MathDB

On a circle,

n \geq 3

points are marked. Each marked point is coloured red, green or blue. In one step, one can erase two neighbouring marked points of different colours and mark a new point between the locations of the erased points with the third colour. In a final state, all marked points have the same colour which is called the colour of the final state. Find all

n

for which there exists an initial state of

n

marked points with one missing colour, from which one can reach a final state of any of the three colours by applying a suitable sequence of steps.

Problem Statement