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Father and Son


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56 replies to this topic

#1 brhan

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Posted 27 September 2007 - 01:36 PM

The sum of the ages of a father and his son is 66. The father's age is the son's age reversed. Furthermore, the father's age is a multiple of the son's age. How old could they be?

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#2 Writersblock

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Posted 27 September 2007 - 01:53 PM

60 and 6
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#3 cpotting

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Posted 27 September 2007 - 04:14 PM

They could also be 33 and 33 - if you allow for them not being each other's father and son (e.g. Jack, father of Daisy, is 33 and Rob, son of Alfred, is 33)

Okay, that's not what you were looking for - but that's what this forum is all about: finding new ways to look at things.
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#4 unreality

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Posted 27 September 2007 - 09:02 PM

You got to it first cpotting... I was going to say 33 too. A father and a son could be any man (as every man is a son) and someone else that is a father.
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#5 Benson

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Posted 28 September 2007 - 05:24 AM

a : the father's age.
b : the son's age.

so, it says:
1.a+b = 66
2.a = kb (k is a constant)

put second statement to first.
=> b = 66/((k+1))

since it doesn't say k needs to be Nature number.

therefore, b can be any number in between 0 to 50.

PS:
1. It is possible that the father is youger than the son. For example,
a man married with a woman who has a son and the son is older than the man.
2. At least, the father needs to be older enough to get married.
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#6 bonanova

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Posted 28 September 2007 - 06:24 AM

a : the father's age.
b : the son's age.

so, it says:
1.a+b = 66
2.a = kb (k is a constant)

put second statement to first.
=> b = 66/((k+1))

since it doesn't say k needs to be Nature number.

therefore, b can be any number in between 0 to 50.

PS:
1. It is possible that the father is youger than the son. For example,
a man married with a woman who has a son and the son is older than the man.
2. At least, the father needs to be older enough to get married.

Loosely, perhaps, but not precisely:

[1] The problem said multiple. That usually means k is not only a constant, but also an integer.
[2] That would be step-father and step-son.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#7 Benson

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Posted 28 September 2007 - 06:35 AM

Loosely, perhaps, but not precisely:

[1] The problem said multiple. That usually means k is not only a constant, but also an integer.


That "usually" is also loosely, perhaps, but not precisely. :)
Therefore, the precisely answer would be 0 < b <= 28. (boy starts youthhood. :)
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#8 bonanova

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Posted 28 September 2007 - 06:44 AM

OP states .... Furthermore, the father's age is a multiple of the son's age.

If multiple does not mean integral multiple, the statement gives no information.
Every pair of ages, otherwise, could be described as multiples.

So if you reject that as precise, let's affirm it for all practical purposes. :D
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#9 Benson

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Posted 28 September 2007 - 07:24 AM

OP states .... Furthermore, the father's age is a multiple of the son's age.

If multiple does not mean integral multiple, the statement gives no information.
Every pair of ages, otherwise, could be described as multiples.


So if you reject that as precise, let's affirm it for all practical purposes. :D


1. You cannot ask a "puzzle question" to be "precised".
2. Furthermore, if father's age is 46 years old and son's age is 20 years old, the father's age is a multiple of the son's age when we "precisely" count the age into minutes or seconds. Therefore, besides the father is older enough to give a birth, the son could be 10, 12, 16, 20 or other normal ages. :)
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#10 bonanova

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Posted 28 September 2007 - 07:37 AM


OP states .... Furthermore, the father's age is a multiple of the son's age.

If multiple does not mean integral multiple, the statement gives no information.
Every pair of ages, otherwise, could be described as multiples.


So if you reject that as precise, let's affirm it for all practical purposes. :D



1. You cannot ask a "puzzle question" to be "precised".
2. Furthermore, if father's age is 46 years old and son's age is 20 years old, the father's age is a multiple of the son's age when we "precisely" count the age into minutes or seconds. Therefore, besides the father is older enough to give a birth, the son could be 10, 12, 16, 20 or other normal ages. :)


Nope, nope, and ... nope.
Not unless you assume the question asks the ages in those units for which the multiples are integral -- minutes, seconds.
You obviously did not assume that -- years are the only units mentioned in your answer.
You're dancing around the issue pretty well, but you're running out of places to hide. :D

Precision or looseness aside, it's nice to be consistent. B))
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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