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.
