MathDB

Given a

n\times m

grid we play the following game . Initially we place

M

tokens in each of

M

empty cells and at the end of the game we need to fill the whole grid with tokens.For that purpose we are allowed to make the following move:If an empty cell shares a common side with at least two other cells that contain a token then we can place a token in this cell.Find the minimum value of

M

in terms of

m,n

that enables us to win the game.

Problem Statement