Question 88
Some points are marked on a circle. Each marked point is coloured red, green or blue. In one step, one can erase two marked points of different colours that have no marked points between them 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 positive integers $n$ 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.