Two friends, Alex and Bob, go to a bookshop, together with their sons Peter and Tim. All four of them buy some books. Each book costs a whole amount of shillings.

When they leave the shop, they notice that both fathers have spent 21 shillings more than their respective sons. Moreover, each of them paid per book the same amount of shillings as the number of books that he bought.

The difference between the number of books that Alex bought and that Peter bought is five.

Who is the father of Tim?

from the problem:

''When they leave the shop, they notice that both fathers have spent 21 shillings more than their respective sons. Moreover, each of them"

"each of them" I took to refer to the fathers only, because the fathers are the subject of the sentence immediately preceeding this one, (not the fathers and the sons).  Also the first sentence "Two friends, Alex and Bob, go to a bookshop."  Two friends (i.e. the fathers) is also the subject.

I seem to be the only one who took that stance so far.  Grammatically, I believe I am correct.  Not meaning to nitpick, but am I right.  The author also made the same conclusion as is clear by reading the solution.  I could not figure out how to solve it the way I thought about it.  If this is correct, it changes the problem.  Can anyone still come up with a solution?  Saying that the fathers each spent n^2 for their books but not necessarily their sons.

Great problem, regardless.

Posted by john on 2005-03-11 19:10:51