MathDB

Let

m

and

n

be positive integers. A people planted two kind of different trees on a plot tabular grid size

m \times n

(each square plant one tree.) A plant called inpressive if two conditions following conditions are met simultaneously: i) The number of trees in each of kind is equal; ii) In each row the number of tree of each kind is diffrenent not less than a half of number of cells on that row and In each colum the number of tree of each kind is diffrenent not less than a half of number of cells on that colum.
a) Find an inpressive plant when

m=n=2016

; b) Prove that if there at least a inpressive plant then

4|m

and

4|n

Problem Statement