By William Briggs

The publication is skinny yet jam-packed with flesh.

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**Additional info for Ants, Bikes, and Clocks: Problem Solving for Undergraduates**

**Sample text**

Sometimes it helps to assume the perspective of another person or object in the problem, and then ask if the problem is easier to solve. We return to this idea in Chapter 5 when we discuss relative velocity. But here is an example that illustrates the point. 8 Coincident clock hands. At what time (exactly) between 1:00 and 2:00 do the hands of a clock coincide? Solution 1: One of many solutions to the problem begins with the key insight that at the moment of coincidence, the two hands have moved for the same length of time starting at 1:00.

There is a nice algebraic way to analyze measuring problems like the one just presented. It also answers the question of when such measuring tasks are possible. In general, suppose that we have two jugs with capacities of j and K gallons, and suppose that we are asked to finish with G gallons in one of the jugs; in the above example, we have J = 3, K = 5, and G = 1. Chapter 4. How Do You Do It? 2. Measuring 1 gallon using a 3-gallonj ug and a 5-gallonjug. Jug status (0,0) (3,0) (0,3) (3,3) (1,5) (1,0) Move Both jugs empty Fill 3-gallon jug from well Empty 3-gallonjug into 5-gallonjug Fill 3-gallon jug from well Fill 5-gallon jug from 3-gallon jug Empty 5-gallon jug into well There are three basic moves in problems of this sort: fill an empty jug from the well, empty a full jug into the well, or empty a full jug into another jug.

What is the minimum number of trips needed for the man to cross the river with his three possessions? Show how it is done. (ii) <> (Tartaglia's Bride Problem). This time three beautiful brides and their jealous husbands come to a river. The ferry boat holds only two people. Furthermore, no woman may be alone with a man unless her husband is present. How can all three couples cross the river in the minimum number of trips? 2. Measuring problems. In all of these problems, the containers have no markings, so fractions of the full volume cannot be measured.