How to write a mystery?

I have long been hugely impressed by mystery writers. How do they concoct such complicated plots, which they strategically open to us as they go along? I have no idea, of course, but here is one possibility: perhaps they are as mystified about the outcome as we are. Maybe they make up the plot as they go along, without the outcome already having been decided, so that they "discover" what happened as we do. I wonder.