The Impossible Football Game Math Puzzle

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Can you solve the impossible American football game math problem? Here's the problem: Suppose A-B is an impossible American football game score. What are the values and A and B? Consider the values that maximize A+B-in other words, find the largest possible values of A and B that make the score impossible. There is only one combination that is correct. Consider the rules of American football to help you solve: a safety or returned two-point conversion gains two points; a field goal gains three points; a touchdown gains six points; a touchdown and a one-point conversion gains seven points; and a touchdown and a two-point conversion gain eight points. What is the maximum impossible score of an NFL football game?

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Key Facts In This Video

  1. An American football team can score 2, 3, 6, 7, or 8 points at a time. 00:28

  2. If a and b are relatively prime, then the largest possible score is ab-a-b. 01:53

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