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)