That Old Troll Problem

Algebra Level 3

You are on your way to pay a visit to your Grandma, who lives at the end of the valley. It's her birthday, and you want to give her two of 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 kind trolls, they each give you back a single cake. What is the least number of cakes you have to leave home with?


  • Your Grandma does not have the necessary items to make a cake at her place and she has no neighbours

  • There is only one possible route from your house to your Grandma's

  • The only troll toll accepted is in the form of cakes

  • The toll must be paid each time a bridge is crossed

P.S. Remember you are paying a visit. You will surely need to return


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