who is which
Written on 7:48 pm by Vja Students
You are confronted with three bankers, one from Albania, one from America, and one from Austria. You do not know which is which, but you do know that one always tells the truth, a second always lies, and a third sometimes lies and sometimes tells the truth. How many questions are needed to identify their respective nationalities?
Solution::
Not more than 4 questions will be necessary, but sometimes (in one case out of three) 3 questions will suffice.
1st question (addressed to the 1st banker): "If I asked you whether the 2nd banker is an equivocator (i.e. a person who sometimes tells lies and sometimes tells the truth), would you say yes?" If he answers yes, we know that the 3rd banker cannot possibly be an equivocator and we accordingly address our subsequent questions to him; if the 1st banker answers no, we know that the second banker is not an equivocator and we ask him our subsequent questions.
2nd question (addressed to the 3rd or the 2nd banker depending on whether the answer to the 1st question was yes or no respectively): "If I asked you whether the 1st banker is Albanian, would you answer yes?" If the answer is yes, the 3rd question (asked to the same person as the 2nd question) is: "If I asked you whether the 2nd banker is American, would you say yes?" By elimination, we know the identity of the 3rd banker also.
If, on the other hand, the answer to the 2nd question is no, two further questions will be required (a total of 4). 3rd question: "If I asked you whether the 1st banker is American, would you say yes?" If the answer is yes, we know that the 1st banker is American; if it is no, we know that he is Austrian. In either case we require one further question (the 4th question) to identify the two remaining bankers.
Since the 1st question 'eliminates' the equivocator, we know that the remaining questions are addressed to someone who is consistently honest or consistently dishonest; and the questions are so worded that the answers will be the same whether he is honest or dishonest. The moral is that consistently dishonest people are far more dependable than those who occasionally tell the truth.
