Example: A race. Stan placed exactly in the middle among all runners in a race. Dan was slower than Stan, in 10th place, and Van was in 16" place. How many runners were in the race? Solution: Step one: Understand the problem and organize the given information. We are given three pieces of information: (1) Stan placed exactly in the middle among all runners; (2) Dan was slower than Stan, in 10" place; and (3) Van was in 16" place. We might draw a picture to organize this information: 16 10 Last place First place Van Dan Stan Step two: Devise a strategy. Of the three given facts, which one gives us an opening on a solution? In fact (1), the words "Stan placed exactly in the middle" means that there were as many runners faster than Stan as slower than Stan. Here is the key insight: There must have been an odd number of runners in the race. Just to get a feeling for the possibilities, let's draw another picture. Let's try a race with five runners. 5 16 10 3 1