Discrete Mathematics
# Grid Walking

If Anna only moves right or up or down, and isn't allowed to retrace her steps, how many ways does she have to get to Ben?

I was on vacation in England, and wanted to visit the Tower of London. The roads were laid out on a grid map, and and the castle was 4 blocks north and 5 blocks east. I also wanted to visit the Apple store along the way, and check out the new IWatch.

If I were to travel only north and east, how many routes did I have to get to the castle?

I was on vacation in England, and wanted to visit the Tower of London. The roads were laid out on a grid map, and and the castle was 4 blocks north and 5 blocks east. I also want to get at least one ice cream cone along the way. I knew that there were 2 ice cream shops that I could use, and they were conveniently located at an intersection.

If I were to travel only north and east, how many routes did I have to get to the castle?

$P$ to $Q$?

How many distinct paths consisting of steps only right or down are possible fromI was on vacation in England, and wanted to visit the Tower of London. The roads were laid out on a grid map, and and the castle was 4 blocks north and 5 blocks east. Unfortunately, there was some police activity near the hotel, and that intersection was blocked off so I could not go through it.

If I were to travel only north and east, how many routes did I have to get to the castle?