4. The numbers from 1 to 10 are written on a board. It is allowed to erase any two numbers $x$ and $y$, and instead write the numbers $x-1$ and $y+3$ on the board. Could it be that after some time, the numbers on the board are $2,3, \ldots, 9,10,2012$?
4. Suppose we managed to get the numbers $2,3, \ldots$, 9,10,2012 on the board. Notice that after each operation, the sum of the numbers on the board increases by 2. Initially, it was 55. That is, after each operation, the sum of the numbers on the board will be odd. However, the sum $2+3+\ldots+10+2012=2066$ is even. Contradiction.

Answer: could not.