and .
There are a positive integer number, , of independent vectors, , where runs from 1 to . A trip starts from the appropriate of components and goes to a destination vector of positive integer components. A step of a trip consists of adding to a single component of the taxi's current position vector which was initially of components. How many distinct routes would accomplish this trip?
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
Make a grid of points that is 4 by 4. This is one more than 3 because zero is included. Starting in one corner, label the points when both routes to the point are available with the sum of the two ways to the point. Continue this process until the far corner is reached. If you did this correctly, then you will see the answer is 20