More difficult Mensa question....
11 April 2001, 12:11 AM
#1
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I think the answer is 2, 6 and 6.
Reasoning as follows:
Possibilities are
2, 2, 18 Total 22
2, 3, 12 Total 17
2, 4, 9 Total 15
2, 6, 6 Total 14
3, 3, 8 Total 14
3, 4, 6 Total 13
After M2 goes outside, he knows the house number, so the only reason that he still doesn't know is that there are two answers giving the same total as the house number (14).
However, when M1 says that his youngest child is Anne, he knows that the answer can't be 3, 3, 8.
Hence 2, 6, 6.
Pete
Reasoning as follows:
Possibilities are
2, 2, 18 Total 22
2, 3, 12 Total 17
2, 4, 9 Total 15
2, 6, 6 Total 14
3, 3, 8 Total 14
3, 4, 6 Total 13
After M2 goes outside, he knows the house number, so the only reason that he still doesn't know is that there are two answers giving the same total as the house number (14).
However, when M1 says that his youngest child is Anne, he knows that the answer can't be 3, 3, 8.
Hence 2, 6, 6.
Pete
11 April 2001, 11:19 AM
#4
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Picture the scene ... two mathematicians are talking to each other, the following conversation occurs:
M1: I have three children
M2: Really, how old are they?
M1: The product of their ages is 72
M2: Hmm ... Could you narrow it down some more?
M1: The sum of their ages is the same as the number of this house
M2: Oh ... wait there, I'll be back ...
(Mathematician2 exits stage left)
(Pause ... in which time Mathematician1 entertains the audience with his juggling skills)
(Mathematician2 enters stage left)
M2: ... I still don't know!
M1: My youngest child is called Anne
M2: AHA!!!
What are the ages of Mathematician1's children?
M1: I have three children
M2: Really, how old are they?
M1: The product of their ages is 72
M2: Hmm ... Could you narrow it down some more?
M1: The sum of their ages is the same as the number of this house
M2: Oh ... wait there, I'll be back ...
(Mathematician2 exits stage left)
(Pause ... in which time Mathematician1 entertains the audience with his juggling skills)
(Mathematician2 enters stage left)
M2: ... I still don't know!
M1: My youngest child is called Anne
M2: AHA!!!
What are the ages of Mathematician1's children?
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11 April 2001, 11:57 PM
#8
Why isn't 1, 4, 18 = 23, on Pete's original list? - or even 1, 2, 36 = 39 - you have to consider at least the possibility that Mathematician1 may be very 'energetic' and maybe married a second time 
- at least give him the benefit of the doubt
Mick
- at least give him the benefit of the doubt Mick
12 April 2001, 08:05 AM
#10
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Ca,
House number issue:
The point is, that mathematicians are very wise people, and he doesn't know the answer rightaway. If he had found the answer to be 3,4,6 - he could've been sure of that, because no other combination gives the same sum 3+4+6=13. However, there are two combinations 3,3,8 and 2,6,6 which both give the same sum (14). THAT's why he couldn't know the childrens' ages. You might think this logic stinks, and so did I, but the point is, again, he is a _mathematician_, and he thinks like one.
Youngest child is called Anne:
point is, there IS a youngest child. No two children share the same age. This rules out 3,3,8.
-Fernis
House number issue:
The point is, that mathematicians are very wise people, and he doesn't know the answer rightaway. If he had found the answer to be 3,4,6 - he could've been sure of that, because no other combination gives the same sum 3+4+6=13. However, there are two combinations 3,3,8 and 2,6,6 which both give the same sum (14). THAT's why he couldn't know the childrens' ages. You might think this logic stinks, and so did I, but the point is, again, he is a _mathematician_, and he thinks like one.
Youngest child is called Anne:
point is, there IS a youngest child. No two children share the same age. This rules out 3,3,8.
-Fernis
12 April 2001, 09:49 AM
#11
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<BLOCKQUOTE><font size="1" face="Verdana, Arial">quote:<HR>Originally posted by Ari Fernelius:
<B>Ca,
House number issue:
The point is, that mathematicians are very wise people, and he doesn't know the answer rightaway. If he had found the answer to be 3,4,6 - he could've been sure of that, because no other combination gives the same sum 3+4+6=13. However, there are two combinations 3,3,8 and 2,6,6 which both give the same sum (14). THAT's why he couldn't know the childrens' ages. You might think this logic stinks, and so did I, but the point is, again, he is a _mathematician_, and he thinks like one.
Youngest child is called Anne:
point is, there IS a youngest child. No two children share the same age. This rules out 3,3,8.
-Fernis[/quote]
Fernis,
OK, I'm with you so far. But going back to the oringal post, the only info we have is that the product of their ages is 72 and the sum, of their ages is the same as the house.
I still don't see how 2, 6, 6, is invalid, if one assumes that Anne is 2.
Maybe I am getting confused with what the likely ages are and what the actual proven ages are (without making assumptions)
C
<B>Ca,
House number issue:
The point is, that mathematicians are very wise people, and he doesn't know the answer rightaway. If he had found the answer to be 3,4,6 - he could've been sure of that, because no other combination gives the same sum 3+4+6=13. However, there are two combinations 3,3,8 and 2,6,6 which both give the same sum (14). THAT's why he couldn't know the childrens' ages. You might think this logic stinks, and so did I, but the point is, again, he is a _mathematician_, and he thinks like one.
Youngest child is called Anne:
point is, there IS a youngest child. No two children share the same age. This rules out 3,3,8.
-Fernis[/quote]
Fernis,
OK, I'm with you so far. But going back to the oringal post, the only info we have is that the product of their ages is 72 and the sum, of their ages is the same as the house.
I still don't see how 2, 6, 6, is invalid, if one assumes that Anne is 2.
Maybe I am getting confused with what the likely ages are and what the actual proven ages are (without making assumptions)
C
12 April 2001, 12:05 PM
#13
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<BLOCKQUOTE><font size="1" face="Verdana, Arial">quote:<HR>Originally posted by Fast_Blue_Scooby:
<B>Picture the scene ... two mathematicians are talking to each other, the following conversation occurs:
M1: I have three children
M2: Really, how old are they?
M1: The product of their ages is 72
M2: Hmm ... Could you narrow it down some more?
M1: The sum of their ages is the same as the number of this house
M2: Oh ... wait there, I'll be back ...
(Mathematician2 exits stage left)
(Pause ... in which time Mathematician1 entertains the audience with his juggling skills)
(Mathematician2 enters stage left)
M2: ... I still don't know!
M1: My youngest child is called Anne
M2: AHA!!!
What are the ages of Mathematician1's children?[/quote]
Who says that the house is numbered 14?
What is the significance of the youngest child being called Anne?
C
<B>Picture the scene ... two mathematicians are talking to each other, the following conversation occurs:
M1: I have three children
M2: Really, how old are they?
M1: The product of their ages is 72
M2: Hmm ... Could you narrow it down some more?
M1: The sum of their ages is the same as the number of this house
M2: Oh ... wait there, I'll be back ...
(Mathematician2 exits stage left)
(Pause ... in which time Mathematician1 entertains the audience with his juggling skills)
(Mathematician2 enters stage left)
M2: ... I still don't know!
M1: My youngest child is called Anne
M2: AHA!!!
What are the ages of Mathematician1's children?[/quote]
Who says that the house is numbered 14?
What is the significance of the youngest child being called Anne?
C
12 April 2001, 12:11 PM
#14
This could get a bit complex... but If Mathematician1 realy gets on with his kids he will know how they talk...
Kid1 'How old are you then?'
Kid2 'I'm 6 1/2'
Kid1 'I'm older than you I'm 6 3/4'
Kid3 'Well I'm older than both of you I'm 6 and 10 months, Ner Ner..'
So... Let the smart arsed Mathematician2 sort it out now
Mick
PS why are people still writing here ? - I?T'S BEDTIME !!!!!!!!!!!!!
Kid1 'How old are you then?'
Kid2 'I'm 6 1/2'
Kid1 'I'm older than you I'm 6 3/4'
Kid3 'Well I'm older than both of you I'm 6 and 10 months, Ner Ner..'
So... Let the smart arsed Mathematician2 sort it out now
Mick
PS why are people still writing here ? - I?T'S BEDTIME !!!!!!!!!!!!!
12 April 2001, 02:30 PM
#16
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<BLOCKQUOTE><font size="1" face="Verdana, Arial">quote:<HR>Originally posted by ca:
<B>
.
I still don't see how 2, 6, 6, is invalid, if one assumes that Anne is 2.
Maybe I am getting confused with what the likely ages are and what the actual proven ages are (without making assumptions)
C[/quote]
2,6,6 is the correct answer. Come on down and join the muppet forum
<B>
.
I still don't see how 2, 6, 6, is invalid, if one assumes that Anne is 2.
Maybe I am getting confused with what the likely ages are and what the actual proven ages are (without making assumptions)
C[/quote]
2,6,6 is the correct answer. Come on down and join the muppet forum
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