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Question 102407: Census taker is asking Mrs. Smith
ct: how old are your children?
ms: I have no 1 year olds, the sum of their ages equals our house number, the product of their ages is 90
ct: this is not enough information
ms: you are right, the kid across the street is older than my oldest
How old are Mrs. Smith's children
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! It appears as if you have left something out of this problem. As you wrote it, there are
only three constraints:
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(1) there are no 1 year olds
(2) the sum of the children's ages is the house number and it is unknown
(3) the product of the children's ages is 90
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Here are possible solutions:
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Solution 1 - Her children are 2, 3, 3 (3-year old twins), and 5. There is no 1-year old, the
sum of their ages is 13 and that is the house number. And the product of 2 times 3 times 3 times 5
is 90. All constraints are met.
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Solution 2. Her children are 3, 5, and 6. There is no 1-year old. The sum of their ages is
14 and that is the house number. And the product of 3 times 5 times 6 is 90. All the conditions
are met by this answer also.
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Solution 3. Her children are 3, 3, and 10 (again 3-yr old twins). There is no 1-yr old. The
sum of their ages is 16 and that is the house number. And the product of 3 times 3 times 10
is 90. All the conditions are met by this answer also.
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Solution 4. Her children are 2 and 5 and 9. There is no 1-yr old. The sum of their ages
is 16 and that is the house number. And the product of 2 times 5 times 9 is 90. So this
set of children meets all the conditions for the answer.
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There are more answer sets that meet the conditions required of the answer.
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The fact that the kid across the street is older than her oldest has no bearing on the problem.
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Did you leave something out???
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