I have accepted a job in a major metropolitan area. I have requested that my employer find me an apartment less than a mile from the office so that I can walk to work everyday. I also want my home to be located so that I can take a different route every day for 5 years. I work 5 days a week, 50 weeks a year. Streets in the area are on a grid of squares, each 1/16 mile on the side, so my home must be fewer than 16 blocks from work. (Assume paths do not overlap themselves, and each "step" must decrease the distance between me and the office.)
a. At how many different sites could my apartment be located?
b. What is the nearest I can live to my office and still have access to enough different routes?
c. At which sites could I get the most number of routes? For how long could I work before running out of routes if my apartment is located at a site of maximum routes?
Honestly, I'm terrible at these kinds of problems and I have no clue how to even begin this. Any help would be greatly appreciated.