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.
You Lie! Max, Sam, and Brett were playing basketball. One of them broke a window, and the other two saw him break it. Max said, “I am innocent.” Sam said, “Max and I are both innocent.” Brett said, “Max and Sam are both innocent.” If only one of them is telling the truth, who broke the window? (September 21, 2008)
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