The question I brought you today is not made by me, it's from one my favourite books - Mensa Logic Questions.

I personally like this question very much. This question is very well-known, so you might know the answer.

Here we go!

Matt met the old friend Dave.

Then Matt asked Dave his chilren's ages.

Dave answered "**The product of my children's age is 36.**"

Then Matt said, "**I have no idea what your children's ages are.**"

Dave said, "**The sum of their age is house number across the street.**"

Matt said again, "**I still have no idea.**"

Dave added, "**The oldest one has red hair.**"

Then Matt goes like "**OH!**" and could knew their ages.

What are ages for those three children?

flflvm97
Dec 14, 2014

#8**+13 **

Thanks flflvm97

I have given this the green Puzzle icon. :)

And I have added it to the Sticky Topic "Puzzles"

Maybe when you become comfortable with the forum you might like to organise our puzzles for us.

I have saved most of the good ones but I just 'shove them in' They are not actually organised at all. :(

If you - or anyone else want a job like this then message me please.

Melody
Dec 14, 2014

#1**+5 **

Ok, 36 factorized is 2*2*3*3

Their ages can thus be:

4, 3 and 3 y/o sum: 10

6, 2 and 3 y/o sum: 11

9, 2 and 2 y/o sum: 13

36, 1 and 1 y/o sum: 38

18, 2 and 1 y/o sum: 21

12, 3 and 1 y/o sum: 16

9, 4 and 1 y/o sum: 14

6, 6 and 1 y/o sum: 13

After Dave told Matt the sum of the ages, he still didn't know what their ages was. This is bacause the sum of their ages is 13, the only sum with more than one possibility. Lucky number, eh?

Then Dave tells Matt that there is an "oldest one". Now it's only one possibillity:

9, 2 and 2.

Guest Dec 14, 2014

#2**0 **

I got a good riddle!

Peter lives in a green house. His neighbours have exactly two neighbours. Peter's neighbours live in red houses: one to the left and one to the right. Both his neighbours are neibours to one blue house. Yet Peter's left neighbour has a neighbour who live in a green house.

Why is this?

Guest Dec 14, 2014

#4**0 **

**This question has several solutions**. Why do you assume three children? There also could be two or four children.

If there are four children then they could be 2, 2, 3, 3 years. Two sets of twins. Twins still have an eldest usually by a few minutes, but the integer age will be identical.

If there are two children they could be 1 and 36, or 2 and 18, or 3 and 12, or 4 and 9, or twin six-year-olds (still with an “older one”).

**From the readers point of view, this question does not have an exclusive solution.** The person to whom it was asked could look at the address then derive the solution, but not the reader.

Nauseated
Dec 14, 2014

#5**0 **

Hi Nauseated

the last sentence is

"What are the ages of those 3 children."

We did have to make some assuptions. Like that Matt can see the house number of the house across the street and that if two children have the same year age that there is not an older one.

And that Matt is able to deal with all this logic while drinking with his mate.

But most of these are reasonable assumption for a puzzle like this one.

I thought it was a great puzzle.

Thanks flfl :)

Melody
Dec 14, 2014

#6**0 **

Hi Melody

**The last sentence is a question implying a “fact” not otherwise in evidence.** The phrasing implies that there should be explicit evidence, but there is not.

*We did have to make some assuptions. Like that Matt can see the house number of the house across the street and that if two children have the same year age that there is not an older one.*

The assumption that “. . . *that Matt can see the house number* . . .” may be valid, but is irrelevant because we do not have, and should not need, that information.

* . . . if two children have the same year age that there is not an older one.*

This is not a valid assumption because many families have twins. The three children solution for this very question demonstrates younger twins, and in fact there is an older one, because the simultaneous birth of twins is an extremely unlikely event. I.E an unreasonable assumption.

**These are logic questions; specifically implication logic questions that should resolve to a point solution without ambiguity.** That is, if it is properly written, **the solution should not require any assumptions, conjectures, speculation, or guessing to determine a solution, or set of solutions.** Note that in logic, “implication” is not the same as “assumption.”

*And that Matt is able to deal with all this logic while drinking with his mate.*

Downing a few good belts may, in fact, help with the nauseating ambiguities by implying (making an assumption of) a “fact” contained only in the explicit question portion at the end of the statements.

* But most of these are reasonable assumption for a puzzle like this one.*

**A reasonable assumption is to have a logic puzzle that doesn’t need assumptions.** If this was the case then it would be an OK puzzle.

This puzzle is not bad. I am saying, based on the statements, there are several solutions. The three children solution is only one.

Nauseated
Dec 14, 2014

#7**0 **

Ok Nauseated. It would have been better if it were worded so that there were no ambiguities but I still liked it.

Thanks flfl

Melody
Dec 14, 2014

#8**+13 **

Best Answer

Thanks flflvm97

I have given this the green Puzzle icon. :)

And I have added it to the Sticky Topic "Puzzles"

Maybe when you become comfortable with the forum you might like to organise our puzzles for us.

I have saved most of the good ones but I just 'shove them in' They are not actually organised at all. :(

If you - or anyone else want a job like this then message me please.

Melody
Dec 14, 2014