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Succinct Age Settlement (Posted on 2010-02-09) Difficulty: 2 of 5
The socialite Anne said to fellow socialite Claire, "I have three daughters. Can you figure out the ages of each of them knowing that the sum of their ages is 11?"

"That is not enough information," replied Claire.

"The product of their ages is either 16 years less or, 16 years more than your age," added Anne.

"Still not enough information." replied Claire after careful thought.

"The daughter whose age, in years, is the greatest is learning to play chess." said Anne.

Claire was then immediately able to determine the ages of Anne’s three daughters.

What are their ages?

No Solution Yet Submitted by K Sengupta    
Rating: 1.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Not enough information | Comment 3 of 7 |
Not so fast.  Even if the socialite's age is an integer, nobody said that the children's ages were.  There are a lot of other possibilities.

For instance,

ages           product
2/3, 4/3, 9   8
1/2, 4, 9/2   9
1/2, 5/2, 8  10
3/2, 3/2, 8  18
3/2, 7/2, 4  21
5/2, 5/2, 4  25

There is just not enough information to solve this, unless we assume (as the socialite did) that all three children are celebrating their birthday today.

Or maybe socialites don't do fractions?

  Posted by Steve Herman on 2010-02-09 15:02:22
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