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Wouldn't scale and viscosity play a role? Seriously, imagine a river vs a capillary tube. Also how many dimensions? And forces involved? Is that a blockage between 2 and 3? Are the walls breakable? How will the fluid hold air? Are the lines into structure 5 lower than the walls? Is this in a vacuum?
you may be overthinking it
There is no mention of any fluid involved, just a faucet. So lets think inside of the box and assume we have some form of 2d-gravity and it is going to rain a newtonian fluid? I think most surface area on the top is draining into 5. If it snows the whole sheet can turn white and the problem is gone, too.
I came in to comment, "it probably would probably be 5, but I think it would depend on the flow rate?"
But reading the other comments, it looks like I'm OOTL on something? 🧐
There might be something further upstream. All the way upstream.
spoiler-title
point zero, in fact
5
I got it! First, the free floating faucet will drop into bucket one. The impact will certainly break its connecting tube and broken 1 + faucet collapse into 4. Therefore 4 will be broken but full of shards.
The faucet
I wish these were drawn as closed containers
We'll done.
It's a sad day. They all stay empty. Such a loss.
The number of people in these comments who already understand the self-siphoning nature of water with zero explanation required makes me so proud to be here among them.