Thursday, October 24, 2013

Tennis Balls

Along with coaching, I captain two men's tennis teams.  It's pretty cool.  We have a team of 12-16 guys and on any given night we play eight: three doubles matches and two singles matches.  We have a fun team and we (surprise, surprise) pretty much always go out and celebrate afterward, win or lose.

And by celebrate I mean go out and drink beer.  Our latest favorite watering hole is the Groveland Tap. Excellent beer selection and a good happy hour menu.

If you're counting, we have five tennis matches per night.  Our home courts are at Fred Wells Tennis & Education Center in St. Paul and they are great hosts.  There are five tennis courts in the back bubble and those are the ones we play on.  Here's an overhead view of the facility in the summer when the bubble isn't up.

(As an aside, it's odd that they aren't oriented north-south, as is the convention in the U.S.)

Put this information about the courts in your back pocket for a minute while I introduce the other part of the story.

As a home captain, I have to provide balls for all five matches. My favorite ball is the Pro Penn.

When we play a match, we need to keep track of our balls. Every match gets a can of three balls and we don't want them to get mixed up with those on adjacent courts. To this end, Penn (and every other ball manufacturer) is helpful. They put numbers on their balls so that they don't get mixed up.

The problem is, Penn only numbers balls 1-4 and we have 5 courts. So two matches will have the same numbers on their ball. I need to keep those balls away from each other.  One possible favorable distribution of balls would look like this:

And this would be an unfavorable distribution of balls, because the 1's on the adjacent courts could get mixed up:

Because it is desirable to let the players open the cans (there's a certain thrill to it, even if you've opened thousands in your life), I as captain have to shake the cans and rotate the balls to see the numbers through the wrapper. It's kind of a pain and the other night as I was rotating the balls so that I could give the right numbers to the right players, I thought,

"Is it worth it? How likely is it really that two consecutive courts will end up with the same ball if I do it completely at random?"

And this is how I introduced combinatorics to my HL Math class.

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