Question 101
An isolated island has the shape of a circle. Initially there are $9$ flowers on the circumference of the island: $5$ 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, 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?
Is it possible (for some configuration of initial $9$ flowers) to get all red flowers after finitely many years?