MathDB

Let

n

be a positive integer. Find all integers

k

among

1,2,\dots,2n^2

which satisfy the following condition: ・There is a

2n\times 2n

grid of square unit cells. When

k

different cells are painted black while the other cells are painted white, the minimum possible number of

2\times 2

squares that contain both black and white cells is

2n-1

Problem Statement