Posted by Tyler on Friday, September 21, 2007 at 4:52pm.
In a little town in West Michigan lives a math professor, who hears one day that the barber has three children. So, on the next visit to the barber, the professor casually inquires, "I have heard you have three children, is that right?" "Yes!" says the barber. "Well, how old are they?" "You are the math professor, aren't you? I tell you, if you multiply the ages of the three, you'll end up with 36." "All right!" the professor answers and walks home. The next day the professor comes back to the barber shop and says: "With the information you have given me, it is impossible to figure out how old your kids are." Then the barber says: "Very good, I see you are a good mathematician. If you add the ages of the three, the sum will be the number of my house." So, the professor walks out, looks at the house number and returns home. Still the professor can't find the solution. The next day, the professor tells the barber that there still must be some information that's missing. "Yes, you are very clever!" says the barber. "The next information I'm giving you is the last word I'm saying about the age of my children. Now you will have enough information. Don't come back again and ask for more. The youngest has blonde hair." The professor goes home and figures out the answer.
What are the ages of the barber's children, and how did the professor figure it out?

Math  bobpursley, Friday, September 21, 2007 at 5:23pm
What are the whole number factors of 36? A kid with blonde hair is not 1. Brothers/sisters cannot be the same age.

Math  Tyler, Friday, September 21, 2007 at 9:19pm
The only possible answers I found were 1, 1, 36
1, 2, 18
1, 3, 12
1, 4, 9
1, 6, 6
2, 2, 9
2, 3, 6
2, 4, 4
3, 3, 4
9, 2, 3

Math  Tyler, Friday, September 21, 2007 at 9:21pm
2, 3, 6
9, 2, 3
So, Im still trying to narrow it down.

Math  Frank, Saturday, September 22, 2007 at 11:34am
If the sum of the ages were unique, then the mathematician would have been able to solve it after the second piece of information...
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