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.
Locking Boxes You and I each have one lock and a corresponding key. I want to mail you a box with a ring in it, but any box that is not locked will be emptied before it reaches its recipient. How can I safely send you the ring? (Note that you and I each have keys to our own lock but not to the other lock.) (May 4, 2004)
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