Ages of Three Children

Date: 9/4/96 at 20:40:5
From: Mrs. Barbara M. Ardell
Subject: Ages of Three Children

During a recent census, a man told the census taker that he had three  
children. When asked their ages, he replied, "The product of their 
ages is 72. The sum of their ages is the same as my house number."
  
The census taker ran to the door and looked at the house number.  
"I still can't tell," she complained.  The man replied, "Oh that's 
right,  I forgot to tell you that the oldest one likes chocolate 
pudding."  

The census taker promptly wrote down the ages of the 3 children.  How 
old are they?

Jason Ardell

Date: 9/5/96 at 13:47:14
From: Doctor Tom
Subject: Re: Ages of Three Children

Hi Jason,

After I know that the ages multiply to 72, here is a complete
list of the possibilities:

Ages:            Sum of ages:
1 1 72            74
1 2 36            39
1 3 24            28
1 4 18            23
1 6 12            19
1 8 9             18
2 2 18            22
2 3 12            17
2 4 9             15
2 6 6             14  **
3 3 8             14  **
3 4 6             13

Note that every combination of possible ages which has a product of 72 
has its own unique sum of ages - except for 2, 6, 6 and 3, 3, 8, both 
of which share the sum of 14. Since the census taker can't figure out 
the ages after looking at the house number, the house number must be 
14, because then the ages could be either 2, 6, 6 or 3, 3, 8.

Now, the next clue is that the _oldest_ child likes chocolate pudding. 
This means that there is _one_ oldest child. Well, there is no oldest 
child of the ages are 2, 6, 6, so the ages of the children must be 3, 
3, and 8 years old.

-Doctors Tom and Chuck,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/