## Monday, March 20, 2006

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 in dollars. When they leave the bookshop, they notice that both fathers have spent 21 dollars more than their respective sons. Moreover, each of them paid per book the same amount of dollars as books that he bought. The difference between the number of books of Alex and Peter is five.

Who is the father of Tim?

1. THe mailman

2. I suppose the mailman could be his father... ;-)

For each father-son couple holds: the father bought x books of x dollars, the son bought y books of y dollars. The difference between their expenses is 21 dollars, thus x^2 - y^2 = 21.
Since x and y are whole numbers (each book costs a whole amount of dollars), 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.

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