This past Sunday, the Super Bowl (the final playoff game of the American football season) was held. The Kansas City Chiefs beat the San Francisco 49ers by a score of 31-20. Let us analyze this result 8 using the fact that in American football, most scoring happens in units of 3 (field goal) or 7 (touchdown plus one-point conversion).
(a) For each of the two teams, find all of the ways to write their score as some number of 3s plus some number of 7s. In this part, we are only keeping track of the total number of summands of each type, 9 not the order. [
(b) Using your answer to (a), find all of the sequences of scoring plays that could have led to the final score. Represent each scoring play as a tuple with the first element representing the team ("KC" or "SF") and the second element representing the score (3, 7). Your answer should consist of a list/tuple in which each entry is a list/tuple of scoring plays.
(c) Write down the sequence of scoring plays that took place in real life and confirm that it appears in your answer to (b).