MathDB

In an

m \times n

grid, each square is either filled or not filled. For each square, its value is defined as

0

if it is filled and is defined as the number of neighbouring filled cells if it is not filled. Here, two squares are neighbouring if they share a common vertex or side. Let

f(m,n)

be the largest total value of squares in the grid. Determine the minimal real constant

C

such that

\frac{f(m,n)}{mn} \le C

holds for any positive integers

m,n

CSJL

Problem Statement