Bulgarian National Mathematical Olympiad

We describe winning strategy for Ivan. He divides the table into $502$ tables $2\times 4$ and a table $2\times 2$. Then he puts his first domino in the table $2\times 2$ (no matter in which row). Peter is forced to put his domino in a table $2\times 4$. Now Ivan puts a domino in any place in the same table. It is easy to see that Ivan has one more way to put a domino in the same table and after two moves each the cells from this table are all covered. After covering all cells in all $2\times 4$ tables it is Peter's turn and he has no move. Therefore Ivan wins.