During the recent Winchester 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 apple pie
-- a favorite dessert of many of the children
here in the Shenandoah Valley."
The census-taker promptly wrote down the ages
of the three children.
How old are they?
Solution to the Problem:
The ages of the three children must be 3, 3, and 8,
and the address is 14.
The following are the only combinations of three ages
whose product is 72:
| 1st Child
|
2nd Child
|
3rd Child
|
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
|
Except for two of the combinations, their sums are
all different, so the census worker would have been
able to determine the ages of the children if the
address had been any of the different ones.
As she needed more information, however, the address
must have been 14, a total shared by two combinations:
2, 6, 6, and 3, 3, 8.
So when the father indicated
that he had an
oldest child, she
eliminated the first possibility, which had two
"oldest," leaving only 3, 3, and 8 as the answer.