Solution to: Buying Books
For each father-son couple holds: the father bought x books of x shillings,
the son bought y books of y shillings.
The difference between their expenses is 21 shillings, thus x2 - y2 = 21.
Since x and y are whole numbers (each book costs a whole amount of shillings), there are two possible solutions: (x=5, y=2) or (x=11, y=10). Because the difference between Alex and Peter is 5 books, this means that father Alex bought 5 books and son Peter 10. This means that the other son, Tim, bought 2 books, and that his father is Alex.