Hello jack action it's a nice video but I wish it went a bit further to demonstrate the point I have been making. To see what this is I'll firstly summarise, what has been my contribution to this thread.
From post 34 and onwards my main stance has been that Tank A filling up first is not necessarily the answer but is a possible answer. fahraynk gave it as a possible answer in the opening post. Take a look.
Whether A is the answer or not depends on average flow rates. It can be explained in terms of physics or in terms of general knowledge. In a nutshell If water flows in faster than it leaves A will fill up first. If not F will fill up first. It's easy and its obvious. But does water flow in faster than it leaves? The question can be answered only if the relevant information is known. Without the information the best that can be done is to make assumptions. And I think assumptions should be justified.
I don't know what the question compiler had in mind when setting the question but I made an assumption that I later realized couldn't be justified. By looking at the diagram and comparing the drop size to the outlet pipe radius I assumed that the outlet pipes were capillary tubes. But then I realized that the diagram, which I assume to be a schematic diagram.may not be drawn to any sort of scale. The best I can now say about the tubes is that they might be capillaries.
The structure of the tubes is relevant and I pointed out that pipe radius is a factor that affects the flow rate. But a general opinion seemed to be that pipe radius is irrelevant. If it is irrelevant are the other factors that affect flow rate irrelevant as well? Can I ignore pressure for example? Or can I be selective in what I ignore and forget about pipe radius etc but consider pressure because pressure is needed to move the water along. I'm not being nit picky but trying to highlight the fact that care needs to be taken when making assumptions that cannot be justified in terms of the information that is known. I have been using a bit of basic physics here and I know I'll probably get criticised again for using it, but I'm just pointing out some of the thoughts that came to me when I first looked at the problem.
In later comments it was pointed out that the puzzle was not a physics puzzle. But I didn't know that. After all I came across it in a physics forum. But I took the advice and afterwards avoided the tricky stuff and tried to keep everything in terms of general knowledge only. I tried to prove something which should be obvious.
I tried different ways to get my point across and thankfully received some feedback that addressed the points I was making. That includes from yourself. I particularly like the video you found and I think it gives a convincing demonstration that for a fast enough flow rate through the pipes F is the answer. But I would love to get my hands on the equipment and demonstrate the effects of varying the flow rates and in particular I would reduce the flow rates through the pipes eg by using a series of pipes of reducing radii. Then you will see that for a slow enough flow rate A is the answer.
As you said "nothing beats the real thing" and hopefully I may be able to find a video or something that backs up my analysis. I think I may be able to find details of experiments that used to be carried out in UK high schools when viscosity was on the syllabus. Such experiments are relevant to the puzzle discussed here.
In the meantime you may see the significance of the picture I found. And just to add a little physics,(sorry) if the radius of the tube is halved the flow rate reduces to one sixteenth of its original value. That's assuming laminar flow and Poiseuilles formula.
