One of the most popular features in the journal Mathematics Teacher, published by the National Council of Teachers of Mathematics, is the monthly calendar. It provides an interesting, unusual, or challenging problem for each day of the month. Some of these exercises, and others later in this text, are chosen from these calendars (the day, month, and year of publication of each problem are indicated). The authors want to thank the many contributors for permission to use these problems.
Use the various problem-solving strategies to solve each problem. In many cases there is more than one possible approach, so be creative.
Cross-Country Competition The schools in an athletic conference compete in a cross-country meet to which each school sends three participants. Erin, Katelyn, and Iliana are the three representatives from one school. Erin finished the race in the middle position; Katelyn finished after Erin, in the 19th position; and Iliana finished 28th. How many schools took part in the race? (May 27, 2008)
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