# Downtown walking distances

We began our second session by noticing that in a perfect city grid such as (some of) Boise’s downtown and north end, there are a lot of ways to get from point A to point B. So how many are there really?

In the beginning we made the simplifying assumptions that we will only count “direct paths”, that is, paths that have the minimal distance. But even with this assumption there are still many ways to get there!

This led us to a number of different questions:

• How many ways are there to go $n$ blocks north and $m$ blocks east on a grid?
• What kind of pattern do you see if $n$ is fixed at $1$? At $2$? etc.
• If you do allow paths that are not optimal (but still don’t backtrack), how much does the count increase?