Assuming that the flow of water is slow so that bottle 1 doesn't fill up first, which bottle fills up first?
Water will begin flowing into 2 before 3 from 2 bottle 6 will fill before any other
From my perspective, it seems as though the 6th bottle with fill up first.
This is because the water will run to bottle 2 after bottle 1 fills up to the bottom pipe.
And once bottle 2 fills up at the bottom pipe as well, then bottle 6 will fill up first because it will have the most water.