“I hear some youngsters playing in the back yard,” said Jones, a graduate
student in mathematics. “Are they all yours?” “Heavens, no,” exclaimed
Professor Geller, the eminent number theorist. “My children are playing
with friends from three other families in the neighborhood, although our
family happens to be largest. The Tribbiani’s have a smaller number, the
Greens have still a smaller number, and the Buffays have the smallest
number of all.” “How many children are there altogether?” asked Jones.
“Let me put it this way,” said Geller. “There are fewer than 18 children,
and the product of the numbers in the four families happens to be my
house number which you saw when you arrived.” Jones took a notebook
and pencil from his pocket and started scribbling. A moment later he
looked up and said, “I need more information. Is there more than one
child in the Buffay family?” As soon as Geller replied, Jones smiled and
correctly stated the number of children in each family. Knowing the house
number and whether or not the Buffays had more than one child, Jones
found the problem trivial. It is a remarkable fact, however, that the
number of children in each family can be determined solely on the basis of
the information given above! How many children are in each family?