Question 26
An $n \times n$ square board is given, where $n$ is an odd positive integer. Each of the $2n(n+1)$ unit segments delimiting the unit squares is coloured either red or blue. It is known that there are no more than $n^2$ red unit segments.
Prove that there is a unit square on the board whose border comprises at least three blue segments.
Prove that there is a unit square on the board whose border comprises at least three blue segments.