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Succinct Age Settlement (Posted on 2010-02-09)

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)

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analytical solution

| Comment 1 of 7

based on the first 2 clues I built the following table

d1 d2 d3 product p-16 p+16

1 1 9 9 -7 25

1 2 8 16 0 32

1 3 7 21 5 37

1 4 6 24 8 40

1 5 5 25 9 41

2 2 7 28 12 44

2 3 6 36 20 52

2 4 5 40 24 56

3 3 5 45 29 61

3 4 4 48 32 64

so based on the second clue this can be narrowed down to

1,2,8 with their product being 16 less than 32

and 3,4,4 with their product being 16 more than 32

with the final clue we can eliminate 3,4,4 since there is not a single oldest child.

thus the children's ages are 1,2 and 8.

Edited on February 9, 2010, 12:07 pm

Posted by Daniel on 2010-02-09 12:01:26

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