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?

This puzzle is very similar to The three daughters (pid=237) by maverick posted 2002-10-31.

The key to the number of possibilities is the given statement that "Claire was then immediately able to determine the ages of Anne's three daughters." As such, the ages of the three daughters would be positive integers.
As Claire was unable to determine the age after being given that the product of their ages was a difference of 16 to her own, it can be deduced that the difference to the product was 32, and the ages were either (1, 2, and 8) or (3, 4, and 4). With Claire's age revealed to be 32, and with the clue that infers the eldest daughter's age, in years, is unique among the three, the solution to the ages of the daugters is 1, 2, and 8,

Edited on February 9, 2010, 10:41 pm

Posted by Dej Mar on 2010-02-09 22:38:20