American Football Scoring


There are a few ways we can score in American Football:

  • 1 point - After scoring a touchdown, the team can choose to score a field goal
  • 2 points - (1) after scoring touchdown, a team can choose to score a conversion, when the team attempts to score a secondary touchdown or (2) an uncommon way to score, a safety is score when the opposing team causes the ball to become dead
  • 3 points - If no touchdown is scored on the possession, a team can attempt to make a field goal
  • 6 points - Awarded for a touchdown

Given the above the potential point values for American Football are:

  • 2 points - safety
  • 3 points - only field goal
  • 6 points - only touchdown
  • 7 points - touchdown + field goal
  • 8 points - touchdown + conversion

Given a score value, can you write a function that lists the possible ways the score could have been achieved?

For example, if you're given the value 10 the potential values are:

  • 8 points (touchdown + conversion) + 2 points (safety)
  • 6 points (only touchdown) + 2x2 points (safety)
  • 7 points (touchdown + field goal) + 3 points (only field goal)
  • 5x2 points (safety)
  • 2x2 points (safety) + 2x3 points (only field goal)


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