I think the monsters are let there by elevators

I mean, they are put into the rooms behind the grating which are the elevators

. The floors of the smaller arenas open, when the elevator goes up and close when it goes down.
The problem is there are only 4 of these rooms and 8 arenas, heh.
But I cant see better option. There are no gate through which the animals could be let in and the small doors through which we enter are often too small. If someone did the gates, it is hard to imagine where would they lead, because there are no corridors.
In fact it is hard to find out the complete path where the animals are moved, so everything is possible, with rebuilding a bit the arena
