need a difficult question!

Reaper 392 said:
My heuristics lectures are full of awesome puzzles. Here's one I really liked:

Two men meet on the street. They haven't seen each other for many years. They talk about various things and then after some time one of them says: "Since you're a professor of mathematics I'd like to give you a problem to solve. You know today is a very special day for me: All three of my son's celebrate their birthday this very day! So can you tell me how old each of them is?"

"Sure" Answers the mathematician, "but you will have to tell me something about them."
"OK, I'll give you some hints," replies the father of the three sons, "The product of the ages of my three sons is 36"
"That's fine" says the mathematician, "but I will need more than just this"
"The sum of their ages is equal to the number of windows in that building." says the father pointing at a structure next to them.
The mathematician thinks for some time and replies, "Still, I need an additional hint to solve your puzzle."
"My oldest son has blue eyes," says the father.
"Oh that is sufficient!" exclaims the mathematician and gives the father the correct ages of his sons.

How old are the three sons?
Click to expand...

3, 3 and 4?

EDIT: need another clue such as how many windows are in the structure? :p
 
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Reaper 392 said:
My heuristics lectures are full of awesome puzzles. Here's one I really liked:

Two men meet on the street. They haven't seen each other for many years. They talk about various things and then after some time one of them says: "Since you're a professor of mathematics I'd like to give you a problem to solve. You know today is a very special day for me: All three of my son's celebrate their birthday this very day! So can you tell me how old each of them is?"

"Sure" Answers the mathematician, "but you will have to tell me something about them."
"OK, I'll give you some hints," replies the father of the three sons, "The product of the ages of my three sons is 36"
"That's fine" says the mathematician, "but I will need more than just this"
"The sum of their ages is equal to the number of windows in that building." says the father pointing at a structure next to them.
The mathematician thinks for some time and replies, "Still, I need an additional hint to solve your puzzle."
"My oldest son has blue eyes," says the father.
"Oh that is sufficient!" exclaims the mathematician and gives the father the correct ages of his sons.

How old are the three sons?
Click to expand...

arctine said:
3, 3 and 4?

EDIT: need another clue such as how many windows are in the structure? :p
Click to expand...

You have all the clues you need

for anyone that wants to know the answer and how to get there the solution is in the spoiler
The first clue to work with is the obvious one, that their ages multiply to make 36. this gives you 8 possible answers.

36, 1, 1
18, 2, 1
12, 3, 1
9, 4, 1
9, 2, 2
6, 6, 1
6, 3, 2
4, 3, 3

It is obvious that the next clue involves the sum of their ages. We don't know how many windows were in the building but any extra information is helpful

36, 1, 1 = 38
18, 2, 1 = 21
12, 3, 1 = 16
9, 4, 1 = 14
9, 2, 2 = 13
6, 6, 1 = 13
6, 3, 2 = 11
4, 3, 3 = 10

We don't know how many windows the building had, but the mathematician did. The mathematician asked for more information meaning that knowing the number of windows left more than one possible solution.

The only duplicate total we have is 13, leaving with two possible solutions

9, 2, 2 = 13
6, 6, 1 = 13

The final clue is that his eldest son has blue eyes. obviously knowing one of the children has blue eyes doesnt help, but knowing that one of the children is older than the other two certainly does. it eliminates the last remaining wrong answer to leave the ages as 9, 2, 2

(personally I don't like that last clue because technically two children cant come out at exactly the same time, but the 9 year old is clearly the eldest in the other solution)
 
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