Puzzle This
After all my recent talk of Ferrets and Pinkberry, it’s high time for something more technical. Here is a puzzle my housemate told me about a month ago. Below the fold is my computer science style derivation of the answer.
A young man is committed to marry one of three identical sisters. Despite their genetic similarity, one of the sisters always lies, one always tells the truth, and the third lies only sometimes. Also, the sisters themselves can always tell each other apart. The young man is permitted to ask one of the women, chosen at random, a single yes-no question. Based on this single response, he must select his bride. Being a man who values certainty, his goal is to select either the sister that always tells the truth, or the sister that always lies. What question should he ask?
Whatever question is asked, the response is either yes or no. When the question is asked to the sister that sometimes lies the response is meaningless. Regardless of what she says, the man must select one of the other two sisters. Since the man does not know which sister he is addressing, his question and response to it’s answer must always be the same. Thus his response to the answer must always be to select one of the two sisters he did not address.
So the man needs a question that differentiates between the two sisters not being addressed. When the sister that sometimes lies is addressed, it doesn’t matter which other sister is chosen. When the sister who always lies is addressed, however, the truthful sister must be selected, and when the sister who always tells the truth is addressed, the sister that always lies must be selected.
The man’s question must cause the always lying sister to identify the truthful sister, and the truthful sister to identify to the always lying sister. Since the lying sister always lies, the question should ask her to identify the sister that sometimes lies, while at the same time ask the truthful sister to identify the sister that always lies.
One such question is “Which of your two sisters always lies, or if neither always lies, which sometimes lies?” A much nicer version of this question is: “Which of your two sisters lies more?”. To turn this into a yes-no question, the man can simply point to one of the other two sisters and ask “Does she lie more than your other sister?”.
In the end, this puzzle has a nice short answer. From a computer science perspective, I think understanding how one can arrive at this answer is what’s interesting.