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Interesting non-programming problem

 
Joel McNary
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While this is Programming diversions, there do seem to be an awful lot of mind-teasers. So, allow me to contribute:
From More games For The Superintelligent, by James Fixx (p. 26):
"Two men are talking. One says to the other, 'I have three sons whose ages I want you to ascertain from the following clues. Stop me when
you know their ages.
'1. The sum of their ages is thirteen
'2. The product of their ages is the same as your age.
'3. My oldest son weights sixty-one pounds.'
'Stop,' says the second man. 'I know their ages.'
What are they?"
 
Jason Menard
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6, 6, and 1?
 
HS Thomas
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9 ,2 and 2 ?
A 61 lb 9 year old is unbelievable.
Unless this is a trick question and 13 is not decimal!
regards
 
Bhau Mhatre
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7,5,1 ?
I did not do any calculations. Just guessed that Jason's values 6,6,1 could be correct. But since the question reads 'oldest son' I made it 7,5,1
 
Carl Trusiak
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One clue is the number of clues. Since the person needed three clues, the first 2 where not enough. There are two answers which give a sum of 13 and the same product.
6 6 1
9 2 2
Now, if you concider that twins are the same age and one can't be called the oldest (You you refer to them as the oldest 2) the answer is
9 2 2
 
Jason Menard
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Rechecking my facts I have to change my answer to 8, 4, and 1.
Really it seems we have to make too many assumptions in this one...
1) The oldest son is of average weight for his age
2) the two men speaking are roughly the same age
There is no definite reason to make these assumptions, but making them does give us some parameters within which to operate.
The first assumption is the easiest to swallow. The average weight of an eight year old male is ~61.25 pounds. The average weight of a 7 yr old boy is 54.5 lbs, and for a 9 yr old it's 69 lbs.
If the second assumption holds, then it would seem that the father should likely be in his 30's. The age set of (8,4,1) seems to produce the most reasonable result, giving an age of 32 when multiplied and meeting the requirements for summing to 13, as well as metting the assumption that the boy is of average weight for his age. An age set of (8,3,2), while valid in and of itself, would mean that assumption #2 does not hold.
[ August 24, 2003: Message edited by: Jason Menard ]
 
Bhau Mhatre
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Hey, the second man knew his own age. So why did he wait for the third clue?
How many combinaitons of three numbers x,y,z produce 13 as its sum and identical products? If we can find that, we can find the answer. I mean if all the different combinations of x+y+z=13 produced unique x*y*z products, then the man would not need to know the third clue about the weight. Right?
 
HS Thomas
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Originally posted by Jason Menard:
2) the two men speaking are roughly the same age


Where is this assumption made ?
regards
 
Bhau Mhatre
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Originally posted by Mumbai cha bhau:
Hey, the second man knew his own age. So why did he wait for the third clue?
How many combinaitons of three numbers x,y,z produce 13 as its sum and identical products? If we can find that, we can find the answer. I mean if all the different combinations of x+y+z=13 produced unique x*y*z products, then the man would not need to know the third clue about the weight. Right?

oops! isn't that what Carl Trusiak already said?
[ August 22, 2003: Message edited by: Mumbai cha bhau ]
 
Joel McNary
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Yes, Carl is right on the money with the solution. The man has a 9 year old and twin two-year olds.
And sixty-one pounds is not really unbeleivable for a nine-year old. I'm pretty sure that I was somewhere in that vicinity at that time.
 
HS Thomas
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Well, the rationale behind my answer, 9,2 and 2
were that:
1: you needed the highest age possible where the weight 61 Ibs was believable and which would give you
2: the product of their ages being the age of a man.
Starting from 10 years , the product would have given the age of the man as 21 years ( 10 * 2 * 1). The title man ,at this age, is debatable
Then I reduced the age of the eldest to 9 years, the product would have given the age of the man as 36 years ( 9 * 2 * 2).
The fact that the younger two were twins was purely co-incidental.
If the product would NOT have given the man a plausible age I would have kept reducing the age of the eldest.
So why can't I be right ?
And is Jason necessarily wrong! He has added the criteria that the two men are about the same age , while making sure the father is old enough to have 3 kids of different ages.
So I think , in the real world mine and Jason's answers were also correct.

regards
[ August 23, 2003: Message edited by: HS Thomas ]
 
Vivek Kumar
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-------------------------------------
"Two men are talking. One says to the other, 'I have three sons whose ages I want you to ascertain from the following clues. Stop me when
you know their ages.
'1. The sum of their ages is thirteen
'2. The product of their ages is the same as your age.
'3. My oldest son weights sixty-one pounds.'
'Stop,' says the second man. 'I know their ages.'
What are they?"
-------------------------------------
Hey guys, the eldest being 61 lbs is of no consequence. And neither does the age of second man matters except for fact that 6,6,1 and 9,2,2 both have same product and no two other combinations have same product. So I strike out 10,2,1 & 8,4,1 and others because then second man would have known the answer after second hint itself. So after second clue, the only options are 6,6,1 and 9,2,2. Third clue tells us that there is an eldest!!! .
So ages must be 9,2,2.
 
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