Al, Beth, Carl, and Dawn are
sitting around a table at a bar, as Al
tries to guess Beth’s age. They all
know she is at least 21, or she wouldn’t
have been allowed into the bar. Al
asks Beth five questions, pausing for
contemplation after each question:
1. Is your age a multiple of 17?
2. Is your age a multiple of 3?
3. Is your age a prime number?
4. Are you older than I am? (Beth
knows Al’s age.)
5. Have you celebrated your 51st
birthday?
At this point, Al announces that he has
deduced Beth’s age, but Beth tells him
he is wrong. Carl, whose age is a prime
number, has been listening to this
conversation and is able to correctly
deduce Al’s age. From his knowledge
of Beth, he surmises that she has not
answered all the questions truthfully
and guesses that she has alternated
correct and incorrect answers. He
knows that Beth is older than he is,
and although he has guessed correctly
how many of Beth’s answers are
incorrect, he has assumed the wrong
ones. So, when he announces what
he has deduced as Beth’s age, Beth
tells him he is also wrong.
Finally, Dawn who has also been listening in and is sharper than Carl, guesses
correctly which of Beth’s answers are
incorrect. Now, knowing that Beth is
younger than she is, Dawn is able to
correctly announce Beth’s age.
What
are the ages of Al, Beth, Carl, and
Dawn, and what are Al’s and Carl’s
incorrect guesses?
It may help to
know that Dawn’s age is divisible by
13 and they all know that their ages
are all different.
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