# Problem 23 Solution

You point to either path and say, "Are you from this village?" If the person answers 'yes' then you are pointing to the truthful village, if they answer 'no' then you are pointing to the lying village.

This is not the only answer that works but is the simplist I have heard so far.

I continue to receive a lot of e-mail on this problem from people who don't understand or disagree with my solution. Before you question me on this answer these four questions:

1. If you point to the truthful village what will a truthful person say in answer to your question?
2. If you point to the truthful village what will a untruthful person say in answer to your question?
3. If you point to the untruthful village what will a truthful person say in answer to your question?
4. If you point to the untruthful village what will a untruthful person say in answer to your question?
The answers to these questions are: 1. "yes", 2. "yes", 3. "no", 4. "no".

Note that in the two cases where the answer is "yes" you are pointing to the truthful village and in the two cases where the answer is "no" you are pointing to the untruthful village. Thus you can tell from the reply to which village you are pointing. You do not have to know to whom you are speaking.

Another possible solution which I have heard is to ask "Which path would a person from the other village say leads to the truthful (or untruthful) village?" Regardless of whom you speak to the answer will filter through one lie, so the person will point to the lying village if you ask for the truthful village, and vise versa.

Michael Shackleford, A.S.A.