MathDB

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.

Problem Statement