Question 169
Adalbert and Babette play dominoes on a rectangular grid 2 cells high and 2018 cells wide. Adalbert starts by placing a $1 \times 2$ domino in horizontal position, so that it covers exactly two cells of the grid. Then Babette likewise plays a $1 \times 2$ domino in vertical position, and so on. The first player who can no longer play without overlapping a domino already placed loses. Show that Adalbert has a winning strategy.