Question 180
A person wants to plant two different kinds of tree on a plot tabular grid size $m \times n$ (each square planted one tree). A planting way is called impressive if two following conditions are satisfied
i) The number of trees in each kind is equal.
ii) The difference between the number of two kinds of tree in each column and each row is at least $\frac{m}{2}$ and $\frac{n}{2}$ respectively.
a) Find an impressive planting way when $m = n = 2016$.
b) Prove that if there exists an impressive planting way then $m, n$ is divisible by 4.
i) The number of trees in each kind is equal.
ii) The difference between the number of two kinds of tree in each column and each row is at least $\frac{m}{2}$ and $\frac{n}{2}$ respectively.
a) Find an impressive planting way when $m = n = 2016$.
b) Prove that if there exists an impressive planting way then $m, n$ is divisible by 4.