The Walk to 15th and M
The thriving metropolis of Podunk is laid out in squares. A man who lives at 8th Street and Avenue F bowls at alleys located at 15th Street ( which is seven blocks north) and Avenue M (which is seven blocks east).
It is a nice fourteen-block walk, so every time he bowls he walks back and forth. Since all streets are equally desirable for walking he chooses his route at random except that he plans to use every possible route before repeating any particular one.
How many possible route are there? How many routes would there be between any two north and east points on a map?
