Risk Latte - The Paradox of the Unexpected Hanging

Quiz #1
The Paradox of the Unexpected Hanging

“Taken from Mark Rubenstein's web site www.in-the-money.com


A man was sentenced on Saturday. "The hanging will take place at noon," said the judge to the prisoner, "on one of the seven days of next week. But you will not know which day it is until you are informed on the morning of the day of the hanging."

Can the judge's sentence be carried out?


  Answer

It seems not. If the man has not been hung by next Friday, he will then know that he must be hung the next day. However, this would contradict the judge's assertion that he will not know until the next morning. Thus we can rule out next Saturday as the day for the hanging. Then, by the same reasoning, if the man has not been hung by next Thursday, he will then know that he must be hung on Friday (since, as we have seen, he cannot be hung on Saturday). Again, thus would contradict the judge's assertion that he will not know until the next morning. Thus we can also rule out next Friday as the day for the hanging. In a similar manner, we can rule out each of the five other possible days. It appears that the judge's sentence cannot be carried out.

As it happened, the man was hung on Tuesday and he did not know in advance, as the judge had promised, that he would be hung on that day!



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