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I think that the most of you are familiar with similar kind of problems / riddles:

enter image description here

I always said that it depends upon the velocity with which the fluid comes out from the faucet. It doesn't seem wrong to me: if a great amount of water comes out, jar number 1 will be filled almost immediately. If instead it comes out slowly, then it will probably be $3$).

Question: am I right in supposing that? I mean it depends on the velocity, right? (And yes, on the area of the faucet, and probably on the density / viscosity of the fluid too).

Is there a mathematical way to solve problems like this, besides just looking at the drawing?

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This is rather a trick question than a scientific one. The author probably did not intend any profound scientific answer... It is more about noticing that there is no connection to jars 4,5 and 6 as well as the fact that there is a hole in jar 7.

Since you do want to discuss it scientifically, you have to acknowledge that you do not have enough information about the system. As you pointed out, it depends on the water flux, the openings etc... And I agree with you, it will probably be either 1 or 3 depending on those parameters. It could be 2 though if the line from 1 to 3 is extremely narrow but the line from 1 to 2 is extremely wide and the water flux is large enough. Then again, if the whole in number 7 is really small and the flux is large, it could also fill up first... The idea was probably to refer to communicating vessels with some added tricks.

To sum it up, you don't have enough information about the system to solve it accurately.

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