In January 2014, the company Quicken Loans made news by announcing that it would pay $1 billion to the person who submitted the perfect NCAA bracket for the men's Division I tournament that year. The company bought an insurance policy from Warren Buffett's holding company Berkshire Hathaway to cover the cost of any prize money.
Assume that everyone in the United States filled out many brackets and that all of the brackets produced in this way were different. How many brackets would each person have to fill out to make sure that altogether all of the possible outcomes of the 63 games where represented?
Use the fact that the population of the United States at this time was 317,622,403 people. Also, your answer should be a whole number since we can not make a portion of a bracket.