Question 4
Consider a polygon with $m+n$ sides where $m,n$ are positive integers. Colour $m$ of its vertices red and the remaining $n$ vertices blue. A side is given the number $2$ if both its end vertices are red, the number $1/2$ if both its end vertices are blue and the number $1$ otherwise. Let the product of these numbers be $P$. Find the largest possible value of $P$.