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.


2 Answers 2


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:









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


  • $\begingroup$ And please help to format, i couldn't do the cool hide answer thingy $\endgroup$ Commented Jun 3, 2016 at 21:52
  • $\begingroup$ Yep, you got it correct. Shame on all those people claiming that a 1 year old can't push tiles on a piano! $\endgroup$
    – Skydiver
    Commented Jun 3, 2016 at 21:53
  • $\begingroup$ @Skydiver Your puzzle was impossible without this assumption before your edit... $\endgroup$
    – Fabich
    Commented Jun 3, 2016 at 22:06
  • 1
    $\begingroup$ @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. $\endgroup$
    – Tony Ruth
    Commented Jun 3, 2016 at 23:25
  • 2
    $\begingroup$ My big problem with this puzzle is that you will always have a youngest even with twins. Somebody was born last. $\endgroup$ Commented Jun 5, 2016 at 15:16

Answer no longer valid after edit

They are

6, 3 an 2


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

  • $\begingroup$ 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. $\endgroup$ Commented Jun 3, 2016 at 20:34
  • $\begingroup$ @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 $\endgroup$
    – Fabich
    Commented Jun 3, 2016 at 20:42
  • $\begingroup$ 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 :) $\endgroup$
    – user812786
    Commented Jun 3, 2016 at 20:52
  • $\begingroup$ @whrrgarbl without the "no tricks involved" I would have said : this is impossible, she can't play piano before 2" $\endgroup$
    – Fabich
    Commented Jun 3, 2016 at 20:54
  • $\begingroup$ 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. $\endgroup$
    – Skydiver
    Commented Jun 3, 2016 at 21:39

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