n\) Flags forming a Diverse Set.
I Need A bit of help In Understanding the Last Part of the Problem.