Going to grandmas house,granny likes cakes,and its her birthday,I want to give her cakes I have made,between my house and grandmas,I have to cross 7 bridges,but each bridge has a troll,before I can cross each bridge,I have to give them half of my cakes I am carrying,but they are kind trolls,they give me back a single cake,how many cakes do I have to leave home with to make sure I arrive at grandmas with 2 cakes

The answer is 2 cakes

if we make the amount of cakes C
and each bridge a b c d e f g in relation to bridge 1 2 3 4 5 6 and 7
and we know that we arrive with 2 cakes; or after the 7th bridge we have 2 cakes; So we know that g=2

after the 6th bridge or f=(e/2)+1

We know that after the 7th bridge we have 2cakes or (f/2)+1=g=2

(f/2)+1-1=2-1
(f/2)+0=1
f/2*2=1*2
f=2

It's a loop therefore no matter how many bridges you go over, as long as they take away half of your cakes and give you one back; you'll always have the same amount of cakes

Hope that helps
-ZacheryA