Help with crazy puzzle!

aspoestertjie

Hi! Could anyone help me with this puzzle please? Its probably really easy and I just cant see it, but it's driving me nuts..

Here it is: A census taker arrives at a woman's house and wants to know the ages of her daugters. She answers: "If you multiply their ages the answer is 72, if you add them the answer is the number of my house which you can see."

The census taker tells her that this is not enough information to determine their ages. "Well," the woman says, "I can tell you that my eldest daugter has a cat with a wooden leg."

"Ah, now I know their ages!" replies the census taker.

What are their ages?

Thanks so much!

Newaglish

I presume they are 12, 3 and 2. The house number clue is a red herring and the wooden legged cat is only to show that one daughter is eldest and thus there are no twins.

By that logic, the only three (whole) numbers that multiply out to 72 are 12, 3 and 2.

Erm, that doesn't really feel like the right answer but it's the best guess I can come up with!

EDIT: Yeah, they could also be 24, 3 and 1

Boxman

Why do you assume there are 3 daughters Newaglish?

Welruc

There probably 6, 4 and 3 added together this gives 13. Usually 13 is not used as a house number hence the info was no good to the guy. As for the cat with the wooden leg i have no idea.

j@utis

'eldest daughter has a cat with a wooden leg'... means there are younger twins, 3 year olds, and eldest daugther is 8year old.

census needed more information because house number was 14 (which comes up twice on the list below).

3+4+6 = 13
2+4+9 = 15
2+6+6 = 14
3+3+8 = 14
2+3+12 = 17
1+9+8 = 18
1+6+12 = 19
2+2+18 = 22
1+4+18 = 23
1+3+24 = 28
1+2+36 = 39
1+1+72 = 74

j@utis

j@utis wrote:

means there are younger twins,

Why?

Also, as has been pointed out, why does there have to be 3 daughters?

am i missing something?

Pines

To chime in with Boxman and $hifty, what's wrong with the answers "8 and 9" or "12 and 6", or "2 and 2 and 3 and 6".

You can of course add as many 1 year-old daughters as you like (or as the woman can cope with) to any of these answers and they are still good.

Tree

none of pines pair's add to fourteen though.

Pines

Tree wrote:

none of pines pair's add to fourteen though.

Why do you think she lives at number 14?

bbbbb

j@utis wrote:

'eldest daughter has a cat with a wooden leg'... means there are younger twins, 3 year olds, and eldest daugther is 8year old.

I think j@utis is right.

To expand further, look at the information again:
1) ages multiply to 72. Factors are 2x2x2x3x3. So the ages have to be some combination of these. Tried to work these out (& what they add up to) but I'm a bit tired...
2x2x2x3x3 12
4x2x3x3 12
2x2x6x3 13
2x2x2x9 15
4x6x3 15
8x3x3 14
2x6x6 14
2x2x18 22
4x18 22
2x36 38
9x8 17
6x12 18

2) adding the ages gives the house no., but this isn't enough info implies it must be one of the combinations (like 14) that occurs twice.

3) the eldest daughter has a cat with a wooden leg, which implies that there is an eldest & not twins, so that gives us 8x3x3 rather than 2x6x6.

Still not entirely happy though. Fair enough to eliminate the combinations with triplets, but 2x2x18 & 4x18 are also a valid solution.

Talliesin

We can rule out those two combinations because there is an "eldest" and hence there are at least three. This leaves us with:

2x2x2x3x3 12
4x2x3x3 12
2x2x6x3 13
2x2x2x9 15
4x6x3 15
8x3x3 14
2x6x6 14
2x2x18 22

However, since there is no reason why we should leave out triplets beyond "fair enough to" (not a valid approach to a logic puzzle; after all quite often the answer to such puzzles depends on not discounting such possibilities) it's still not complete.

The original version of this puzzle stated that there were three daughters, (and that the multible of them was 36).

okgirl

So what is the answer? And where is the original question?

tech77

Talliesin wrote: »

We can rule out those two combinations because there is an "eldest" and hence there are at least three. This leaves us with:

2x2x2x3x3 12
4x2x3x3 12
2x2x6x3 13
2x2x2x9 15
4x6x3 15
8x3x3 14
2x6x6 14
2x2x18 22

However, since there is no reason why we should leave out triplets beyond "fair enough to" (not a valid approach to a logic puzzle; after all quite often the answer to such puzzles depends on not discounting such possibilities) it's still not complete.

The original version of this puzzle stated that there were three daughters, (and that the multible of them was 36).

So Talliesin from that are you saying it could be either:

4x2x3x3: 12 (eldest is 4)
or
8x3x3: 12 (eldest is 8)
or indeed
either of the above plus any additional number of 1 year olds (triplets/quadruplets/quintuplets/sextuplets/septuplets(sp?)/octuplets etc).

Which means the Census taker doesn't actually know the answer but only thinks he does.
Which means his logic is fallible.

Given that his logic is questionable this further undermines the whole riddle even more fundamentally TBH.

Talliesin

Yes. Someone either got the question muddled slightly along the way, or tried to change it while keeping the basic math the same, but made a mistake.

The original is:

A man in my neighbourhood has three daughters. One day when I asked their ages he said:

"The product of their ages is 36".

When I still couldn't find their ages he said:

"Ok. I'll give you another clue: the sum of their ages is same as the number of my house".

I knew the number but still couldn't calculate their ages. So the man gave me a last hint, he said:

"My eldest daughter lives upstairs".

Finally I was able to find their ages. Can you?

Given the analysis above of the related question, this version should be pretty trivial.