The man asks the mathematician how old his children are.

The mathematician, who always replies in riddles said,

"I now have three children.

The sum of their ages is equal to the number of windows on the building in front of you

and the product of their ages equals 36."

The friend then says "I need one more piece of information."

The mathematician then replies "My youngest child has blue eyes."

What are the ages of the mathematicians three children?

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Let's say that the ages of the children are x,y,z. One fact we know is that xyz = 36. The list of possibilities are:-36,1,1 - sum is 38

18,2,1 - sum is 21

9,4,1 - sum is 14

9,2,2 - sum is 13

6,6,1 - sum is 13

6,3,2 - sum is 11

If we weren't in the sum = 13 situation then the guy wouldn't need any further info. So we're in a 9,2,2 or 6,6,1 situation.

I think we're meant to read into the last piece of info that the elder two are twins, rather than the younger two - so that there is indeed a "youngest" and so we're in the 6,6,1 situation.