Date: 02/20/2002 at 11:54:45 From: Christina Subject: Census Taker The census taker says, "I need to know the ages of your children." The mother replies, "I have no one-year-olds. The product of my children's ages is 90, and the sum of their ages is the same as my house number." The census taker replies. "I can see the house number but I still need more information." The mother says, "You're right. You also need to know that the boy across the street is older than my oldest child." The census taker says, "Thank you, I now know the ages of your children." What are the ages of the children, and what is the house number and the age of the boy across the street?
Date: 02/20/2002 at 12:14:02 From: Doctor Peterson Subject: Re: Census Taker Hi, Christina. Make a list of all ways to factor 90 (with no ones): 2*3*3*5, 2*3*10, and so on. One of those sets of factors gives the ages. Add the factors in each case; if the house number is that value, the census taker knows that those are the ages - unless there are two possibilities that give the same sum. So the ages must be one of those sets. Which one? Since knowing that the oldest child is younger than the boy across the street tells the census taker the answer, we can presume that the census taker has already been across the street and knows that age. What age will give enough information for him to now determine the answer uniquely? - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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