It seems that everywhere you go in Uruguay, you take a number. And wait: the bank. The hardware store. The vegetable stand in the féria (street market). Welcome to Uruguay: please take a number. Though it takes some getting used to, in general the system works well.
When we started our residency process, there was a number dispenser on the wall of the residence section. When you went in, you took a number.
One day it was empty, and you had to wait in line at the reception desk, to be given a number based on which of the two number dispensers you would have previously used (the office has a residence section and a gratuitous-paperwork section). Often as not, you could explain by simply pointing to the appropriate empty number dispenser.
Then one day they only gave out numbers at 12:45 for the residence section that opened at 1:00. With no room for a line (the reception desk meanwhile giving out numbers for the gratuitous-paperwork section), a crowd gathered, more or less keeping track of who was before whom before piling into the reception desk line at 12:45 .
Now they give out only 100 numbers a day, starting at 9:00, and open the residence section at 11:00. Why not give out numbers at 10:45 for a section that opens at 11:00? Well, because the inevitable long line for residence-section numbers blocks the main entrance, hence access to the gratuitous-paperwork section, which opens earlier than the residence section.
And to think: I never saw a line at the (now empty) number dispenser on the wall of the residence section. I have pointed out before that many things seem to be improving here (and will post one again tomorrow). Unfortunately, the bureaucracy at Migración is not one of them.