The picture you see above has had over 100 responses on Quora, but almost all of them have their own reasons, and none of them is fully sure of the answer. So we decided to have a crack at it ourselves.
As much as we want to make every question a simple black and white issue, it rarely ever is the case. And just one glance at the question makes it clear that the question is far more than just being solvable using intuition. The exact answer would indeed depend on the variables, conditions and other assumption about the conditions such as temperature, fluid properties, pressure, etc.
In a bid to not make this a complex fluid mechanics problem, we will try to solve it just intuition, no matter how counter-intuitive this strategy might seem to an engineer. Pot 1 and 2 can surely be eliminated using basic physics since they will drain out the water to the lower and Pots 3 and 4, but it too is subject to a low flow rate. In case the flow rate from the source is high enough, pots 1,2,3,4 will fill up sequentially.
Coming to the next pots, 3 and 4 would fill up at the same time theoretically if we assume that all tanks and pipe connections are identical and the room conditions are constant and the fluid being used is, in fact, water. Low flow rates change that order with 3 filling first, then shortly followed by 4. However, with the lack of data, the differences between the heights of pots 1 and 2 as well as the clear angle of the connection between pots 3 and 4 leaves a lot to simplifying assumptions.
What is your verdict on this interesting problem? Comment below!