MathDB

Given positive integers

n

and

k

n > k^2 >4.

In a

n \times n

grid, a

k

-group is a set of

k

unit squares lying in different rows and different columns. Determine the maximal possible

N

, such that one can choose

N

unit squares in the grid and color them, with the following condition holds: in any

k

-group from the colored

N

unit squares, there are two squares with the same color, and there are also two squares with different colors.

Problem Statement