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.
Palindromic Number (Note: A palindromic number is a number whose digits read the same left to right as right to left. For example, 383, 12321, and 9876789 are palindromic.) The odometer of the family car read 15951 when the driver noticed that the number was palindromic. “Curious,” said the driver to herself. “It will be a long time before that happens again.” But 2 hours later, the odometer showed a new palindromic number. (Author’s note: Assume it was the next possible one.) How fast was the car driving in those 2 hours? (December 26, 1998)
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