The Blind Mathematician

[Miss Perfect]

Someone posted this at another forum, and I found it intersting to share:

 

Once upon a time a king wanted to hire the best Mathematician in his kingdom to work in his palace. His servants brought to him the best two mathematicians, one of them was blind. The king told both mathematicians that he can't hire both so he will ask a question and whoever answers gets the job.

 

The king said: "I have three sons, whoever guesses their ages will be hired." The king told them that if they multiply the ages of his sons the result will be 36. Both mathematicians told the king that this information is not enough. The king then said: "The number of windows in the building across the street is equal to the sum of the ages of my sons." The first mathematician (who can see) counted the windows, and told the king that he still could not figure it out. The Blind mathematician (who could not count the windows) told the king that he does not have an answer. The king then said: "My oldest son has red hair." Right away the blind mathematician gave the correct answer and got hired.

 

The question is: How did the Blind guy know the answer and what is the answer?

 

PS There are no tricks in this puzzle; you just have to think logically. Assume the ages are whole numbers!

[NPK]

[hide]The redhead is the eldest and the other 2 may be twins. redhead = 9; twins = 2 years old ??? [/hide]

[Miss Perfect]

That's right! But you should explain how to get the answer!

[NPK]

[hide]Well, he said the eldest is a redhead, so you assume that the others are not. (Not a good assumption but anyway...)

One way for the other sons to both not be redheads is for them to be twins, with different colour hair.

 

Maybe my reasoning was wrong and my guess was lucky...using that logic the ages could have also been 1 (twins) and 36 (redhead) OR 3 (twins) and 4 (redhead).

 

[/hide]

[Miss Perfect]

This redhead thing is only 1 of the clues!

[NPK]

[hide]The building across the street has 13 windows, but the mathematician who can see this still doesn't know the ages of the sons because there are 2 possibilities: 2+2+9=13; 6+6+1=13. When the blind mathematician knew there was an oldest son, the second of the possibilities can't be right, because that combination isn't compatible with there being an oldest son.[/hide]

[Miss Perfect]

Well done! That's right!

[The Spith]

You didn't include that there are 13 windows

[timo]

You didn't include that there are 13 windows

Figuring that out is part of the problem; the blind mathematican wasn´t told that number, either.

[hide] 13 is the only number of windows from which the seeing mathematican couldn´t tell the ages; the blind one just has to put a little faith in the skill of his colleague. [/hide]

[Miss Perfect]

Thanks for the nice explanation, Atheist!

[Severian]

So what is wrong with 1,2,18?

 

1*2*18=36 and 1+2+18=21 windows.

 

After all, the other mathematicain may just be an idiot.

[Miss Perfect]

So what is wrong with 1' date='2,18?

 

1*2*18=36 and 1+2+18=21 windows.

 

After all, the other mathematicain may just be an idiot.[/quote']

 

Then we must assume that the king was an idiot who even bother to invite this person!

Anyway I think it's a very easy puzzle, but most of people think that the blind mathematician was a good biologist who knew people's hair change color to red at a certain age, and therefor they can't solve it!

 

who knows? perhaps this mathematician got stuck on the red hair if he wasn't blind!