Three towns - Ambridge, Bordertown, and Capeside are each connected by a network of roads. There are 82 ways to get from Ambridge to Bordertown, including those routes that pass through Capeside. There are 62 ways to get from Bordertown to Capeside, including those routes that pass through Ambridge. The number of ways to get from Ambridge to Capeside, including those ways passing through Bordertown, is less than 300.

How many ways are there to get from Ambridge to Capeside, including those routes that pass through Bordertown?

   If the roads from A to B are equal to x
and the roads from B to C are equal to y
and the roads from A to C are equal to z,

then x + y*z = 82
       y + x*z = 62
and  z + x*y = "N"   (an integer less than 300)

By trial and error I found (x,y,z) = (5,7,11)
which makes "N" = 46.

So 46 is one answer, but I haven't proven that it's unique.

Posted by Larry on 2009-01-24 13:54:52