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Thus we assume that on a direct route, she always travels along a street in a direction that gets her closer to point B. Devise a Plan The map in Figure 1. Thus we make a diagram that allows us to concentrate on the essential information. See the figure at the left. Because there are many routes, we consider the similar but simpler diagrams shown below. The number at each street intersection represents the number of routes from point A to that particular intersection.

It appears that the number of routes to an intersection is the sum of the number of routes to the adjacent intersection to its left and the number of routes to the intersection directly above. For instance, the number of routes to the intersection labeled 6 is the sum of the number of routes to the intersection to its left, which is 3, and the number of routes to the intersection directly above, which is also 3.

Review the Solution Ask yourself whether a result of 35 seems reasonable. If you were required to draw each route, could you devise a scheme that would enable you to draw each route without missing a route or duplicating a route?

The number in each hexagon represents the total number of different routes that a ball from A can take to reach the top of that particular hexagon. A ball dropped from A on striking the vertex of an hexagon has equal probablility of going to either left or right. So the ball can have many different routes to reach a paticular hexagon. When the ball touche a vertex, it can either go left or right.

Lockwood's primary interest today is helping developmental math students overcome their challenges in learning math. Richard Nation received a B. Nation taught math at Palomar College in California, where he was on the faculty for 20 years. He has over 38 years' experience teaching mathematics at the high school and college levels. He is the co-author of several Aufmann titles. Nation's professional interests include the impact of technology on curriculum development and on the teaching of mathematics at the precalculus level.

Daniel Clegg received his B. He is currently a professor of mathematics at Palomar College near San Diego, California, where he has taught for more than 20 years.

He has also assisted James Stewart with various aspects of his calculus texts and ancillaries for almost 20 years. For example, sending information across the Internet is better understood when one understands prime numbers; the perils of radioactive waste take on new meaning when one My library Help Advanced Book Search. Aufmann , Joanne Lockwood , Richard D. If you no longer have access to the e-mail address associated with your account, contact Customer Service for help restoring access to your account.

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