Counting configurations - Colegiul National C. Negruzzi (Iași - Roumanie)

Problems that require determining the number of configurations of a possible map are essential for combinatorial problems and algorithms for computer programming. We want to present how many combinations of painting the sectors of the circle are possible, if the adjacent colours cannot be the same. We will solve this in the particular case of 12 sectors and 5 colours and then we will find a generalisation. Moreover, we want to find out the number of configurations (which respect the same conditions) without rotations .