SE-SKOLORNAS 2007 Problem 5

Anna and Brian play a game where they put the domino tiles (of size $2 \times 1$ ) in a boards composed of $n \times 1$ boxes. Tiles must be placed so that they cover exactly two boxes. Players take turnslaying each tile and the one laying last tile wins. They play once for each $n$ , where $n = 2, 3,\dots,2007$ . Show that Anna wins at least $1505$ of the games if she always starts first and they both always play optimally, ie if they do their best to win in every move.