MathDB

10

Part of 2023 Baltic Way

Problems(1)

Colored points on a circle

Source: Baltic Way 2023/10

11/11/2023
On a circle, n≥3n \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 nn for which there exists an initial state of nn 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.
combinatorics