Ask Marilyn ® by Marilyn vos Savant is a column in Parade Magazine, published by PARADE, 711 Third Avenue, New York, NY 10017, USA. According to Parade, Marilyn vos Savant is listed in the "Guinness Book of World Records Hall of Fame" for "Highest IQ."
In her Parade Magazine column of May 25, 1997, Marilyn assumes that the only possible eye colors for the Brown brothers are blue and brown. She also assumes that when two of them go anywhere together, the two are a random selection of all the Brown brothers. Based upon these assumptions, she concludes that there are a minimum of four Brown brothers, two with blue eyes and two with brown eyes.
In the absense of these assumptions, there are a minimum of three Brown brothers, two with blue eyes, and one with eyes of some other color.
I enjoy your column, it sometimes makes me think.
There are only 2 statements in your answer on May 25th that are correct with the possible exception being "I hope that was clear!"
1st: "There must be at least three Brown brothers"
2nd: "And forget the Brown sisters"
Since the question states "What's the smallest number of brothers that must be in the Brown family" The answer as you state is clearly three because anything over three is not the smallest number of brothers that must be in the Brown family. The odds of running into any group of brothers does not relate to the question.
It would seem that you fell for the hint even though you state "forget them", otherwise how could you make the statement "There must be at least three Brown brothers--including at least two blue-eyed brothers and at least one brown-eyed brother." I believe that statement should have read "There must be at least three Brown brothers--including at least two blue-eyed brothers and at least one brother with eyes of a color other than blue."
In conclusion and in the interest of brevity we will forget a zillion meetings, probability, etc. Only half of the question can be answered and it was when you said "There must be at least three Brown brothers". What color are their eyes can not be answered with the information given unless you are using a logic that escapes the rest of us.
In a subsequent email, Joe wrote:
After a little thought I figure the smallest number of Brown brothers is two. One brother has blue eyes and the other brother wears his blue contacts only half the time.