## MatheMUSEments

Articles for kids about math in everyday life, written by Ivars Peterson for Muse magazine.

## July 2, 2007

So it's already been a pretty tough school year? Some of your grades are OK, but others are quite dismal (especially that test you took the day after staying up way too late playing Guild Wars online)? Luckily, your teacher says you can drop a single test. Alright! But wait, which one?

The answer is easy if all of the tests are worth the same number of points. You simply drop the lowest score. But, if the tests are worth different numbers of points, dropping the lowest score isn't always the best strategy. Consider the following example.

On the first quiz, you score 80 out of 100 points, and get an 80 percent. On the second quiz, you score 20 out of 100: 20 percent. On the third quiz, you score 1 point out of 20: a miserable 5 percent. Without the option to drop one quiz, your final grade would be 101/220, or 46 percent. Ouch.

If you drop your lowest score (1 point out of 20), your final grade would be 100/200, or 50 percent. Ouch again. But, if you drop the score on the second quiz instead, your final grade would be 81/120, or 67.5 percent. Still not rocketing your way to the academic honors list, but, OK, you're passing.

In this case, it pays to work out all possibilities before deciding which grade to drop. Dropping your lowest score (or your lowest percentage) wouldn't guarantee that you'll end up with the best possible result.

It gets even trickier if you're allowed to drop two or more scores from your total. And if you're dealing with a lot of scores, it could take you a long time to calculate all the possibilities to find the result that helps you the most, and who wants that?

Math professor Jonathan Kane of the University of Wisconsin at Whitewater and his son Daniel, a student at the Massachusetts Institute of Technology and twice a member of the U.S. Mathematical Olympiad team, to the rescue. After the problem came up in conversation during a 10K run, they worked out a fancy formula that pinpoints the scores you should drop to get the best possible result, and created a computer program that allows your teacher to do these calculations quickly and easily.

AND, if you just mention casually that you're aware of their work, that will probably get you five bonus points.

Muse, October 2006, p. 33.