Question 5
There are $n$ chameleons standing in a circle. Some of them are colored red and the others are colored green. Every minute, some of the chameleons change their color from red to green or vice versa in accordance with the following rule: a chameleon changes its color if and only if both its neighbours have the same color. Suppose that after $2n$ minutes all chameleons have the same color as at the beginning. Prove that there are two chameleons in the circle that have changed their color the same number of times.