To Grandmother's House We Go

You are on your way to visit your Grandma who lives deep in the forest. It is her birthday and you want to give her the cakes you've baked. Seven bridges lie between your house and her house. Under each bridge lives a troll. Each troll demands a toll. Before you can cross their bridge, you have to give them half of the cakes you are carrying. Fortunately, they are kind trolls, so they each give you back a single cake.

How many cakes do you have to leave home with to make sure that you arrive at Grandma's with exactly 2 cakes?

Answer

The answer is 2. At each bridge you are required to give half of your cakes, and you receive one back. Which leaves you with 2 cakes after every bridge.