Finding Pathways from A to B: Strategies for Test Prep

[dontdisturbmycircles]

Homework Statement

I am studying for a test on Monday,

I am making myself problems and I don't know how to do this one.

http://img175.imageshack.us/img175/8076/pathwayhf7.jpg

How many ways are there to get from A to B?

The middle is a "pond" and there are pathways on all sides of the pond.

Homework Equations

I ussually do these with permutations, for example of there is a grid in which you have to travel down 8 and right 5 I find out how many distinct permutations there are of DDDDDDDDRRRRR and that is the answer. Of course this only works for simple pathway problems and is useless in this scenario.

I know that I will be facing problems like this on my test so I need a better strategy, can someone help me find one?

The Attempt at a Solution

 

[dontdisturbmycircles]

Nevermind, I think that the best way to tackle these is just to add up the number of ways of getting to each point and then use that to derive the number of ways to get to the next point. Then just rinse and repeat.

 

[AlephZero]

Nevermind, I think that the best way to tackle these is just to add up the number of ways of getting to each point and then use that to derive the number of ways to get to the next point. Then just rinse and repeat.

That's about as good as it gets, in the general case.

Unless there are some restrictions on how you move, the number of paths is infinite, since you can go round a closed loop any number of times. In your "permutations of DDDDDDDDRRRRR" example you seem to be assuming you can only move down and right.