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m blue and n red vertices on a m+n polygon, numbering sides

Source: Singapore Junior Math Olympiad 2017 2nd Round p4 SMO

March 26, 2020

Coloringcombinatorics

Problem Statement

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