## ISL 2010 C2

For discussing Olympiad Level Combinatorics problems
Abdullah Al Tanzim
Posts: 20
Joined: Tue Apr 11, 2017 12:03 am

### ISL 2010 C2

On some planet, there are $2^N$ countries $(N\geq 4)$.Each country has a flag $N$ units wide and $1$ unit high composed of $N$ fields of size $1\times1$, 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 into an $N\times N$ square so that all $N$ fields on its main diagonal will have the same color.Determine the smallest positive integer $M$ such that among any $M$ distinct flags, there exist $N$ flags forming a $DIVERSE$ set.
Everybody is a genius.... But if you judge a fish by its ability to climb a tree, it will spend its whole life believing that it is stupid - Albert Einstein

Abdullah Al Tanzim
Posts: 20
Joined: Tue Apr 11, 2017 12:03 am