Re: the unexpected hanging

From: Lee Corbin (
Date: Sun May 13 2001 - 16:35:17 MDT

Spike brings up the "Unexpected Hanging" (see below).

The way I think of it, the prisoner wins if when the
judge comes into his cell, the prisoner is (a) not
surprised, and (b) can explain logically to the judge
why he is not surprised. Otherwise, he loses.

Now the prisoner wins if, as Spike relates, the judge
shows up on Friday and says "ah ha!". The prisoner
calmly retorts that since the sentence has to be carried
out on one of Monday, Tuesday, Wednesday, Thursday, or
Friday, (if it is to be carried out at all), and since
the first four are now impossible, the judge has failed
to surprise him, and so he must go free.

But would you believe the prisoner if you came for him
on Thursday, and he made the following argument? "Your
Honor, I knew that you would come today. Why? Because
it was clearly stated that you were to surprise me. As
is easy to see, you could not surprise me if you came
tomorrow. Therefore it was obvious, as soon as I got up
this morning, that today would be the day, so you have
failed to surprise me, so I get to go free."

Unlike Spike's claim, the resourceful prisoner says
something quite similar, but more elaborate, on Wednesday
as well (since Friday and Thursday are clearly crossed
off as possibilites).

Explaining exactly where and how the prisoner goes wrong
isn't easy.


>A prisoner is sentenced to the ultimate punishment. He is
>told his execution will take place on some unspecified day,
>Monday thru Friday inclusive. The judge specifies that the
>prisoner will not know which day he is to meet his fate until
>the day of his demise. Sitting forlornly in his cell, it occurs
>to him that his date with destiny cannot be on Friday, for if
>he is still among the living on Thursday midnight, then he
>would *know* he is to be executed on Friday, which violates
>the judge's stipulation that he will not know the date of his
>execution. Similarly, he cannot be executed on Thursday, for
>he already determined his date cannot be Friday, so if he is
>still with us on Wednesday midnight, then similarly Tuesday
>midnight, and so on.
>The prisoner determines by this line of reasoning that his
>execution cannot take place according to the judge's
>instruction. A greatly relieved prisoner is startled by the
>hangman, who shows up Wednesday morning.
>Those that are following this thread and the previous
>threads regarding probability of record primes, do ponder
>this apparent paradox of the unexpected hanging so you
>will be ready for where I am going with the notion of
>probability distribution functions and their relationship
>to the unexpected singularity. Comments and questions
>welcome in the meantime, while I go sample sushi
>restaurants. {8^D 0==== spike

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