Originally Posted by Adraco

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Water flows downwards, always looking for a lower position, based on gravity.

Let's take it from the beginning:

A: Will "never fill up" since it will quickly feed water into B.
B: Will also "never fill up" since it will quickly feed water into C.
C: Will fill "halfway up" and then start feeding water into J, since the pipe into D is blocked.
D: Will not fill at all, since the only pip leading into it, is blocked. Thereby neither E or G will get any water since their only connection is from D.
E: Will not fill at all, since no water will ever come into D.
F: Pass for now...
G: Will not fill at all, since no water will ever come into D.
H: Will not fill at all, since the only pipe leading into it is blocked.
I: Will only start filling up once J is almost full, since the water needs to move up in the pipe and will only do so with high water pressure in J.
J: Will fill amost halfway up and then start feeding water into L, which is placed lower than I.
K: Will take a very long time to fill up since it will take a long time for I to ever get any water into it.
L: Will get water from J pretty quickly and feed into F.

Correct answer is that the F bucket will fill up first.
Because,
Water will flow from A to B to C
then start filling J halfway up and then flow over into L
L will immediately start filling up the pipe and start pushing water into F.
Since the highest position in F is still at a lower point than the pipe leading into L, F will be completely filled up first.

F is the correct answer.