Eight volumes of a mathematics encyclopedia are standing in order (left to right) on a book shelf. Each volume is 1 1/4 inches think, counting the covers which are each 1/8 inch thick. If a bookworm eats from the first page of Volume One straight through to the last page of Volume Four, including the intervening covers, how many inches has the bookworm devoured its way through?
Hint: Set eight books on a shelf and use a string to model the path of the worm.
Solution Commentary: Rather than provide a solution, some other questions will be asked.
First, suppose the library involved N volumes, aagin arranged in order of Volume One through Volume N. Construct a formula for finding the length of the "dinner" path for the bookworm?
Second, if the eight volumes had been placed in a random order on the shelf, what is the smallest and largest distances the bookworm could have eaten?