Question 363785: You are on your way to visit your Grandma, who lives at the end off the valley. It's her birthday, and you want to give her the cakes you've made.
Between your house and her house, you have to cross 7 bridges, and as it goes in the land of make believe, there is troll under every bridge! Each troll, quite rightly, insists that you pay a troll toll. Before you can cross their bridge, you have to give them half of the cakes you are carrying, but as they are knid trolls, they each give you back a single cake.
How many cakes do you have to leave home with to make sure that you arriive at Grandma's house with exactly 2 cakes?
Found 2 solutions by amoresroy, robertb:
Answer by amoresroy(361)   (Show Source):
You can put this solution on YOUR website! You leave home with 2 cakes.
No matter how many bridges you will cross, you will always end up with 2 cakes for your Grandma.
Please let me know if you need clarifications. Thanks.
Answer by robertb(5830)  (Show Source):
You can put this solution on YOUR website! If he leaves home with x cakes, then by the times he leaves the 1st bridge, he has  cakes. When he leaves the 2nd bridge, he has  cakes. When he leaves the 3nd bridge, he has  cakes. If there are n bridges, then inductively when he leaves the nth bridge, he must have  +...+ cakes. this must be equal to 2. Hence
+...+ .
 ,
 ,
 ,
 ,
 , or x=2.
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