An isolated garden has the shape of a circle. Initially, there are 9 flowers on the circumference of the garden: 5 of the flowers are red and the other 4 are yellow. During the summer, 9 new flowers grow on the circumference of the island according to the following rule: between 2 old flowers of the same color, a new red flower will grow, and between 2 old flowers of different colors, a new yellow flower will grow. During the winter, the old flowers die, and the new survive. The same phenomenon repeats every year.
Is it possible (for some configuration of initial 9 flowers) to get all red flowers after finitely many years?
I do not think this is possible because in order to get all of the flowers to become red you first need to get all of the flowers to become yellow. In order for all of the flowers to become yellow we will need the colors of the flowers to alternate and we will need an even number of flowers for these alternating flowers to make all of the new flowers yellow, therefore it is impossible.
Is it impossible and is my reasoning correct?