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Did You Find Out? Get the Answer to the Riddle of E-News Issue No. 3, September 2017

2017-07-26

Between Truth and Lies

Two means of escape
Find out which escape route the thief chose!

A police inspector wants to solve a theft and is close to tracking down the thief. Reconstructing the crime, he needs to follow the escape route, and wonders which of two possible paths the thief had selected. In order to clarify this, the police inspector interviews three witnesses. Therefore, he is allowed to ask two questions, each question to one person. Among the witnesses are a notorious liar, a totally honest person, and someone who lies on occasion. The police inspector does not know which of the three witnesses is always ying, occasionally lying, or always telling the truth.

How should the police inspector proceed in order to find out which escape route the thief took? What questions should the inspector ask?


Solution

The first question to ask a witness is:

Which of these other witnesses is more likely to tell the truth?

The answers have to be divided into three possible cases:

  1. The question was addressed to the truthful witness who would point to the occasional liar.
  2. The question was addressed to the notorious liar. The truthful answer would be to point to the "always honest" witness. But, as a notorious liar, he selects the occasional liar (as in case 1).
  3. The "occasional liar" was asked. He points arbitrarily towards the liar or the truthful witness.

Looking at the answers, you see that the "occasional liar" is either the questioned witness or the one to whom the other witnesses point to. Meaning, the person who is not questioned or pointed to by the other witnesses cannot be the "occasional liar". The person always says the truth or the untruth. The police officer now asks a second, more complicated question to this particular witness:
 

Which escape route would the witness who does not occasionally lie indicate ?

The following two cases are possible:

  1. The one to whom the second question is asked always tells the truth. If the other witness (who is not the occasional liar) is questioned, this person would always point the wrong way. So, to answer the question truthfully, the truthful witness also indicates the wrong escape route.
  2. The question is addressed to the notorious liar. If the question is addressed to the witness who always says the truth, the liar would point to the escape route used by the thief. Since the question "which way would the other person point to" was posed to the liar, he would, of course, not indicate the route that the honest witness would point to. Thus, he would indicate the wrong escape route.

In both cases, the interviewees point out the incorrect escape route. Now, the police inspector simply has to choose the other path to successfully complete his investigation and catch the thief.


To solve this riddle, it is necessary to ensure that the first question eliminates the possibility that the second question is addressed to the "occasional liar". If you have identified a person who always behaves the same way (regardless of whether he always lies or always tells the truth), then you can solve the riddle with the help of an appropriate second question.


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