Looking at the image, we need to determine which cup will fill first based on the paths of the liquid.
Upon examining the structure of the pipes leading to each cup, it appears that many of the paths are blocked or obstructed.
The path to cup 1 is blocked.
The path to cup 2 is also blocked.
The path to cup 4 is blocked.
Cups 5, 6, and 7 are all located in branches further down the system, and their paths are either obstructed or long.
Cup 3 is the first one without any blockage or obstruction along its path, so it will fill first.
Thus, the answer is Cup 3.