🚀 go-pugleaf

> 	There was a question that appeared in a math contest a while 
> back. That I need the solution for. Can't remeber the  exact details but 
> it's been racking my brains for the past week. I believe the three main 
> points are :
> 	1. Three girls the product of their ages is 72.
> 	2. The sum of their ages is their house number (unknown)
> 	3. The oldest likes strawberry pudding
> 
> 	What are their ages?

Oh, I liked this one! If I remember correctly, the product is 36, not
72. The additional details are as follows:

A man is collecting information for a census. A woman in a house
doesn't give the man her three daughters' ages, but he tells him that
the product of their ages is 36, and the sum of the ages equals our
house number. The man says: `But I can't determine your daughters'
ages with that! I need more information!'. The woman says: `Oh! The
oldest one plays the piano [or doesn't like TV, or anything you
want]'. The man then says: `Thanks! That's enough.'

The solution goes like this:

1. Make a list of all the triples of numbers (natural numbers, for the
   picky ones) whose product is 36.

2. For each of these triples, compute the sum of the three numbers. If
   the number of the house appeared only once as the sum of a triple,
   then the sum and the product would be enough to determine the ages of
   the girls. This is not the case, since the man `needs more
   information'. The only number that appears more than once as the sum
   of a triple in the list is 13: 1+6+6=2+2+9=13. Therefore the house
   number must be 13.

3. The last piece of info contains a distractor (plays the piano, likes
   strawberry pudding, etc.); the important thing is that there is _one_
   oldest girl. Thus, the ages are 2, 2 and 9 (and not 1, 6 and 6, in
   which case we should talk about the _two_ oldest).

Luis