Fun Puzzle

algebrapro18

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I was readking In Code by Sara Flannery last night. Its a book about cryptography and it had this really good math puzzle in it and I was wondering if anyone could solve it. I couldn't but thankfully she gave the solution in the book and I can't believe I didn't get it. Here is the puzzle:

An insurance salesman knocks on the door of a home in a housing development. When the woman answers the door he asks "How many children do you have?" She replies "Three." When he asks "What are there ages?" She decides that he is to cheeky and refuses to him. After he apologizes for his apparent rudeness he asks for a hint about the children's ages. She says "If you multiply their three ages you get 36." (Their ages are exact numbers). He thinks for a while and then asks for another hint. When she says "The sum of the ages is the number of the house next door" the salesman quickly hops the fence to determine this number. This done, he returns to the lady and asks for a final hint. "All right", she responds "the eldest of my children plays piano." He then knows there ages, do you?

Anyone willing to give this a go?
 

clixpix

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It's either, isn't it?

2 x 3 = 6

6 x 6 = 36

Right?


2 x 2 = 4

4 x 9 = 36

Why aren't both right?
 

carolpetunia

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I came up with 3x3x4, 1x6x6, 2x3x6, 1x2x18, 2x2x9... obviously, there's something else that's supposed to give it away. Something about the piano, or at least that's what we're supposed to think. Pianos have 88 keys, but I see no connection there...

This is a book about cryptography. So how could cryptography figure into this? Hmmm.
 

laureen227

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Originally Posted by CarolPetunia

I came up with 3x3x4, 1x6x6, 2x3x6, 1x2x18, 2x2x9... obviously, there's something else that's supposed to give it away. Something about the piano, or at least that's what we're supposed to think. Pianos have 88 keys, but I see no connection there...

This is a book about cryptography. So how could cryptography figure into this? Hmmm.
i think, since the salesman got to see the house number, that those numbers should be revealed, myself.
that said - i don't do ANY math unless required to!
btw - pianos have 88 keys, but an octave only has 11 white keys - plus 5 black ones.
 

carolpetunia

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Originally Posted by laureen227

i think, since the salesman got to see the house number, that those numbers should be revealed...
Good point! Maybe that's why this appears to be unsolvable with only the information provided...?
 

kluchetta

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I kind of think it's 1, 4, and 9. Added together is 13 - somehow I think that's a better number than 10 for a house, LOL.


Plus, not a lot of 6 year olds play the piano. (Of course I did, but I was a prodigy.)



j/k
 

butzie

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Call the 3 children's ages a, b and c (Arnold, Barbara and Candy, for example).

Then the first fact (product is 36) tells us a x b x c =36

The second fact ( sum is the number of the house next door) tells us
a + b + c = n where n is some unknown number.

At this point, the salesman doesn't know the answer, so there must be at least 2 sets of number that satisfy both conditions. The third fact is that the "eldest of my children plays piano", which implies there is only 1 eldest. The ages are all integers.

So - the prime factors of 36 are 3, 3, 2, 2, 1 so we look for 2 combinations of these that add to the same number:

9, 2, 2 - sum 13
6, 6, 1 - sum 13

The second set doesn't have a unique "eldest", so it must be the first set - 9, 2 and 2.

Again, from DH who has a BS in MechEng from Cornell and an ME from MIT.
 

kluchetta

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Originally Posted by butzie

Call the 3 children's ages a, b and c (Arnold, Barbara and Candy, for example).

Then the first fact (product is 36) tells us a x b x c =36

The second fact ( sum is the number of the house next door) tells us
a + b + c = n where n is some unknown number.

At this point, the salesman doesn't know the answer, so there must be at least 2 sets of number that satisfy both conditions. The third fact is that the "eldest of my children plays piano", which implies there is only 1 eldest. The ages are all integers.

So - the prime factors of 36 are 3, 3, 2, 2, 1 so we look for 2 combinations of these that add to the same number:

9, 2, 2 - sum 13
6, 6, 1 - sum 13

The second set doesn't have a unique "eldest", so it must be the first set - 9, 2 and 2.

Again, from DH who has a BS in MechEng from Cornell and an ME from MIT.
Why not 9, 4 and 1?
 

kluchetta

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Originally Posted by butzie

Call the 3 children's ages a, b and c (Arnold, Barbara and Candy, for example).

Then the first fact (product is 36) tells us a x b x c =36

The second fact ( sum is the number of the house next door) tells us
a + b + c = n where n is some unknown number.

At this point, the salesman doesn't know the answer, so there must be at least 2 sets of number that satisfy both conditions. The third fact is that the "eldest of my children plays piano", which implies there is only 1 eldest. The ages are all integers.

So - the prime factors of 36 are 3, 3, 2, 2, 1 so we look for 2 combinations of these that add to the same number:

9, 2, 2 - sum 13
6, 6, 1 - sum 13

The second set doesn't have a unique "eldest", so it must be the first set - 9, 2 and 2.

Again, from DH who has a BS in MechEng from Cornell and an ME from MIT.
Why not 9, 4 and 1?


ETA: Oops, I can't add...9+4+1 /= 13 doh!
 
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algebrapro18

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I will type up the solution tomorrow but its 2,2, and 9 and she tells you why there is only one solution. And I gave you guys all the info you needed.
 
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algebrapro18

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Originally Posted by butzie

Call the 3 children's ages a, b and c (Arnold, Barbara and Candy, for example).

Then the first fact (product is 36) tells us a x b x c =36

The second fact ( sum is the number of the house next door) tells us
a + b + c = n where n is some unknown number.

At this point, the salesman doesn't know the answer, so there must be at least 2 sets of number that satisfy both conditions. The third fact is that the "eldest of my children plays piano", which implies there is only 1 eldest. The ages are all integers.

So - the prime factors of 36 are 3, 3, 2, 2, 1 so we look for 2 combinations of these that add to the same number:

9, 2, 2 - sum 13
6, 6, 1 - sum 13

The second set doesn't have a unique "eldest", so it must be the first set - 9, 2 and 2.

Again, from DH who has a BS in MechEng from Cornell and an ME from MIT.
VERY VERY good I'm impressed. Thats the exact solution.
 

kristykitty

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But why does the sum have to equal 13? It doesn't say what the house number has to be.

It could be 9,4, and 1. She said "my eldest plays piano". That doesn't mean the younger siblings have to be the same age.


So confused!
 

laureen227

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Originally Posted by KristyKitty

But why does the sum have to equal 13? It doesn't say what the house number has to be.

It could be 9,4, and 1. She said "my eldest plays piano". That doesn't mean the younger siblings have to be the same age.


So confused!
normally, the house next door matches your own in as far as even/odd numbers are concerned. so if your house an even number, so do your next door neighbors - odd numbers would be across the street.
so if the next door house is 14, then her house would be either 12 or 16.
 

kristykitty

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Originally Posted by laureen227

normally, the house next door matches your own in as far as even/odd numbers are concerned. so if your house an even number, so do your next door neighbors - odd numbers would be across the street.
so if the next door house is 14, then her house would be either 12 or 16.
oh I see. I must be really dumb because I still don't get it!


It never says whether her house or her neighbors house is even or odd. So couldn't her neighbor's house easily be 14, and her house be 12 or 16?


I'm sorry I'm so dumb and need things spelled out!
 
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