Problems(1)
In an m×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 mnf(m,n)≤Cholds for any positive integers m,nCSJL combinatoricsgridIMOC