Let's consider a robot on an m x n grid of squares $($that is$,$ m rows and n columns$).$ The robot starts in the top$-$left square, and its target is at the bottom$-$right. The robot has two moves available to it $--$ it can move one square to the right, or one square down $$ so it must make a combination of rightward and downward moves to reach its target. It follows that the robot will take $($m $+$ n $2)$ steps to reach its target.

Here are two such paths it could take: