Vacuum Salesman [duplicate]

A vacuum salesman rings on the door of a woman, trying to sell her a vacuum. The woman declines the continous offers and gets annoyed by the persistent salesman. She eventually offers to buy a vacuum from him if he can name the ages of her three daughters based on the following information:

The product of the ages of my daughters is 36 and their sum is our house number.

The salesman takes a walk around the block, of course seeing the house number. He eventually ends up back at the woman's doorstep, complaining that there still is a missing piece of information. The woman agrees and tells him:

My youngest daughter plays piano.

He immediately knows the ages of the three daughters, successfully selling the woman a vacuum.

What are the ages of the three daughters?

PS: There are no tricks involved, all necessary information is contained in what the woman says.

I would say the answer is

6, 6 , 1.

I don't think the unrealistic 1 year old playing piano was intended. The real information was lying in, there being a youngest.

You know since the vacuum cleaner (after looking at the number) didn't know the answer. There must be a more combination with that sum. So calculating the sums:

36+1+1=38

18+2+1=21

12+3+1=16

9+4+1=14

9+2+2=13

6+6+1=13

6+3+2=11

4+3+3=10

(All combination. The only possibility is 6,6,1 and 9,2,2 But knowing there is a youngest, that must be

6,6,1

• Yep, you got it correct. Shame on all those people claiming that a 1 year old can't push tiles on a piano! Commented Jun 3, 2016 at 21:53
• @Skydiver Your puzzle was impossible without this assumption before your edit... Commented Jun 3, 2016 at 22:06
• @Viktor Jeppesen add spoiler hiders by using >! at the beginning of a line. It's kinda annoying though because you have to put an empty line after the spoiler block, and you cannot put multiple paragraphs into one block. Commented Jun 3, 2016 at 23:25
• My big problem with this puzzle is that you will always have a youngest even with twins. Somebody was born last. Commented Jun 5, 2016 at 15:16

Answer no longer valid after edit

They are

6, 3 an 2

Because

36 = 36*1*1 = 18*2*1 = 12*3*1 = 9*4*1 = 9*2*2 = 6*6*1 = 6*3*2 = 4*3*3

I assume every body is older than 1 (because the youngest can play piano)

$36 = 9*2*2 = 6*3*2 = 4*3*3$
There is a youngest daughter (there can't be 2 youngest daughters) so they are 6, 3 and 2

But :

- You can be younger even if you have the same age
- I don't know any 2 years old girl who plays piano

• Was about to answer this, and also think the riddle was lacking in that you have to assume ruling out the equations with one is a given. Commented Jun 3, 2016 at 20:34
• @Spacemonkey I know another version of it where the salesman knows the house number (but not the reader) and still can't conclude. So we know it is 6/6/1 or 9/2/2 and as there is a "youngest" we know the solution Commented Jun 3, 2016 at 20:42
• This reasoning was my first thought, too, but the woman could have multiple children the same "age" but still a distinct "youngest" if they are adopted or < 12 months apart.. maybe the puzzle is not meant to be that complicated though :) Commented Jun 3, 2016 at 20:52
• @whrrgarbl without the "no tricks involved" I would have said : this is impossible, she can't play piano before 2" Commented Jun 3, 2016 at 20:54
• Who says that slamming around on the piano isn't playing it? All a matter of perspective. Also, it is assumed that the daughters can only have integer ages, meaning that for example all 10 year olds are the same age. Commented Jun 3, 2016 at 21:39