all colourings of all pos.ntegers either red or green under 3 conditions
Source: Dutch BxMO TST 2011 p1
August 24, 2019
ColoringRedGreencombinatorics
Problem Statement
All positive integers are coloured either red or green, such that the following conditions are satisfi ed:
- There are equally many red as green integers.
- The sum of three (not necessarily distinct) red integers is red.
- The sum of three (not necessarily distinct) green integers is green.
Find all colourings that satisfy these conditions.