Maybe it's our tendency to overcomplicate things, but this problem should be a lot easier than it is. However, this photo continues to frustrate brilliant minds across the internet. The question has over 100 responses and counting on Quora, and they're not simply "Number 3." Some users crafted 300 words explanations defending their positions.
So what's the answer?
Well, like most things in science, it depends on the variables, conditions and what you assume about ideal conditions. Some people say tank 3, others swear on 3 and 4 simultaneously.
The easiest thing to do is eliminate pots 1 and 2 as answers because of basic physics. Pots 3 and 4 would have to fill up first before 2 and 1. The next steps are where it gets tricky.
In a theoretical world, pots 3 and 4 fill up at the same time. That assumes all tanks and pipe connections are identical, room temperature and pressure is constant, and the fluid being used is, in fact, water.
[Image Courtesy of Nirav Adroja/Quora]
Or, if you're like others answers, you consider the flow rate. A ton of pressure and a high flow rate would mean the pots fill up sequentially 1, 2, 3, and 4. However, most people are assuming a low, constant flow rate for this (we assume due to the droplets on the original picture). Low flow rates change that order with 3 filling first, then shortly followed by 4.
The diagram in question is a communicating vessel, a set of containers containing homogenous fluid. When that liquid finally settles, it balances out to the same level across containers regardless of shape or volume. However, the heights of pots 1 and 2 leave a little bit of frustration, as does the angle of the connection between pots 3 and 4.
The answers surrounding this question are great, and you can clearly see a line drawn between the engineers and the physicists.
The only way to really know, however, is to test the theory. And it's only a matter of time before someone gets frustrated enough with previous answers and indecisiveness and decides to build their own version of this mind game.