Guv, Lior & kedaman - An Amazing Puzzle

[DavidHooper]

Once upon a time, a salesman approached an old lady in order to sell her children some goods. He asked how many children she had and how old they were.

The old lady replied that she had 3 children. She told him the product of their ages was 36 and that the sum of their ages was on the nextdoor house.

So, the salesman jumped over the fence and looked at the number on the nextdoor house. He returned to the old lady and told her he could not complete the problem without more information.

The old lady consented to give him one more item of data. She said 'The eldest child plays the piano'.

Your problem: what are the ages of the 3 children?

I promise this problem is completely soluble! Just to clarify: you don't get told the number on the nextdoor house!
Best of luck...

[Illuminator]

Wasn't this question asked before? It is simple enough when you work out the combinations.

[Guv]

Illuminator is correct. I counted 8 possibilies for the ages, including 1, 1, & 36 which is obviously not correct.

If you check them all, it does become obvious.

[DavidHooper]

ok, ok. guv, you probably have the correct answer. for everyone else, here is how you begin to go about it:

1)Split 36 into prime factors: 2,2,3,3
2)Also use 1 as a factor so 1,2,2,3,3
3)Use these to get combinations.
1,1,36
1,2,18
1,3,12
1,4,9
1,6,6
2,2,9
2,3,6
3,3,4
4)Now can you finish it off?

[kedaman]

1+1+36=38
1+2+18=21
1+3+12=16
1+4+9=14
1+6+6=13 <- A
2+2+9=13 <- B
2+3+6=11
3+3+4=10
If the sum is 13, then there's still not enough info, and since the eldest child
has to be older than the others, it's the B alternative.

[DavidHooper]

yer you got it.