CONO-SUR 2010 Problem 4

Pablo and Silvia play a game on a $2010\times{2010}$ board. First Pablo fills in each cell with an integer. Then Silvia repeats the following operation as many times as she likes: she picks three cells that form an L, like in the figure, and adds 1 to each number in the three cells. Silvia wins if she makes all of the number multiples of $10$. Demonstrate that Silvia can always pick a succession of operations such that she wins the game. ._ _ _ _ _ _ || || ||| ||| ||| ||| || ||