Question 73
We are placing red and blue balls on the circle. In the beginning there are exactly two red balls on the circle. We are allowed to perform the following operations:
i) add one red ball and change the colour of its neighbouring two balls (red to blue and vice versa);
ii) remove one red ball and change the colour of its neighbouring balls.
Is it possible that after a finite number of operations we obtain
a) $2013$ red and $2013$ blue balls;
b) exactly two blue balls? (Kvant 8/1981)
i) add one red ball and change the colour of its neighbouring two balls (red to blue and vice versa);
ii) remove one red ball and change the colour of its neighbouring balls.
Is it possible that after a finite number of operations we obtain
a) $2013$ red and $2013$ blue balls;
b) exactly two blue balls? (Kvant 8/1981)