Cannot be done with one question if there are two who may be from the same tribe:
Assume two Indians, A and B. There are four possibilities:
Both are whitefeet, so they both tell the truth
Both are blackfeet, so they both lie.
A is a whitefeet, who always tells the truth. B is a blackfeet, who always lies.
A is a blackfeet, who always lies, and B is a whitefeet, who always tells the truth.
First question, asked of A:
What will B say when I ask him to predict your answer if I ask you what color your feet are.
If both are whitefeet, A would answer the underlying question by saying “I have white feet.”
B would predict that A would say that.
A truthfully says that B would predict that A would answer by saying that A has white feet..
If both are blackfeet, A would answer the underlying question by lying: “I have white feet.”
B would predict that A would answer the question by saying, “I have black feet”, which is a lie because a blackfeet would say that he had white feet, so a liar would predict that he would say just the opposite.
This means that A would say that B would predict, “A would say that he has white feet.” Which is the truth, but we didn’t ask A what color feet he had.
If A is a whitefeet and B is a blackfeet, A would have answered the basic question by telling the truth: “I have white feet.
B would have to say that A would say he has black feet, because he has to lie.
A, knowing that B would lie, would have to predict that B would say that A has black feet.
If A is a blackfeet and B is a whitefeet, A would have answered the basic question by saying that he has white feet (a lie).
B would say when asked that A would say he has white feet, because that’s the truth about the lie A would tell.
A would then say that B would say that A has black feet.
If the answer to the first question is white feet, then you know that both of them are from the same tribe, since that’s the only combination that elicits that answer. Ask A: What will B say if I ask him what color his feet are? If B is a blackfeet, he will answer the question by lying: I have white feet. A would then predict that B would answer black feet, since he has to lie. If both of them are white feet, B would say I have white feet and A would agree with him. Thus, if A answers black feet, you know they both have black feet. If A answers white feet then you know that they both have white feet.
If the answer to the original question was black feet, you know that one of them has black feet and the other has white feet.
Ask A: what will B say when I ask him what color feet he has.
IF A is a whitefeet, he knows that B will answer that he has white feet, and will tell the truth: B will say that he has white feet.
If A is a blackfeet, he knows that B will truthfully say, “I have white feet”, so he will say, “B will say he has black feet.
