Doorstep Survey

[toucana]

A statistician is carrying out a doorstep survey of the ages of children in families. He rings the door-bell of a maths teacher who says  -->  "Well let's see: I have three children. The product of their ages is 36, and the sum of their ages is the same as the number of this house".

The canvasser frowns and says -->  "I still need a hint here".

 The maths teacher says -->  "OK, my eldest kid just started piano lessons"

"That's all I needed to know" says the canvasser, and walks away filling out the form.

Q1. What were the ages of the children ?

Q2. What was the number of the house ?

-------------------------------------------------

 

Spoiler

Solution:

The children were  aged 9.2.2 The house was number 13. -  There are eight possible ways of factorising 36 as the product of three non-zero integer numbers. Two of these ways (9.2.2) and (6.6.1) both add up to 13. The other 6 ways add up to different and unique totals. The fact that the canvasser had to ask for a hint, even though he already knew the number of the house (he was standing at the door) indicates that the house number must have been 13. Had it  been any other number, he would have solved the riddle immediately without asking further questions, because the other six possible factor sums have unique solutions. House number 13 is the only ambiguous case with two possible solutions. When the maths teacher said that he had an eldest child, the canvasser knew that their ages must be 9.2.2, because  the only other possible solution (6.6.1) requires the two older children to be twins of the same age, in which case there could not be a single "eldest child"

 

[John Cuthber]

Children's ages are not generally integers.

 

[Externet]

Twins of 3 and a 4.   Number 10  🤔

2, 3 and 6.  Number 11 🤔

1, 4 , 9  Number 14 🤔

Twins of 2 and a 9  Number 13 🤔

[TheVat]

SPOILERS (hide button, again, not showing up on tablet)

 

 

 

 

 

If I'm following this, then the guy needs a hint because there must be two sets of factors which give the house number.  In which case, the piano lessons is going to resolve which set.  So...piano is irrelevant (no definitve age for that), which only leaves "eldest" as relevant.  Ahh!  I think that's it.  So, 13.  9, 2,2.

[toucana]

This particular teaser originally turned up some years ago  in one of the DALnet IRC channels where I was an @   - I thought the guy was trolling us at first with an incomplete problem. I put it up here, mainly because I was curious to see if the spoilers button was working at all  - in the light of TheVat reporting problems with it  - and  it is on my Mac.

On the subject of using integer values to express a child's age - according to the UK Office of National Statistics - (in the 2021 UK census at least): -

 

Quote

"Age is derived from date of birth, and derives the age at a person's last birthday"

https://www.ons.gov.uk/census/censustransformationprogramme/questiondevelopment/demographyquestiondevelopmentforcensus2021

[TheVat]

3 hours ago, Externet said:

  🤔

🤔 🤔 

🤔

SPOILERS (I think the eyeball button, for hiding, is only obscured on certain Chrome tablets - a quirk which remains a mystery)

 

Do you see why only your last answer fits the conditions of the puzzle?  There is only one house number for which there are two solutions, so that house number is the one that would require a further hint for the canvasser.  Your last house number has another set of factors that will also add to that same number, but which make the reference to a singular eldest child problematic.  (I got it, but my first answer didn't fully spell that out)

[Sensei]

10 hours ago, John Cuthber said:

Children's ages are not generally integers.

LOL. This applies not only to children..

 

 

[Externet]

House numbers are.  But seen a NN 1/2 a couple of times...🙂

The way I see it is the statician knowing the house number, selects the ages from the several possibilities.