Welcome to Week 11 of the Wednesday Morning Math Challenge. You can find solutions to the Week 10 puzzles here, along with — more importantly — discussions of some ways to approach them. Remember that the real goal here is to think creatively.
This week, we’re going to have a little bit of fun with football.
1. Suppose you’re the head coach of the Washington Sentinels. You’re trailing Detroit by 14 points with no timeouts and two minutes left in the fourth quarter. Your quarterback, Shane Falco, runs in for a touchdown. Suppose your kicker, Nigel Gruff, has a 97% one point conversion rate, and Falco and the offense have a 47% two point conversion rate. Do you go for one or two? Why?
2. What is the lowest two point conversion rate for which you would want to go for two?
3. Now, consider the unit square in two dimensional space, 0<x<1,0<y<1. Let x and y be the two point and one point conversion rate of a given team. In what region would you go for one in this circumstance? In what region would you go for two?