Question 124
Consider a $2024 \times 2024$ grid fully tiled using $1 \times 2$ and $2 \times 1$ dominoes without overlap. A robot is placed on one of the cells. It moves from one cell of a domino to the other, then continues in the same direction to the next domino, if such exists; otherwise, it stops. Is it possible for the robot to eventually return to its starting cell?