Hey guys. I have a doozy of a maths riddle that I haven't been able to solve. Here's hoping that you might be able to.​

How old are they?

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One of Peter’s former students from university, Michael, visited him unexpectedly one day. They had not seen each other for a long time and Peter asked if Michael had had any children. When Michael replied that he had three children, Peter asked how old they were. Michael replied that the product of their ages was 72 and that by a strange coincidence the sum was the same as the number part of his car’s number plate. Peter went outside to look at the car, but came back and said that Michael was not playing fair as this was not enough information. Michael agreed and added that the eldest played basketball every Saturday. Peter then told Michael the ages of his children.


How old are Michael’s children?


(There may be twins or triplets and the ages are whole numbers)

1. Australian Number plates consist of three letters and three numbers. For example, FJH 123.

2. The basketball reference, I believe, was an indication to the word "eldest" which I assumed meant that the oldest child was not a twin or triplet.


I have a list of permutations for 3 numbers that will have a product of 72:

1-8-9
1, 3, 24
1, 4, 18
1, 36, 2
1, 1, 72
1, 6, 12

2, 3, 12
2, 4, 9
2, 6, 6
2, 24, 3
2, 2, 18

3, 4, 12
3, 6, 4
3, 8, 3: SOLVED. Answer.
3, 12, 2

4, 6, 3
4, 9, 2

Edit: This was solved in 5 minutes. Admittedly, Google helped. Match the products with the sum and find out which once repeats. That was 2, 6, 6 and 3, 3, 8 at 014. The "oldest" implies that there the largest number is singular, hence, 2, 6, 6 is out and 3, 3, 8 is the winner

 

Peter has the sum and the product.

We only know the sum.

Knowing those two things doesn't solve it.

Which means the possible answers are the permutations having the SAME SUM.

Which are 2, 6, 6 and 3, 3, 8.

Since the younger are twins, answer is 3, 3, 8.

EDIT: Also, you can always... http://en.wikipedia.org/wiki/Ages_of_Three_Children_puzzle

 

For those that are curious at to what the detailed solution is: http://mathforum.org/library/drmath/view/58492.html
Also, I still can't believe you never thought to google it...

 

I might get flamed for this but how about a Puzzles Thread?

 

I did google it...but I was too specific with the wording and didn't get any hits.

 

mathematical problem children product 72

My first try to see an optimal solution.

In fact, any puzzle, old, new, a few tries with google and you will get it.