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# Father and Son

## Question

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?

Father: 60 years old

Son : 6 years old

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60 and 6

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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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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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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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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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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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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.

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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.

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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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.

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.

Precision or looseness aside, it's nice to be consistent.

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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.

There's no need. You can still use Year to count in minutes, seconds or even to nano seconds. For example, 2.5 years.

Precision or looseness aside, it's nice to be consistent.

Yes, that's true. So, that "66" is pretty precision, therefore, we should precisely count their birth "time".

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Maybe 24 and 42 the father had his son when he was 18.

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first response was 11-55 which would work except for the whole Father-AB and Son-BA - thing

So im going with 60-6!

Right?

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Maybe 24 and 42 the father had his son when he was 18.

Nope ... 24 is not multiple of 42. Try again ...

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Hi there! This is my first post. Unfortunately I do not have the answer, but I would like to give some input.

06 and 60 isn't a bad idea, although personally I would not count it because I do not think that the age of 6 can really be called "zero six". Although in puzzles you never know!

Anyway, if it weren't for the pesky condition that the age of the father has to be a multiple of the age of the son then other answers would be:

Father 51 and son 15 or father 42 and son 24 (answer also given by diamnds).

Reversals are fine, sums are fine, but damn that multiple condition!

Having done way too much maths today due to this puzzle I would now deem it very likely that the answer must be given in the form of the number of months, not years. Am I correct or would it be too easy to tell?

Would anybody care to do the calculations using months as a new angle? (Using months as the next possible unit is far more likely than nano seconds...) I've been working at it for almost an hour now and the closest I got was the father being 591 months (49,25 years) old and the son being 195 months (16,25 years) old, together 65,5 years old (786 months).

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The easiest way to look at this is to consider a number 'xy' where x is the tens digit and y the units digit. The number is therfore equal to 10x+y. In this example, you can see that since one number/age is the other one backwards, they add to give 10x+y+10y+x=11(x+y). So:

11(x+y)=66

(x+y)=6

Simple trial and error then means that if 'xy' is a multiple of 'yx' then the numbers must be 06 and 60 or 33 and 33. The latter is clearly not right for a father and son, so the father must be 60 and the son 06

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33 and 33 is correct assuming the father is dead lol i r the win

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33 and 33 is correct assuming the father is dead lol i r the win

What a morbid path to a cheap answer.

I love it!

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Yep I think that was what we first said

*edit* I checked, writersblock said 60 and 6, then me and cpotting said 33 and 33 cuz it said "father and son" it doesn't require that the father is the father of the son

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Having a son at 54??

Not sure if I would do that... Made me think about my life....

Anyhow, age seems to be always an approximation and never exact. You are 18 years old for 364 days!

And in all preceding similar puzzles, this was the assumption hidden in the OP.

So I'm not sure we should go into semesters or trimesters or months or days or weeks or hours or minutes or seconds or horoscope ...

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I tried doing this riddle in months as opposed to years. The sum would be 792 months (66*12). I don't think there's a natural number which, when reversed and added to itself, equals 792. In fact, there must be a terrific few numbers which have that property, supposing we stick with natural numbers. The riddle further constrains by making one a factor of the other.

I was debating the "legality" of coming up with an answer in months and transforming that answer into years, where the years would be a non-natural number (id est, have a decimal point). I then questioned the validity of the debate, wondering if an answer in terms of 'years' was even required. I re-read the riddle, and it does say that the sum of the ages is 66. Note: not 66 years. So while my delving into months as an alternate way of answering this riddle proved fruitless, it could be that the beings with which this riddle is concerned are not human, and that 60 and 06 months, weeks, decades, picoseconds, and any other unit of time would work. Imagine having a son at 54 months (4.5 years) old.

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oops

Edited by IThinkImMe
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Couldn't it also be 15 aand 51 <_<

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Couldn't it also be 15 aand 51 <_<

Nope, because 15 is not a multiple of 51.

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How about there is one bloke who is both a father and a son. He's 66 (which is a multiple of 66 and adds up to 66)

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How about there is one bloke who is both a father and a son. He's 66 (which is a multiple of 66 and adds up to 66)

Nope, if he is 66 then his son should be 0 (In order to add-up to 66). Of course 0 is not a multiple of 66

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