# Interesting non-programming problem

posted 13 years ago

While this is Programming diversions, there do seem to be an awful lot of mind-teasers. So, allow me to contribute:

From

"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?"

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?"

Piscis Babelis est parvus, flavus, et hiridicus, et est probabiliter insolitissima raritas in toto mundo.

HS Thomas

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Bhau Mhatre

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Posts: 199

Carl Trusiak

Sheriff

Posts: 3341

posted 13 years ago

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

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

Sheriff

Posts: 6450

posted 13 years ago

Rechecking my facts I have to change my answer to

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 ]

**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

Ranch Hand

Posts: 199

posted 13 years ago

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?

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?

-Mumbai cha Bhau

HS Thomas

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Bhau Mhatre

Ranch Hand

Posts: 199

posted 13 years ago

oops! isn't that what Carl Trusiak already said?

[ August 22, 2003: Message edited by: Mumbai cha bhau ]

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 ]

-Mumbai cha Bhau

posted 13 years ago
Piscis Babelis est parvus, flavus, et hiridicus, et est probabiliter insolitissima raritas in toto mundo.

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.

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

Ranch Hand

Posts: 3404

posted 13 years ago

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

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 ]

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

Greenhorn

Posts: 9

posted 12 years ago

-------------------------------------

"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.

"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.