Student Bill Jones was visitng his Maths Professor at the professors home.
'I hear some youngsters playing in the garden,' said Jones, a graduate
student in mathematics. 'Are they all yours?'
'Heavens, no,' exclaimed Professor Smith, an eminent number theorist.
'My children are playing with friends from three other families in the
neighbourhood, although our family happens to be the largest. The
Browns have a smaller number of children, the Greens have a still
smaller number, and the Blacks the smallest of all.'
'How many children are there altogether?' asked Jones.
'Let me put it this way,' said Professor Smith.
'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 Black family?'
As soon as Smith replied, Jones smiled and correctly stated the number of children in each family.
How many children in each family?