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Solving crimes is not easy.
Sometimes witnesses have false memories, and accused do not always tell the truth when questioned.
In the case of the theft of a valuable watch, which is the subject of this article, there is another special feature.
All suspects are either notorious liars, so they never tell the truth - or they always stick to the truth in everything they say.
Unfortunately, you can't tell which of the two groups they belong to.
Dieter is one of the alleged thieves and is questioned in court.
"Did you ever claim after the clock disappeared that you were
n't the thief
?" Asks the judge.
The answer is: "Yes."
The judge asked: "After the watch disappeared, did you ever claim you were
the thief
?"
We don't know Dieter's answer, but we do know that he answered the question with "yes" or "no".
We also know that the judge passed a judgment immediately afterwards - and that the judge only makes decisions if he is one hundred percent sure about the matter.
What was the verdict?
Please scroll down to find the solution!
Photo: Michael Niestedt / DER SPIEGEL
solution
Dieter was acquitted because he is not the thief.
The first question, whether he ever claimed after the watch disappeared that he was
not
the thief
, Dieter answers with "Yes".
The following table shows Dieter's various possible answers, depending on whether he is lying, telling the truth, or is the thief or not.
Short explanation: If Dieter is the thief and always tells the truth, he can only answer the question with "No".
If he is not the thief and is always telling the truth, the answers "yes" or "no" are possible, depending on whether he has ever claimed that he was not the thief or whether he did not make that claim.
Similarly, the answer options "yes" or "no" if he is the thief and "yes" if he is not the thief also result for a lying Dieter.
The second question, the answer of which we do not know, but which was sufficient for the judge to pass his judgment.
The following answers are possible:
We know that Dieter answered the first question with "Yes".
The thief + truth option is no longer available.
Dieter can still have answered the second question with "yes" or "no", as the table shows.
His answer must have told the judge whether he is the thief or not.
If Dieter had answered "yes", the judge would have known that he was dealing with a liar.
However, he does not know whether Dieter is the thief or not.
As a thief, Dieter would have answered “yes”, as a non-thief “yes” would also be a possible answer alongside “no”.
Therefore the answer cannot have been "yes" because this answer is insufficient for a watertight judgment.
What about the "no" answer?
Dieter can give it as a non-thief telling the truth and as a lying non-thief - but not as a lying thief.
(The option that Dieter is a truth-telling thief is excluded by answering "Yes" to the first question.)
From all this it follows: Dieter is not the thief we are looking for.
However, we do not know how he feels about the truth.
I discovered this puzzling logic in the book "Satan, Cantor and Infinity" by Raymond Smullyan.
If you missed a puzzle from the past few weeks, here are the ten most recent episodes:
One circle, two points
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A triangle the size of the earth
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