### Brain Teasers

# War Prisoner

During the first world war, there was a prisoner who had been captured. When brought to the army headquarters, the prisoner was told that he had a choice to remain silent or say something. He was also told that if he did say something, he would be shot if he spoke the truth or hanged if he had lied. The war prisoner did in fact make a single statement; he said only a phrase and they had to let him go unscathed. What did the prisoner say to get out free?

### Answer

The prisoner told them: "You will hang me."Hide Answer Show Answer

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## Comments

He could also make the statement, "I only tell lies."

Coudn't the people at HQ just say, "Whoops. We messed up!" and shoot him anyway? Just kidding, and fun teaser.

he could also say "hi....how are you"

I've never fully understood the logic of these kinds of teasers.

I agree rose rox. If he told the truth, he would be shot. If he lied, hanged. it is totally impossible to not tell the truth AND not tell a lie.

Here is an explanation:

He says 'I will be hanged'. If it is true, he will be shot, but that makes his statement false, as he is shot, not hanged. Since his statement is false, he cannot be shot; instead, he will be hanged. But if he is hanged, that makes his statement true, so he will be shot, not hanged. In other words, if the statement is true, then it is false; if it is false, then it is true. It is a paradox and is therefore neither true or false, so he is released.

A simpler version of this paradox, known as the 'Epimenides paradox', is 'This statement is false'. This statement cannot be true, for if it were true, it would state that it is false, and it cannot be both true and false. Similarly, if it were false, then its negation must be true, which states that it is true. But again, it cannot be both true and false.

Another interesting variation of this paradox is: ' "yields falsehood when preceded by its quotation" yields falsehood when preceded by its quotation.' This is interesting because it doesn't use self-reference.

This is also similar to the concept which Kurt Godel used to prove the famous Incompleteness Theorem, which shows that there are always unprovable statements in mathematics. The statement he used roughly translates to 'This statement cannot be proven'.

He says 'I will be hanged'. If it is true, he will be shot, but that makes his statement false, as he is shot, not hanged. Since his statement is false, he cannot be shot; instead, he will be hanged. But if he is hanged, that makes his statement true, so he will be shot, not hanged. In other words, if the statement is true, then it is false; if it is false, then it is true. It is a paradox and is therefore neither true or false, so he is released.

A simpler version of this paradox, known as the 'Epimenides paradox', is 'This statement is false'. This statement cannot be true, for if it were true, it would state that it is false, and it cannot be both true and false. Similarly, if it were false, then its negation must be true, which states that it is true. But again, it cannot be both true and false.

Another interesting variation of this paradox is: ' "yields falsehood when preceded by its quotation" yields falsehood when preceded by its quotation.' This is interesting because it doesn't use self-reference.

This is also similar to the concept which Kurt Godel used to prove the famous Incompleteness Theorem, which shows that there are always unprovable statements in mathematics. The statement he used roughly translates to 'This statement cannot be proven'.

What about an opionionated statement?

I'm more confused with that explanation. LOL

I understand.

He could have said, "You will hang me"

or

"You will not shoot me"

Any action done by the jailors would be wrong by their own terms.

UNLESS, they shoot and hang him at the same time.

He could have said, "You will hang me"

or

"You will not shoot me"

Any action done by the jailors would be wrong by their own terms.

UNLESS, they shoot and hang him at the same time.

I get it

I get it

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