# Two old men

1. Jul 23, 2004

### Jin314159

Two old men....

Two old men were talking on the porch.

The first old man says: "I have three daughters. The sum of their ages is equal to the same number as this house's address (we don't know the number, but these two old men do). The product of their ages is 36."

The second old man thought for a moment and says: "That's not enough information."

The first old man says: "My oldest daughter has green eyes."

Then second old man figured out the ages of the first old man's daughters.

What are the ages of the first old man's daughters?

2. Jul 23, 2004

### check

Ooooh, I like this one.
Got it.

3. Jul 23, 2004

### marcus

I aint too proud to say the answer

2, 2, 9

4. Jul 23, 2004

### marcus

the ambiguity (which forced him to say a sentence indicating that
the oldest was one person and not twins) is the possibility of

1,6,6

but it cant be that because the oldest has green eyes so it has to be

2,2,9

5. Jul 24, 2004

### arildno

Unacceptable, unless we are talking about siamese twins
If one of the twins are born prior to the other, we certainly may say that that twin is the oldest

EDIT:
(D**n, I forgot about caesarian(?) birth..)

6. Jul 24, 2004

### The Bob

It is either 2, 3 and 6 or 2, 2 and 9.

As the oldest daughter has green eyes you can assume that the oldest and next oldest are not twins, otherwise it would have been oldest daughters.

7. Jul 24, 2004

### marcus

and I am sticking with that.

I do not think that what you suggest (2,3,6) is a possible answer

I think that because the second man said "that's not enough information"

the point is that if the housenumber had been 11 then he would not have asked for more information because there is no ambiguity: there's only one possible answer (2,3,6 is the only set of positive integers that work)

so we know that the housenumber was NOT 11

the only thing left is for it to be 13
because this has ambiguity----1,6,6 and 2,2,9----and makes a
reason for him to say "that's not enough information"

at that point he is told that one single daughter is the oldest and he knows it is 2,2,9

8. Jul 25, 2004

### The Bob

I know. I believe I was repeating it. Sorry.

9. Jul 25, 2004

### marcus

no problemo The Bob!
BTW I cannot reconstruct from memory a wellknown puzzler about the
3 people and the smudge on the forehead
or someone is wearing a funny hat and they are supposed
to deduce who. Maybe I always avoided getting acquainted
with this problem because I found it taunting. Can you remember or reconstruct it?

10. Jul 25, 2004

### Oyéah

People who have twins or triplets still consider the first born, the oldest, even if they are all the same age. Could they be 12 year old triplets? 3x12? The sum of the age would be the same as the product.

11. Jul 25, 2004

### Chrono

Couldn't you just ask how old the daughters are?

12. Jul 26, 2004

### Math Is Hard

Staff Emeritus
I don't understand why there are two OLD men talking when the daughters are so young. Is this just to throw you off track? And what does the address of the house have to do with it?

13. Jul 26, 2004

### marcus

Mathis, there can be some pretty spry old men
Lets change the subject shall we

14. Jul 26, 2004

### Jin314159

lol... yea, males can continue to procreate well into their 70s.

15. Jul 26, 2004

### The Bob

I remember my thread about hats where there are 4 people and they must deduce what colour hat they have on. I don't think I know what you mean really.

16. Jul 26, 2004

### Math Is Hard

Staff Emeritus

17. Jul 26, 2004

### BobG

I know these two guys. They live on 1313 Mockingbird Lane. (That actually makes a little more sense if you happen to know the first guy has twin daughters - he's used to looking at doubles of the same thing).

Both of these guys are old, but the second is old to the point of senility, which is why he's having trouble remembering the ages of his own granddaughters.

18. Jul 26, 2004

### marcus

Mathis I think you see that we are just fooling around here and should really change the subject of conversation. But just to respond to your question:

no Mathis, the house address is an essential part of the problem
It could have been rephrased by saying that First whispers to the other what the sum of the ages is. the important thing is they both know the sum (even tho we do not)

A. the ages are whole numbers (assumed)
B. the ages multiply to make 36
C. Even though Second O.M. knows the sum, he still cannot deduce

from this one can deduce that the sum is NOT 11
because if it were then he would be able to say 2,3,6
THERE ARE NO OTHER 3 NUMBERS THAT ADD UP TO 11 and multiply to 36.

Also we can deduce the sum is not 10 (he didnt whisper "ten" to his friend) because then the ages would have to be 3,3,4.

Also we can deduce that he didnt whisper "38"
because then the unique possible answer would be 1,1,36

So, mathis, it is as if we can eavesdrop on what he whispers
We also know he didnt whisper "21" for the sum because then
the immediate inference is 1,2,18
And he didnt whisper "16" because then Second O.M. would deduce 1,3,12

So the only thing he can have whispered was "13" because for sum of 13
there are two possibilities 2,2,9 and 1,6,6.

You can check that 13 is the only possible whole number besides what we already excluded. :surprise:

19. Jul 26, 2004

### Math Is Hard

Staff Emeritus
OK, I see what you're saying. It's really only important that both men have knowledge of the sum of the ages of the three daughters, and since both know the house address number, then we can conclude that they do.

20. Aug 8, 2004

### BranMan

ehhhh probably 64