Problem of the Week 22

Every day at noon, a ship leaves San Francisco for Tokyo, and tat the same instant, a ship leaves Tokyo for San Francisco.  Each trip lasts exactly eight days.  How many Tokyo ships will each San Francisco ship meet?


Alternate Problem 22

From A to B there are four possible air routes.  From B to C there are five possible air routes.  From C to D there are thee possible air routes.  How many different trips can be taken from A to D and back without taking the same route on any section of the return trip?


Extension Problem 22

The planet Octera is spherical and separated into eight countries, each occupying one octant of the sphere.  Thus, each country borders three other countries.  In how many different ways can a traveler visit each of the countries exactly once, beginning and ending the trip in the home country?*

*According to the International Law of Octera, no person my cross a point that is common to more than two countries.