A Trip to the Store

To solve this problem, you could split the amount of routes you could travel by their intersections. For example, at the points A, B, C, and D, you can label them as 1 because there is only one way to get to that intersection.

Afterwards, you can then label the intersections below as follows, as the numbers will represent the number of paths you can take to reach the intersection, you could take 6 different routes to reach an intersection labeled with a six:

After that, you can find the rest of the intersections by adding up all of the number above that particular intersection, and the one west of that intersection.

Therefore, we get $\boxed{42}$ as our answer.

This is a recusive relationship f(n) = g(n) - f(n-1) where g(n) = n!/(n/2!)^2 i.e. number of ways from A to B in square grid. This is because the number of ways for the pattern in question is the number of ways we traverse 4x4 minus the missing part which is the original pattern but 3x3.