Question 11
Young Boole has drawn a strip of eight cells, each of which can contain a $0$ or a $1$. Initially every cell contains a $0$. On each move, Boole performs one of the following operations:
Operation a: Replace every $0$ by a $1$ and every $1$ by a $0$.
Operation b: Choose three consecutive cells and, only in those cells, replace every $0$ by a $1$ and vice versa.
How many different combinations of zeros and ones can Boole obtain?
Operation a: Replace every $0$ by a $1$ and every $1$ by a $0$.
Operation b: Choose three consecutive cells and, only in those cells, replace every $0$ by a $1$ and vice versa.
How many different combinations of zeros and ones can Boole obtain?