Mathematicians and their sons
I got this problem from a book. It was and still is one of my absolute favorite problems of all time.
Two mathematicians meet at a coffee shop.
"You have three sons, correct?" Bob says, "what are their ages?"
"The product of their ages is 36" says Bill, " and the sum of their ages is today's date"
"Well, I know the date" bob says, "but that doesn't tell me how old your children are"
"Oh, I forgot to tell you," Bill says, "my youngest one has red hair"
"Ahh, thank you, now I know how old they are" bob replies.
What is the sum of Bill's children's ages?
Assumption/hint: Assume if two children are of the same age, they are born on the same date.
Image credit: Wikipedia Sloan hadfield
The answer is 13.
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There are 8 possibilities for the age products to be 36.
son 1 1 1 1 1 1 2 2 3 son 2 1 2 3 4 6 2 3 3 son 3 3 6 1 8 1 2 9 6 9 6 4 product 3 6 3 6 3 6 3 6 3 6 3 6 3 6 3 6 sum 3 8 2 1 1 6 1 4 1 3 1 3 1 1 1 0
Since Bob didn't know their ages with just the knowledge of the age product and sum, the day must be the 13th since it is the only day with with two possible ages. Finally, since there is a youngest son, the 2,2,9 option can be ruled out since two are the same age and there is no youngest son. Thus the only possibility left is 1 , 6 , 6