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?

Let A = the number of books Alex bought. => A^2= Alex' bill
Similarlly, a^2= Alex' son's bill
B^2= Bob's bill
b^2= Bob's son's bill

A^2 = a^2 + 21 => A^2 - a^2 = (A + a)(A-a) =21 Since the only whole number factors for 21 are (7 and 3) or (21 and 1), Alex bought either 5 books (with his son buying 2) or 11 books (with his son buying 10). The same reasoning applies to Bob and his son.

There is only one combination that allows Alex to buy five books more or less than Peter, and that is: Bob bought 11 books (his bill was 121); Peter is Bob's son and he bought 10 books (his bill was 100); Alex bought 5 books (for 25) and his son Tim bought 2 books (for 4).

Posted by TomM on 2002-05-16 16:37:29