Logic problem..

[harrkev]

I once read this problem in a book... It also gave the answer, but I could not even follow it. So if anybody can figure this one out, let me know.

This is from memory, but you will get the idea.

A man sends millions of spam emails, and is dragged off to court. It is Saturday. The judge (who is known to be COMPLETELY honest) sentences the man to death. And the judge says "Sometime in the next seven days, you will be hung. But the day on which it happens will be a surprise."

Also note that the executions happen in the mornings...

Obviously, the guy is very upset, but later his lawyer tells him: "Don't worry. They CAN'T kill you. Look, the last day that they can kill you is on Friday. But if you wake up Friday morning, then you will be expecting to be killed, which means that it won't be a surprise. So they can't kill you on Friday. But this means that Thursday is the last day that they can kill you. But if you wake up Thursday morning, then you will be expecting to be killed, which means that it won't be a surprise. And so we work backwards, and there is NO day on which they can kill you.

Obviously, the guy is very happy, untill Wednesday morning, when they take him to be hung, and he is surprised.

Can somebody figure out how he simultaneously can and can't be killed?

 

[oneshot47]

He had just deduced that he shouldnt be able to be killed at all, so when they do get him, its a suprise to him. Also we don't know if he is hung, just that hes going to be HANGED. (hung=big dick, hanged=killed)

 

[imgod2u]

The problem is, there's no way he can be expected to be hanged on thursday until it becomes thursday. He can, furthermore, not expect to be hanged on wednesday at all because he could, very well, be hanged on thursday still (as it is not yet thursday or wednesday, so he doesn't know the results of either day). And so, if he is hanged on wednesday or sooner (the "or" part is important), he cannot see it comming for certain until after wednesday night. The logic the lawyer uses doesn't work past wednesday in other words.

 

[TuxDave]

*confused*

The only flaw that I see is that he must wake up everyday expecting to be executed. All the following logic is based on the fact that the next day when they wake up, they'll be expecting to be killed, thus he cannot be killed tomorrow. And to prevent him from being killed today, he has to expect to be killed. When he deduced that he won't be executed and thus never expects to be killed, he violated the logical premises that let him come to that conclusion. He NEEDS to expect to be killed everyday, otherwise his conclusion that he can't be killed won't follow from his logic.

 

[thelordemperor]

Originally posted by: harrkev

Can somebody figure out how he simultaneously can and can't be killed?

He can't, it was all superstition, he was either hanged or not (you only stated he was "taken to be hung").

 

[Mday]

the last day they can kill him is saturday, btw.

 

[Spitwad]

logically speaking, at first he would have been surprised to have been hanged, then his lawyer said he couldn't of been hung because of all that stuff, which allowed for him to be surprised

So using lemmons logic...

p = person
Hx = person hanged
Sx = person surprised

Hp -> Sp

The judge said he could be surprised
Sp
The lawyer said he couldnt be hung if he wasn't surprised
~Hp -> ~Sp

But then the lawyer introduced something that allowed the person to be surprised, so
Sp
which is
~~Sp
Which gets you
~~Hp
Which in the end means he's dead
Hp

 

[chuckywang]

Man, I loved that logic class I took.

My prof. did something just like this puzzle, but with a teacher trying to "surprise" his students with a pop quiz sometime during a month.

 

[CSMR]

Originally posted by: oneshot
He had just deduced that he shouldnt be able to be killed at all, so when they do get him, its a suprise to him. Also we don't know if he is hung, just that hes going to be HANGED. (hung=big dick, hanged=killed)

Your language lesson is right, but that isn't a solution to the problem: the problem is that the man about to be hanged must believe that he will be hanged and also that he won't be hanged.

Originally posted by: imgod2u
The problem is, there's no way he can be expected to be hanged on thursday until it becomes thursday.
The logic doesn't work past wednesday in other words.

It does. On the first day he knows that if he is alive on the last day, he will be hanged then, and also will know that he will be hanged then, but also know what he knows now, that he will be hanged when he does not expect it, which is impossible, so he knows that he won't be alive on the last day. So on the first day he knows that he will be hanged in the next six days, on a day when he doesn't expect it. And so on.
Assumption: he knows that what he knows today he will know in future if he is alive.
So on the first day he must know that he will be hanged today, and also know that he will not be hanged when he expects to be, and since he knows that he will be hanged, he expects to be hanged, and knows that he expects to be hanged, and so knows that he won't be hanged.

I don't see the paradox here. The situation described is a contradictory one - the Judge is known to be correct when he tells the man that he will die in the next seven days when he doesn't expect it is contradictory (when combined with the above rationality assumption) as the argument shows. To clarify the problem of knowledge, the problem remains if we substitute belive for know everywhere.

To simplify the problem, why not have only one day. The Judge says: you will die today and not expect it? This is also contradictory (with the assumption above). Is this considered a paradox?

Or what about this "paradox"?
Two men are fighting a competition. If each knows the other's tactics he will win. (E.g. the game matching pennies.) The honest Judge is still here. He knows the future and tells the men what tactics the other will play. Both men use this information, and so they both win and both lose.

What these "paradoxes" show is that there is a limit to what can be known.

 

[thecrecarc]

ummm... what!?!??! so a guy is hanged witch is not hanged witch means the judge is worng but he is correct huh!??!?!

 

[The Green Bean]

answer is simple

If they cant kill him becuse he is expecting to be killed then he is not expecting to be killed. And if he is expecting to be killed, because hes not expecting them to kill him becuase it is expecting. Then he can't be killed. So depens on the level and depth of thinking. Infinity does not exist, but its still there, therefore he cannot be killed yet he can.

 

[tinyabs]

He has to kill himself in order not to be killed.

 

[Xdreamer]

so therefore if the lawyer had not told him that he could not be hung ... then he would have woken up every day expecting to be killed and therefore could not be killed on that day... thuse in telling the man that he could not be killed, the lawyer made it possible for him to be killed... and is therefore responsible for his death.

 

[Xdreamer]

the moral of the story then is "live one day at a time?"

 

[bobwrong]

Originally posted by: Xdreamer
so therefore if the lawyer had not told him that he could not be hung ... then he would have woken up every day expecting to be killed and therefore could not be killed on that day... thuse in telling the man that he could not be killed, the lawyer made it possible for him to be killed... and is therefore responsible for his death.

Never trust your lawyer.... lol

 

[Ninjazx]

look, he got caught up in believing that he wouldnt be hanged. so.. he was surprised, and hanged, when he wasnt expecting it..

 

[dole]

He expects to be hanged in the morning.
Nothing in the statement guarantees a morning execution, other than tradition.
Couldn't a judge order a sudden midnight execution? Like say on Saturday at 11:59p (the last minute before the judges 7 days are up)
If he lives on Saturday morning he would think he is in the clear.

 

[trexpesto]

They could kill him in his sleep. Sounds humane actually.

 

[BurnItDwn]

They could kill him right away, he probably wouldn't expect that.

 

[BespinReactorShaft]

Kill the lawyer.

 

[kcthomas]

Originally posted by: imgod2u
The problem is, there's no way he can be expected to be hanged on thursday until it becomes thursday. He can, furthermore, not expect to be hanged on wednesday at all because he could, very well, be hanged on thursday still (as it is not yet thursday or wednesday, so he doesn't know the results of either day). And so, if he is hanged on wednesday or sooner (the "or" part is important), he cannot see it comming for certain until after wednesday night. The logic the lawyer uses doesn't work past wednesday in other words.

this is what i was thinking. on wednesday he can still be hanged on either wednesday or thursday. i however can expect to be HUNG every day of the week.

 

[TuxDave]

Originally posted by: kcthomas

Originally posted by: imgod2u
The problem is, there's no way he can be expected to be hanged on thursday until it becomes thursday. He can, furthermore, not expect to be hanged on wednesday at all because he could, very well, be hanged on thursday still (as it is not yet thursday or wednesday, so he doesn't know the results of either day). And so, if he is hanged on wednesday or sooner (the "or" part is important), he cannot see it comming for certain until after wednesday night. The logic the lawyer uses doesn't work past wednesday in other words.

this is what i was thinking. on wednesday he can still be hanged on either wednesday or thursday. i however can expect to be HUNG every day of the week.

nm.. har har har.. i get it