The Mathematician's Riddle

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Status: Finished  |  Genre: Riddles  |  House: Booksie Classic

I hope you're good at math and reasoning, or this riddle will boggle your brain. See if you can solve it.

Two men I knew; one blind, one could see,

Both, the best math'metician claimed to be.

Tired of their dispute, to put them to rest,

I, the king of the land, set them a test.


I welcomed them to my great castle home,

And then I said, sitting back in my throne,

'I have three sons, they were all bor today.

Try to guess their ages, now guess, I say.'


And then, said I, as my hair I did groom,

'Their sum equals the windows in this room.

I wear, fair sirs, I am playing no tricks.

Product of their ages is thirty-six.'


Said the seeing man, 'I still do not know,

Continue; I'm sure the answer will show.'

'This is my last clue,' said I, then I said,

'The oldest of my sons has hair of red.'


Said the seeing man, 'I still cannot tell!

What sort of junk are you trying to sell?'

But then the blind man told the ages three,

And of the windows tthat he could nt see.


So tell me now, are you able to tell?

Can you see what the blind man saw as well?









(Please try to solve before looking at the explanation)


First, an assesment of the clues; the three sons were born on the same day, today, so you're working with integers.  The ages sum to the number of windows in the room, and multiply together to be thirty-six.  Here's a list of the sets of three multiples of thirty-six:

36  1  1

18  2  1

12  3  1

9  4  1

9  2  2

6  6  1

4  3  3

Even knowing the lists of multiples and the number of windows, the seeing man did not know the answer.  Therefore, two or more answers must be possible with the same sum.  So the answer is either  '9  2  2'  or  '6  6  1',  which both sum to 13.  The last clue states that the oldest son has red hair.  Emphasis on oldest.  with '6  6  1', the two oldest are the same age; therefore the ages of the king's three sons have to be nine, two, and two.  Hope you found this riddle neurologically stimulating!


Submitted: April 22, 2012

© Copyright 2022 T M Allen. All rights reserved.

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Very good.

Fri, October 26th, 2012 3:45pm

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