This is sounds a lot like you need a king rat to draw it out.
I recommend inviting some politicians around, tell them there is free stuff and that parliament services will in fact pay them for the afternoon. With a pack of rats running around like that you are sure to entice the problem rat out and probably won't even have to kill it as it will bugger off with the rest of them when the bludging comes to an end, namely when the free stuff stops.
Bookmarks