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.
