Question 56
299 digits $0$ and one digit $1$ are written in a circle. The following moves are allowed:
* from each digit, subtract the sum of the adjacent digits;
* select two digits with exactly two digits between them and increase both by $1$ or decrease both by $1$.
Is it possible to obtain such an arrangement of numbers (after a finite number of such moves), in which there are two adjacent digits $1$, and the rest of the digits are $0$?
* from each digit, subtract the sum of the adjacent digits;
* select two digits with exactly two digits between them and increase both by $1$ or decrease both by $1$.
Is it possible to obtain such an arrangement of numbers (after a finite number of such moves), in which there are two adjacent digits $1$, and the rest of the digits are $0$?