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Ants, Bikes, and Clocks: Problem Solving for Undergraduates by William Briggs

By William Briggs

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28. The double window. Imagine a double window is drilled symmetrically through the center of a sphere. How with the upper darker window fixed and the lower lighter much material is left in the sphere? Use a good picture, but window capable of sliding from fully closed (no overlap no calculus. 34. A safe move. To move a large heavy safe, two with the upper window). When the lower window is half cylindrical bars, 7 inches in diameter, are used as rollers. open, the total amount of light passing through the combined Assuming no slipping, how far forward does the safe move window is 1% less than when the lower window is fully when the bars have made one complete revolution?

A one-mile rail expands by one foot and bows upward along the arc of a circle. How high is the midpoint of the rail from the ground? The curved rail can be approximated by straight line segments. Hint 8: Change perspective. 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.

A surprising result. The 100 numbers in the set flasks with wine, using twice as much wine as water. Which { l , i , | , . . , j g i j } a r e written on a blackboard. One may flask was not filled, and which flasks were used for water erase any two numbers, a and b, and replace them by the and wine? [17] single number a + b + ab. 30. Messy desktop. Fifteen sheets of paper of various one number remains. What is this number? 1. HINT: Find the relationship that describes the number of tickets sold.

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