A Football Puzzle

[Photo by rdesai.]

The MIT Mathmen got the ball on their own 20-yard line for the last drive of the game. They were down by 2 points, so they needed at least a field goal to win the game.

If quarterback Zeno and his offense advanced the ball halfway to the opposing team’s end zone on each play…

Who Won the Game?

If you live outside the U.S., you may need to look up American Football rules to answer these questions.

On which play did the team first fail to make a first down?

Did they succeed in their attempt at a third down conversion?

On which play were they forced to try for a field goal?

The MIT field goal kicker makes 100% of the goals he attempts from 25 yards out, but his percentage goes down 4% for every yard farther than that. What is the probability that he will make the winning goal?

Beware:

In American football, where the goalpost is located at the back of the end zone (above the end line), the ten yards of the end zone are added to the yard line distance at the spot of the hold. … In field goal and extra point attempts, the ball is snapped to a holder lined up about seven yards from the line of scrimmage.

— Field goal (American and Canadian football)