Point A to B
Probability
Level
5
A man is at point A and must reach point B by either moving right one unit or up one unit. How many different paths are there from point A to point B if he cannot exceed the perimeter of the triangle ?
The answer is 227.
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.
1 solution
Consider the following table where each entry stands for a point on the grid and the number is the number of ways how to get to that point, which is the sum of the number of ways to get to the point below and the number of ways to get to the point to the left. I guess this recursive definition is the simplest way to get to the solution of 227.
− − − − − − 1 − − − − − − 1 − − − − − 1 1 − − − − 2 2 1 − − − 5 5 3 1 − − − 1 4 9 4 1 − − 2 8 2 8 1 4 5 1 − 7 6 7 6 4 8 2 0 6 1 2 2 7 2 2 7 1 5 1 7 5 2 7 7 1