Red and blue points on a circle
Source: Kürschák 2004, problem 3
July 13, 2014
combinatorics unsolvedcombinatorics
Problem Statement
We have placed some red and blue points along a circle. The following operations are permitted:(a) we may add a red point somewhere and switch the color of its neighbors,(b) we may take off a red point from somewhere and switch the color of its neighbors (if there are at least points on the circle and there is a red one too).Initially, there are two blue points on the circle. Using a number of these operations, can we reach a state with exactly two red point?