In their village, you have to pay toll at every bridge and there is a bridge every 4 km. Poor Lucy had no money; just her cakes.
The officers at every bridge insisted that she give them half the number of cakes she was carrying. But when they realised it was for her brother’s birthday, they gave back a single cake each time.
How many cakes did Lucy initially have, if she had exactly 2 cakes upon reaching her brother’s house?