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A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire.

He rushed over and pulled a young lady out of the flaming truck. Farmer Brown came out and greatefully thanked the traveling salesman for saving his daughter’s life. Mr. Brown insisted on giving the man a reward for his heroism.

So, the salesman said, “If you insist, I do not want much. Get your checkerboard and place one penny on the first square. Then place two pennies on the next square. Then place four pennies on the third square. Continue this until all 64 squares are covered with pennies.”

As he’d been saving pennies for over 25 years, Mr. Brown did not consider this much of a reward, but soon realized he made a miscalculation on the amount of money involved.

a). How much money would Mr. Brown have to put on the 32nd square?

b). How much would the traveling salesman receive if the checkerboard only had 32 squares?

c). Calculate the amount of money necessary to fill the whole checkboard (64 squares). How much money would the farmer need to give the salesman?