Question 44
The number $2011$ is written on a blackboard. It is permitted to transform the numbers on it by two types of moves:
a) Given a number $n$, we can erase $n$ and write two nonnegative integers $a$ and $b$ such that $a+b=n$.
b) Given two numbers $a$ and $b$, we can erase them and write their difference $a-b$, assuming this is positive or $0$.
Is it possible that after a sequence of such moves, there is only one number on the blackboard and it is $0$?
a) Given a number $n$, we can erase $n$ and write two nonnegative integers $a$ and $b$ such that $a+b=n$.
b) Given two numbers $a$ and $b$, we can erase them and write their difference $a-b$, assuming this is positive or $0$.
Is it possible that after a sequence of such moves, there is only one number on the blackboard and it is $0$?