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You can also find solutions immediately by searching the millions of fully answered study questions in our archive. You can download our homework help app on iOS or Android to access solutions manuals on your mobile device. Asking a study question in a snap - just take a pic. Mathematical Excursions 3rd Edition Edit editions. In the metric system, what is the basic unit of length?

The basic unit of length is meter. That is, all other units of length in metric system are derived from meter. The basic unit of liquid is liter. That is, all other units of liquid measure in metric system are derived from liter. The basic unit of weight is gram. That is, all other units of weight in metric system are derived from gram. Solution Understand the Problem We would not be able to answer the question if Allison retraced her path or traveled away from point B. 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.

To find the total number of possible routes between two point, concentrate on the initial and final point and proceed by first considering motion in one particular direction, say left, this will give one route.

Now, the other route will be the one with all the initial motion in left direction and final motion towards right. Then consider the next possibility where the second last motion is towards right and so on. Write the number of routes in each hexagon and then look for a pattern. From the diagram considered above, a pattern can be observed that, all the outer hexagons have 1 inside them.

So, Hexagon B and F will have value 1. Also note that all hexagons other than the outer ones have value equal to the sum of values of two hexagons on the above row sharing boundary with the hexagon under consideration.


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