Math Problem

[RedArmy]

An insurance salesman is going door to door selling insurance. He arrives at one house and asks the lady about her family and wishes to know the ages of her children. She informs him that she has 3 children but does not wish to disclose information about them to a complete stranger. So he asks for some clues

1) The product of their ages is 36

2) The number of the house next door is the sum of their ages

Edit: (Since some people have a problem with this line, just ignore it...but I'm not removing it) At this point the salesman is pretty sure of his answer, but needs one more clue, so

3) Her eldest child plays the piano.

Straightaway he knows their ages and attempts to sell the woman insurance.

What are the ages of the woman's children and how did the salesman know?

This was a question that our teacher gave to us today in Discrete Mathematics. I know the answer, but I'm not sure how part II really helps anything. Therefore, I'm posting both to see if someone knows, and can explain it. Have fun!

 

[z1ggy]

6, 3, 2...? lol Is this a college course?

 

[RedArmy]

Originally posted by: z1ggy
6, 3, 2...? lol Is this a college course?

I'd be very surprised if there was a high school that taught Discrete Mathematics (not saying it isn't possible, but it would be rare)

Therefore, to answer your question about it being a college course, yes.

 

[Vegitto]

The second and third clue don't add anything. They could be 36, 1 and 1 for all we know. You know, some people make a career out of playing the piano.

 

[RedArmy]

Originally posted by: Vegitto
The second and third clue don't add anything. They could be 36, 1 and 1 for all we know. You know, some people make a career out of playing the piano.

That's what I thought, the third question is definitely needed though...I just don't understand how the second one works...I don't understand the reasoning

 

[Lamont Burns]

36 and a set of 1 year old twins!

That mother really needs to kick out that deadbeat kid. Perhaps tho the 36 year old is disabled and thus still eligible as a dependent.

 

[TuxDave]

The underlying assumption is that all pieces of information are useful. So telling #2 and having the salesman unable to figure out what the age is implies that knowing the sum of the ages AND the product of the ages must still have multiple solutions.

Want me to solve it for you or is that enough?

 

[ryan256]

Could be 6, 3, 2. Could be 1, 4, 9. Without the number mentioned in #2 there is no way to tell for sure.

 

[RedArmy]

Originally posted by: TuxDave
The underlying assumption is that all pieces of information are useful. So telling #2 and having the salesman unable to figure out what the age is implies that knowing the sum of the ages AND the product of the ages must still have multiple solutions.

Want me to solve it for you or is that enough?

I'm staring at the answer right now but I fail to see how out of the possible answers you get, you would be able to use clue 2 to your advantage. It could be any arbitrary number. I would go into detail about it, but I don't want to ruin the question...I'll reword it once someone figures it out.

 

[TuxDave]

Originally posted by: RedArmy

Originally posted by: Vegitto
The second and third clue don't add anything. They could be 36, 1 and 1 for all we know. You know, some people make a career out of playing the piano.

That's what I thought, the third question is definitely needed though...I just don't understand how the second one works...I don't understand the reasoning

Well, ok I guess I can spell it out:

So given that the product of the ages is 36, the salesman won't know how old they are because there are still multiple solutions. (I wrote the sum along side of it to continue my point)

1,1,36 = 38
1,2,18 = 21
1,3,12 = 16
1,4,9 = 14
1,6,6 = 13 <--
2,2,9 = 13 <--
2,3,6 = 11
3.3,4 = 10

The mom then said that the sum was something and the salesman is still unable to figure out the age because the house next door must've been #13. If it was any other sum then he'd be able to deduce what the ages were.

The 3rd clue implies there IS an oldest child and no "tie" for oldest leading to 2,2,9.

 

[ivan2]

Originally posted by: Lamont Burns
36 and a set of 1 year old twins!

That mother really needs to kick out that deadbeat kid. Perhaps tho the 36 year old is disabled and thus still eligible as a dependent.

yup, without giving the number of the next house it could also be 12,3,1 or 6,6,1 or 18,2,1

edit: thanks tuxdave for spelling it out.

 

[ryan256]

Originally posted by: RedArmy

Originally posted by: Vegitto
The second and third clue don't add anything. They could be 36, 1 and 1 for all we know. You know, some people make a career out of playing the piano.

That's what I thought, the third question is definitely needed though...I just don't understand how the second one works...I don't understand the reasoning

Its simple. If the number of the house next door is 11 then we know the ages are 6, 3, 2. If the number however is 14 then the ages are 1, 4, 9.

36 has very few sets of 3 factors. Its not difficult to find a combination that adds up to #2.

 

[memo]

Originally posted by: TuxDave

Originally posted by: RedArmy

Originally posted by: Vegitto
The second and third clue don't add anything. They could be 36, 1 and 1 for all we know. You know, some people make a career out of playing the piano.

That's what I thought, the third question is definitely needed though...I just don't understand how the second one works...I don't understand the reasoning

Well, ok I guess I can spell it out:

So given that the product of the ages is 36, the salesman won't know how old they are because there are still multiple solutions. (I wrote the sum along side of it to continue my point)

1,1,36 = 38
1,2,18 = 21
1,3,12 = 16
1,4,9 = 14
1,6,6 = 13 <--
2,2,9 = 13 <--
2,3,6 = 11
3.3,4 = 10

The mom then said that the sum was something and the salesman is still unable to figure out the age because the house next door must've been #13. If it was any other sum then he'd be able to deduce what the ages were.

The 3rd clue implies there IS an oldest child and no "tie" for oldest leading to 2,2,9.

That was a pretty awesome answer. No wonder I sucked at discrete math in college.

 

[sdifox]

a*b*c=64
a+b+c=d

I don't see how you can derive an deterministic answer from those alone. The oldest kid plays piano, but there is no definite age for anyone to play piano and we don't know d.

TuxDave, are you allowed to brute force list the table of possible combination that way? Discrete Math was eons ago.

 

[RedArmy]

Originally posted by: TuxDave

Originally posted by: RedArmy

Originally posted by: Vegitto
The second and third clue don't add anything. They could be 36, 1 and 1 for all we know. You know, some people make a career out of playing the piano.

That's what I thought, the third question is definitely needed though...I just don't understand how the second one works...I don't understand the reasoning

Well, ok I guess I can spell it out:

So given that the product of the ages is 36, the salesman won't know how old they are because there are still multiple solutions. (I wrote the sum along side of it to continue my point)

1,1,36 = 38
1,2,18 = 21
1,3,12 = 16
1,4,9 = 14
1,6,6 = 13 <--
2,2,9 = 13 <--
2,3,6 = 11
3.3,4 = 10

The mom then said that the sum was something and the salesman is still unable to figure out the age because the house next door must've been #13. If it was any other sum then he'd be able to deduce what the ages were.

The 3rd clue implies there IS an oldest child and no "tie" for oldest leading to 2,2,9.

Oh snap, I get it now. I was looking way too far into it. Thanks for the explanation!

 

[Lamont Burns]

TuxDave wins.

 

[oznerol]

After #1 there are 8 possibilities:
36,1,1 / 18,2,1 / 12,3,1 / 9,4,1 / 6,6,1 / 9,2,2 / 6,3,2 / 4,3,3

After #2 there can still be uncertainty:
6+6+1 = 13, but so does 2+2+9

After #3 I would assume there is no uncertainty left, as it implies an oldest:

So the answer is 9,2,2 for the ages.

However, I don't see why 6,6,1 couldn't technically work, as even with twins there's an "eldest".

Edit: Late to the party.

 

[jjones]

Given the information and those questions, the salesman doesn't have a fucking clue how old they are.

Ha ha, now that I've read TuxDave's reply, I guess it makes sense after all.

 

[mugs]

Originally posted by: TuxDave
The underlying assumption is that all pieces of information are useful. So telling #2 and having the salesman unable to figure out what the age is implies that knowing the sum of the ages AND the product of the ages must still have multiple solutions.

Want me to solve it for you or is that enough?

Or perhaps he doesn't know the sum, but rather two possible sums (two neighbors).

2 + 3 + 6 = 11
1 + 6 + 6 = 13

Of course evens and odds are usually on opposite sides of the street.

And I don't think the "eldest son" clue really rules out the possibility that the two oldest children are the same age, because they could be fraternal twins - a boy and a girl. (I'll grant that the author can assume twins to be the same age, even if one is born earlier)

Edit:
From your solution, 10 and 14 could be neighbors on either side of 12.

Seems like a poorly written problem overall.

 

[CrazyLazy]

nm answered.

 

[waggy]

hmm i don't see this as that hard.


odds are the kids are 1-12 with them owning a piano.

so he is going to try to get her to buy insurance on her for the kids, 3 children's insurance packages and extra insurance on the family heirloom.

 

[RedArmy]

Originally posted by: mugs

Originally posted by: TuxDave
The underlying assumption is that all pieces of information are useful. So telling #2 and having the salesman unable to figure out what the age is implies that knowing the sum of the ages AND the product of the ages must still have multiple solutions.

Want me to solve it for you or is that enough?

Or perhaps he doesn't know the sum, but rather two possible sums (two neighbors).

2 + 3 + 6 = 11
1 + 6 + 6 = 13

Of course evens and odds are usually on opposite sides of the street.

And I don't think the "eldest son" clue really rules out the possibility that the two oldest children are the same age, because they could be fraternal twins - a boy and a girl. (I'll grant that the author can assume twins to be the same age, even if one is born earlier)

Edit:
From your solution, 10 and 14 could be neighbors on either side of 12.

Seems like a poorly written problem overall.

I think you're looking too far into it like I did. Either way, the only solution sets you can end up with is 1,6,6 and 2,2,9. From there you can debate over what the meaning of "twins" means.

 

[MikeyLSU]

Originally posted by: TuxDave

Originally posted by: RedArmy

Originally posted by: Vegitto
The second and third clue don't add anything. They could be 36, 1 and 1 for all we know. You know, some people make a career out of playing the piano.

That's what I thought, the third question is definitely needed though...I just don't understand how the second one works...I don't understand the reasoning

Well, ok I guess I can spell it out:

So given that the product of the ages is 36, the salesman won't know how old they are because there are still multiple solutions. (I wrote the sum along side of it to continue my point)

1,1,36 = 38
1,2,18 = 21
1,3,12 = 16
1,4,9 = 14
1,6,6 = 13 <--
2,2,9 = 13 <--
2,3,6 = 11
3.3,4 = 10

The mom then said that the sum was something and the salesman is still unable to figure out the age because the house next door must've been #13. If it was any other sum then he'd be able to deduce what the ages were.

The 3rd clue implies there IS an oldest child and no "tie" for oldest leading to 2,2,9.

makes perfect sense, but I don't see the wording matching what you said "At this point the salesman is pretty sure of his answer, but needs one more clue, so " that means he has an answer ready, but wants another clue just to make sure. It doesn't say he needs another clue to further narrow down the answer.

I think the wording of the question makes this answer more than one correct. But you are certainly correct.

 

[TuxDave]

Originally posted by: mugs

Originally posted by: TuxDave
The underlying assumption is that all pieces of information are useful. So telling #2 and having the salesman unable to figure out what the age is implies that knowing the sum of the ages AND the product of the ages must still have multiple solutions.

Want me to solve it for you or is that enough?

Or perhaps he doesn't know the sum, but rather two possible sums (two neighbors).

2 + 3 + 6 = 11
1 + 6 + 6 = 13

Of course evens and odds are usually on opposite sides of the street.

And I don't think the "eldest son" clue really rules out the possibility that the two oldest children are the same age, because they could be fraternal twins - a boy and a girl. (I'll grant that the author can assume twins to be the same age, even if one is born earlier)

Edit:
From your solution, 10 and 14 could be neighbors on either side of 12.

Seems like a poorly written problem overall.

I never said that the mother's house was #12? The bigger issue at hand is the fact that people tend to add information to the problem that's not explicitly written. This is an even BIGGER problem when the author of the question assumes that the reader should add unwritten information. You're adding that the house next door is in sequence to the the house he's at. That's not necessarily true.

I do have to agree that when you're trying to deduce and extract every piece of information, the writer has to be very careful on how they word things because it changes the whole meaning of the question. If the question was phrased as "the salesman looks around the corner and sees the house number and still has no clue" then it would be much clearer. We have technically added information that the salesman KNOWS what the next door house number which could be fixed with a small change.

As for the whole twins thing... yeah, that's always up to debate. It's a pretty clever way to try to give some information that sounds useless but still give useful information. If she said I have twins or I have no tie for oldest, that's kind of boring. Would be interesting to hear a new way of saying something random that's still useful.

 

[RedArmy]

Originally posted by: MikeyLSU

Originally posted by: TuxDave

Originally posted by: RedArmy

Originally posted by: Vegitto
The second and third clue don't add anything. They could be 36, 1 and 1 for all we know. You know, some people make a career out of playing the piano.

That's what I thought, the third question is definitely needed though...I just don't understand how the second one works...I don't understand the reasoning

Well, ok I guess I can spell it out:

So given that the product of the ages is 36, the salesman won't know how old they are because there are still multiple solutions. (I wrote the sum along side of it to continue my point)

1,1,36 = 38
1,2,18 = 21
1,3,12 = 16
1,4,9 = 14
1,6,6 = 13 <--
2,2,9 = 13 <--
2,3,6 = 11
3.3,4 = 10

The mom then said that the sum was something and the salesman is still unable to figure out the age because the house next door must've been #13. If it was any other sum then he'd be able to deduce what the ages were.

The 3rd clue implies there IS an oldest child and no "tie" for oldest leading to 2,2,9.

makes perfect sense, but I don't see the wording matching what you said "At this point the salesman is pretty sure of his answer, but needs one more clue, so " that means he has an answer ready, but wants another clue just to make sure. It doesn't say he needs another clue to further narrow down the answer.

I think the wording of the question makes this answer more than one correct. But you are certainly correct.

"Pretty sure" in the sense that 50% is a lot better than 12.5%. If that isn't good enough, just pretend that statement isn't there. It's just to say that a lot of the choices were eliminated.