Question 72
A square with side length $2n + 1$, $n \in \mathbb{N}$, $n \geq 2$, is divided by parallels to its sides into $(2n + 1)^2$ squares and exactly $2n(n + 1)$ of them are colored.
We will call a horizontal line of the large square *nice* if it has more than half of its $2n + 1$ squares colored. Denote $f(n)$ the maximum number of nice lines.
a) Find $f(2)$.
b) Find the smallest positive integer $n$ so that $f(n) \gt 2016$.
We will call a horizontal line of the large square *nice* if it has more than half of its $2n + 1$ squares colored. Denote $f(n)$ the maximum number of nice lines.
a) Find $f(2)$.
b) Find the smallest positive integer $n$ so that $f(n) \gt 2016$.