self Maths Puzzle

You are going to visit your grandmother on Mother's day. You want to give her two cakes. However, to get to her house you must cross seven bridges. At each bridge is a troll who demands ½ of all of your cakes as the price to pass. However, this troll, being a nice troll, feels bad and gives you back 1 of the cakes that he took.
The puzzle to solve: How many cakes must you leave with to be able to give your grandmother 2 cakes

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self Other Question

on tree there are 10 birds are sitting . one of them is fly away. how many birds are remaining An apple costs half a dollar while a pear costs a dollar. Bob at first bought an apple, then he tought: "I already paid half a dollar, and I have an apple that is also worth half a dollar. So if I give teh apple to the shopkeeper, , he would overall receive a dollar from me. That should be enough to get me a pear." Is Bob right?