Now we will come to selective combination category.
In our life we meet very often difficult situations in which we have to take a correct decision, sometimes a life saving one too! In those situations correct thinking to arrive at the correct decision is very much important. For this we have to understand the selective combination problem.
Given below is a problem, ‘Prisoner’s Dilemma’ selected from my collection. Please go through the problem and arrive at the correct solution before referring to the answer given at the end of the problem.
A prisoner is kept in a cell which has two outlets. One leads to gallows, the other to freedom. A guard is posted at each of the outlets. One of them is always truthful and the other never is. The identity of the truthful guard and the liar is however is not known. Nor is the specific outlet which leads the prisoner to freedom. The prisoner is an ex-servant of the prisoner. Hence the latter decides to deal with him more leniently. He visits the cell and informs the prisoner that he is allowed the following two situations 1) The prisoner can ask one question to either of the guards and 2) listen to the reply and select any outlet.
If the prisoner chooses the outlet which leads to the gallows he forfeits his life and if he takes the exit door he is a free man.
What question should the prisoner ask in order to identify the door which will lead him to freedom?
One moment please! Now think for a while to arrive at the correct question.
If you are not able to arrive at the correct one, please go ahead.
After pondering this crucial point, the prisoner formed the following question. He approached the guard standing at one of the outlets and asked him, “If I ask the other guard the question, ‘Does your door lead a person to the exit?’ then what will his reply be?”
If the guard (to whom the prisoner posed this question) says, ‘yes’, then the prisoner takes the same outlet, and if he gets, ‘no’ for an answer, he avoids the outlet.
What is the distinguishing point about the question that enables the prisoner to always get an affirmative answer at the exit?
We know the statement, ‘it is true that Tom is not a scholar’ carries the same message as the sentence, ‘it is not true that Tom is a scholar’. Thus an assertion of a negative is equivalent to a negative of the assertion. Since the question brings into picture both the guards (to combine assertion and negative) one is found to get the same answer at the exit from either guard.
If we think we can ask a much simpler question also to save his life. The question can be posed to either guard and it reads as follows: “is the truthful guard standing at the exit door?’ If the reply is ‘Yes’ take the same outlet and if it is ‘No’ avoid the outlet.
We will see more problems of this nature in our next article.
S. Nagarajan is a vehicle body engineer by profession. He has written more than 1300 articles in 16 magazines and published 18 books. He is revealing Eastern Secret Wisdom through T.V. Programmers, magazine articles, seminars, courses. His e-book
Tags: IQ and Problem solving
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