# Guess the Ages

The noblewoman Alexis said to noblewoman Blythe, “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 Blythe.

“The product of their ages is either 16 years less or, 16 years more than your age,” added Alexis.

“Still not enough information.” replied Blythe after careful thought.

“The daughter whose age, in years, is the greatest is learning to play chess,” said Alexis.

Blythe was then immediately able to determine their ages of Alexisâ€™ three daughters.

Can you tell the Riddledude what their ages are?

### 3 guesses to Guess the Ages

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• the girls were 11 triplets

• Paul

The ages need to add up to 11, when the three ages are multiplied they need to be 16 years Blythe’s age, Blythe needs to be old enough to be considered a noblewoman and the oldest daughter needs to be old enough to learn chess. 9 and twin 1 year olds would make Blythe 25 (too young for a noble), so I’m going with 8, 2 and 1 – 8+2+1=11 and 8x2x1=16 making Blythe 32 and her land owning lug of a husband is 64.

• dude

Congrats Paul!
You nailed the correct answer, but for the wrong reason:

If the product of their ages is either sixteen years more or less than noblewoman Blythe and this is not enough information, this would suggest that there are two combinations of ages that are 32 years apart that fit the criteria.

These being: 1, 2 and 8 (product= 16), as well as 3, 4 and 4 (product = 48).

As the next part of the statement specifies that there is only one older daughter (in years), then the eldest can’t be twins. Therefore the daughters are 1, 2 and 8 years of age.

You worked it out nicely and your reasoning (old enough to play chess) found you the correct answer even though the word “daughter” is singular, so therefore automatically precludes the first combination.
You’re today’s winner!