MathDB

Let

k

n

be positive integers,

k,n>1

k<n

and a

n \times n

grid of unit squares is given. Ana and Maya take turns in coloring the grid in the following way: in each turn, a unit square is colored black in such a way that no two black cells have a common side or vertex. Find the smallest positive integer

n

, such that they can obtain a configuration in which each row and column contains exactly

k

black cells. Draw one example.

Problem Statement