The Jester is visiting his grandmother who lives over the hills and through the woods. Why? Because it's her birthday! On his way, he knows he will meet 7 trolls. Each troll, quite rightly, insists that he pays a troll toll. Before he can pass, he has to give them half of the cakes he is carrying, but as they are kind trolls, they each give him back a single cake.

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How many cakes does the Jester have to leave home with to make sure that he will arrive at Grandmother's house with exactly 2 cakes?