Getting Round the City

The grid below represents a city laid out in "blocks" with all the roads running north-south, or east-west.

Imagine two friends live where the red and blue dots are on the grid.

The animation shows three paths that one friend could choose if he wanted to visit the other.

He likes to find the shortest routes possible, so he always travels north or east, never south or west.


different routes going by blocks on a city grid

How many different paths are there from A to B?


Here are some questions you might like to consider:

If I know the coordinates of two points, can I quickly work out how far I will have to walk to get from one to the other?

Is there a quick way to find all the different paths from one point to another?

Is there a quick way to work out how many different paths there will be?

If I only want to walk a certain number of blocks, can you find a quick way to work out the number of possible places I might finish at?