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Surprise hanging

keithprosser
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1/10/2017 9:30:48 AM
Posted: 3 months ago
An oldy but still a goody.

On Monday a man is sentenced for murder by the judge in the following way:
"You will be hanged at dawn, on one day this week on or by Friday at the latest. However you will not know which day until it arrives'.

The criminal reasons that he can't be hung on Friday morning because he would know when it was going to happen (ie on Friday) once dawn had passed on Thursday, contrary to the terms of the sentence. But if it can't be Friday, it can't be Thursday either, because he'd know it was Thursday after dawn on Wednesay, as Friday was already ruled out.

Similarly, by the same logic he can rule out Wednesday and even Tuesday.

It seems like the hanging cannot be carried out in accordance with the sentence, so he is safe. But on, say, Wednesday he was hanged at dawn, with the hangman pointing out that despite the murderer's argument, the murderer did not know he was about to be hanged that day (having 'proven' it couldn't happen at all) so the sentence was indeed being carried out correctly.

What is wrong with the murderer's argument? It must be wrong because it gets the wrong answer, but I have never been able to work out what is wrong.
Obviously the hanging didn't have to be on the wednesday - tuesday or thursday would work just as well. I am not so sure about Friday though...
Perussi
Posts: 2,373
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1/10/2017 9:50:02 PM
Posted: 3 months ago
At 1/10/2017 9:30:48 AM, keithprosser wrote:
An oldy but still a goody.

On Monday a man is sentenced for murder by the judge in the following way:
"You will be hanged at dawn, on one day this week on or by Friday at the latest. However you will not know which day until it arrives'.

The criminal reasons that he can't be hung on Friday morning because he would know when it was going to happen (ie on Friday) once dawn had passed on Thursday, contrary to the terms of the sentence. But if it can't be Friday, it can't be Thursday either, because he'd know it was Thursday after dawn on Wednesay, as Friday was already ruled out.

Similarly, by the same logic he can rule out Wednesday and even Tuesday.

It seems like the hanging cannot be carried out in accordance with the sentence, so he is safe. But on, say, Wednesday he was hanged at dawn, with the hangman pointing out that despite the murderer's argument, the murderer did not know he was about to be hanged that day (having 'proven' it couldn't happen at all) so the sentence was indeed being carried out correctly.

What is wrong with the murderer's argument? It must be wrong because it gets the wrong answer, but I have never been able to work out what is wrong.
Obviously the hanging didn't have to be on the wednesday - tuesday or thursday would work just as well. I am not so sure about Friday though...

The only way for something not to be a suprise is constantly expecting it.
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Devilry
Posts: 2,094
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1/10/2017 11:02:42 PM
Posted: 3 months ago
Perussi is right. The problem defies solving. Ruling out any day only makes it a day that the hanging could occur.
: : : At 11/15/2016 6:22:17 PM, Greyparrot wrote:
: That's not racism. Thats economics.
Devilry
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1/10/2017 11:12:37 PM
Posted: 3 months ago
It stays confusing on the Friday, though, lol. Is the murderer not also perhaps making an error in forecasting expectation? Is the Friday not only actually ruled out on the Friday?
: : : At 11/15/2016 6:22:17 PM, Greyparrot wrote:
: That's not racism. Thats economics.
Devilry
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1/10/2017 11:17:01 PM
Posted: 3 months ago
I mean the murderer comes out expecting it every day, which is obviously broken. You can only die once.

I dunno man, lol.
: : : At 11/15/2016 6:22:17 PM, Greyparrot wrote:
: That's not racism. Thats economics.
Devilry
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1/10/2017 11:21:40 PM
Posted: 3 months ago
When you least expect me with a time limit = confusing af lol. It's cool.
: : : At 11/15/2016 6:22:17 PM, Greyparrot wrote:
: That's not racism. Thats economics.
skipsaweirdo
Posts: 2,189
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1/11/2017 5:11:54 AM
Posted: 3 months ago
At 1/10/2017 9:30:48 AM, keithprosser wrote:
An oldy but still a goody.

On Monday a man is sentenced for murder by the judge in the following way:
"You will be hanged at dawn, on one day this week on or by Friday at the latest. However you will not know which day until it arrives'.

The criminal reasons that he can't be hung on Friday morning because he would know when it was going to happen (ie on Friday) once dawn had passed on Thursday, contrary to the terms of the sentence. But if it can't be Friday, it can't be Thursday either, because he'd know it was Thursday after dawn on Wednesay, as Friday was already ruled out.

Similarly, by the same logic he can rule out Wednesday and even Tuesday.

It seems like the hanging cannot be carried out in accordance with the sentence, so he is safe. But on, say, Wednesday he was hanged at dawn, with the hangman pointing out that despite the murderer's argument, the murderer did not know he was about to be hanged that day (having 'proven' it couldn't happen at all) so the sentence was indeed being carried out correctly.

What is wrong with the murderer's argument? It must be wrong because it gets the wrong answer, but I have never been able to work out what is wrong.
Obviously the hanging didn't have to be on the wednesday - tuesday or thursday would work just as well. I am not so sure about Friday though...
The prisoner is put in solitary confinement and loses track of time via sensory deprivation carried out by the prison. Making the time unknowm to him or the day...problem solved.
keithprosser
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1/11/2017 6:17:59 AM
Posted: 3 months ago
At 1/10/2017 11:02:42 PM, Devilry wrote:
Perussi is right. The problem defies solving. Ruling out any day only makes it a day that the hanging could occur.
But why does it defy solving? As I see the 'the problem' is to spot what is wrong with the prisoner's logic. It seems to prove the sentence cannot be carried out as specfied, but obviously it can be carried out exactly as specified.

Is logic not upto the task (which leads one to ask what else is beyond it, because it doesn't seem all that complicated) or is logic actually wrong, ie capable of coming up with wrong answers even if it's rules are followed to the letter?

Either way it looks like logic isn't all its cracked up to be. Which I think is a little worrying.
Sidewalker
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1/11/2017 10:34:45 AM
Posted: 3 months ago
At 1/10/2017 9:30:48 AM, keithprosser wrote:
An oldy but still a goody.

On Monday a man is sentenced for murder by the judge in the following way:
"You will be hanged at dawn, on one day this week on or by Friday at the latest. However you will not know which day until it arrives'.

The criminal reasons that he can't be hung on Friday morning because he would know when it was going to happen (ie on Friday) once dawn had passed on Thursday, contrary to the terms of the sentence. But if it can't be Friday, it can't be Thursday either, because he'd know it was Thursday after dawn on Wednesay, as Friday was already ruled out.

Similarly, by the same logic he can rule out Wednesday and even Tuesday.

It seems like the hanging cannot be carried out in accordance with the sentence, so he is safe. But on, say, Wednesday he was hanged at dawn, with the hangman pointing out that despite the murderer's argument, the murderer did not know he was about to be hanged that day (having 'proven' it couldn't happen at all) so the sentence was indeed being carried out correctly.

What is wrong with the murderer's argument? It must be wrong because it gets the wrong answer, but I have never been able to work out what is wrong.
Obviously the hanging didn't have to be on the wednesday - tuesday or thursday would work just as well. I am not so sure about Friday though...

The flaw in reasoning is the idea that he can also rule out every other day except Friday. It's true that if he isn't hung Thursday then he will know it's Friday, so it can't logically be Friday,, but that same logic does not apply to earlier days in the week.

For instance, on Tuesday he won't know if it is going to be Wednesday or Thursday, as the days of the week progress he will be able to know which days are ruled out, but when he is hung Wednesday it is still a surprise because at that time neither Wednesday or Thursday could be eliminated logically.
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
keithprosser
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1/11/2017 11:15:58 AM
Posted: 3 months ago
At 1/11/2017 10:34:45 AM, Sidewalker wrote:
The flaw in reasoning is the idea that he can also rule out every other day except Friday. It's true that if he isn't hung Thursday then he will know it's Friday, so it can't logically be Friday,, but that same logic does not apply to earlier days in the week.

But the original problem is 'which day, Tue, Wed, Thu or Fri?' which, after Friday is eliminated, becomes the similar but reduced problem 'Tue, Wed or Thu?'. Why can't the logic that allowed us to reduce 'TWT or F' to 'TW or T' be used to reduce it it T or W? You say the same logic does not apply but as far as I can see you haven't said explicitly why not.

You may be right in general terms, but I don't think you've identified the precise error in a way that would allow us to formuate a rule so we avoid the same error in future.
The-Voice-of-Truth
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1/11/2017 11:48:27 AM
Posted: 3 months ago
At 1/10/2017 9:30:48 AM, keithprosser wrote:
An oldy but still a goody.

On Monday a man is sentenced for murder by the judge in the following way:
"You will be hanged at dawn, on one day this week on or by Friday at the latest. However you will not know which day until it arrives'.

The criminal reasons that he can't be hung on Friday morning because he would know when it was going to happen (ie on Friday) once dawn had passed on Thursday, contrary to the terms of the sentence. But if it can't be Friday, it can't be Thursday either, because he'd know it was Thursday after dawn on Wednesay, as Friday was already ruled out.

Similarly, by the same logic he can rule out Wednesday and even Tuesday.

It seems like the hanging cannot be carried out in accordance with the sentence, so he is safe. But on, say, Wednesday he was hanged at dawn, with the hangman pointing out that despite the murderer's argument, the murderer did not know he was about to be hanged that day (having 'proven' it couldn't happen at all) so the sentence was indeed being carried out correctly.

What is wrong with the murderer's argument? It must be wrong because it gets the wrong answer, but I have never been able to work out what is wrong.
Obviously the hanging didn't have to be on the wednesday - tuesday or thursday would work just as well. I am not so sure about Friday though...

There is a contradiction here that exists under certain circumstances on the part of the judge's statements.

The judge makes 2 statements: 1) you will be hanged on one of the given days, and 2) you will not know which day. Throughout the week, both statements hold true until you get to Friday, which results in a contradiction, but one that can only exit on that day. If the prisoner is hung by Thursday, then both of the judge's statements will hold true, and no contradiction will exist.

Since a contradiction only exists on Friday, then the further deduction of anything beyond that point is illegitimate thought.
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Sidewalker
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1/11/2017 12:30:18 PM
Posted: 3 months ago
At 1/11/2017 11:15:58 AM, keithprosser wrote:
At 1/11/2017 10:34:45 AM, Sidewalker wrote:
The flaw in reasoning is the idea that he can also rule out every other day except Friday. It's true that if he isn't hung Thursday then he will know it's Friday, so it can't logically be Friday,, but that same logic does not apply to earlier days in the week.

But the original problem is 'which day, Tue, Wed, Thu or Fri?' which, after Friday is eliminated, becomes the similar but reduced problem 'Tue, Wed or Thu?'. Why can't the logic that allowed us to reduce 'TWT or F' to 'TW or T' be used to reduce it it T or W? You say the same logic does not apply but as far as I can see you haven't said explicitly why not.

You may be right in general terms, but I don't think you've identified the precise error in a way that would allow us to formuate a rule so we avoid the same error in future.

I think I have, it isn't a surprise if you can solve for what day it will happen, on Thursday you can solve for what day because all the other days have been ruled out, but that logic doesn't regress because earlier in the week there are more than one day that it could occur.

I think the logic problem works because it kind of pulls a bait and switch on you by giving you a wrong solution to ponder but makes your mind think it's the right solution, it just isn't the case that the inverse of the solution for what day it will be gives you what day it won't be....or something like that.

It reminds me of the logic problem where three guys check into a hotel to share a room, they pay $30 but it's a mistake so they should get $5 back, and a dollar goes missing. Have you ever heard that one and tried to logically unpack it?
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
Sidewalker
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1/11/2017 12:30:58 PM
Posted: 3 months ago
At 1/11/2017 11:48:27 AM, The-Voice-of-Truth wrote:
At 1/10/2017 9:30:48 AM, keithprosser wrote:
An oldy but still a goody.

On Monday a man is sentenced for murder by the judge in the following way:
"You will be hanged at dawn, on one day this week on or by Friday at the latest. However you will not know which day until it arrives'.

The criminal reasons that he can't be hung on Friday morning because he would know when it was going to happen (ie on Friday) once dawn had passed on Thursday, contrary to the terms of the sentence. But if it can't be Friday, it can't be Thursday either, because he'd know it was Thursday after dawn on Wednesay, as Friday was already ruled out.

Similarly, by the same logic he can rule out Wednesday and even Tuesday.

It seems like the hanging cannot be carried out in accordance with the sentence, so he is safe. But on, say, Wednesday he was hanged at dawn, with the hangman pointing out that despite the murderer's argument, the murderer did not know he was about to be hanged that day (having 'proven' it couldn't happen at all) so the sentence was indeed being carried out correctly.

What is wrong with the murderer's argument? It must be wrong because it gets the wrong answer, but I have never been able to work out what is wrong.
Obviously the hanging didn't have to be on the wednesday - tuesday or thursday would work just as well. I am not so sure about Friday though...

There is a contradiction here that exists under certain circumstances on the part of the judge's statements.

The judge makes 2 statements: 1) you will be hanged on one of the given days, and 2) you will not know which day. Throughout the week, both statements hold true until you get to Friday, which results in a contradiction, but one that can only exit on that day. If the prisoner is hung by Thursday, then both of the judge's statements will hold true, and no contradiction will exist.

Since a contradiction only exists on Friday, then the further deduction of anything beyond that point is illegitimate thought.

Yeah, what he said.
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
Devilry
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1/11/2017 12:55:26 PM
Posted: 3 months ago
At 1/11/2017 6:17:59 AM, keithprosser wrote:
At 1/10/2017 11:02:42 PM, Devilry wrote:
Perussi is right. The problem defies solving. Ruling out any day only makes it a day that the hanging could occur.
But why does it defy solving? As I see the 'the problem' is to spot what is wrong with the prisoner's logic. It seems to prove the sentence cannot be carried out as specfied, but obviously it can be carried out exactly as specified.

Well it's like that saying "it'll happen when you least expect it," or whatever like that - normally, that's a saying that sort of covers its own arse; when you're expecting it, you're expecting it not to happen, because it won't be when you expect it - and then you're not expecting it, and it could happen!

The thing about the surprise hanging seems to be that it forces the issue, though. The above is a paradox in itself, a thing falling into infinite regress. But in this riddle when we come to the Friday, the above paradox meets the addendum that the hanging must happen before Friday. Confusion ensues.

Is logic not upto the task (which leads one to ask what else is beyond it, because it doesn't seem all that complicated) or is logic actually wrong, ie capable of coming up with wrong answers even if it's rules are followed to the letter?

Either way it looks like logic isn't all its cracked up to be. Which I think is a little worrying.

I think, A) the "when you least expect me" paradox is going to combat you ever ruling out a day, and B) there's probably just something wrong with the murderer's logic, too, yeah. I don't think he can really rule out any day but the Friday on the Friday, because otherwise on the Monday or Sunday or whatever he's expecting he will die every day of the coming week - and you can only die once! And then it comes to Friday and the paradox bites you on the arse all the same.
: : : At 11/15/2016 6:22:17 PM, Greyparrot wrote:
: That's not racism. Thats economics.
Devilry
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1/11/2017 12:56:57 PM
Posted: 3 months ago
It's a sort of unstoppable force meets and immovable object kinda thing.
: : : At 11/15/2016 6:22:17 PM, Greyparrot wrote:
: That's not racism. Thats economics.
keithprosser
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1/11/2017 1:19:25 PM
Posted: 3 months ago
At 1/11/2017 12:30:18 PM, Sidewalker wrote:
I think the logic problem works because it kind of pulls a bait and switch on you by giving you a wrong solution to ponder but makes your mind think it's the right solution, it just isn't the case that the inverse of the solution for what day it will be gives you what day it won't be....or something like that.

If I understand your solution it is that the reduced problem is different from the original problem. i think that must be the case, but there is still the problem of explicitly identifying why the process of elimination didn't work for the murderer.

When he was arrested it was because the other suspects were eliminated by the enquiry one and we often work by elimination to arrive at a conclusion.

It is one thing to deduce the validity of the sentence using different logic - but whuc step in the murders logic breaks which a law of logic - I think that is still outstanding.

It reminds me of the logic problem where three guys check into a hotel to share a room, they pay $30 but it's a mistake so they should get $5 back, and a dollar goes missing. Have you ever heard that one and tried to logically unpack it?

I do recall it one versino copied off the net:
"Three students checked into a hotel and paid the clerk $30 for a room ($10 each). When the hotel manager returned, he noticed that the clerk had incorrectly charged $30 instead of $25 for the room. The manager told the clerk to return $5 to the students. The clerk, knowing that the students would not be able to divide $5 evenly, decided to keep $2 and to give them only $3.

I see that as a bit different because it's down to an easily spotted (once its been pointed out) bit of misdirection in the way the punchline is constructed, ie

Student pay 3*9, clerk 'keeps 2', that makes 29 so where is the other dollar? The sum of what the students pay and what the clerk keeps is indeed 29. The question lures us into thinking that should add up to 30, but the sum of what the students pay and what the clerk keeps is just what it says on the tin ie 'the sum of what the students pay and what the clerk keeps'. It takes a few moment to realise that it is an almost meaningless number. It doesn't threaten the laws of arithmetic the way the surprisue hanging seems to threaten plain logic.

And of course There's the famous 'Monty Hall' problem as well, where intuition is very misleading but logic and arithmetic come to our rescue, so things seem to run the full range from intution being king to logic ruling...
Sidewalker
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1/11/2017 1:55:49 PM
Posted: 3 months ago
At 1/11/2017 1:19:25 PM, keithprosser wrote:
At 1/11/2017 12:30:18 PM, Sidewalker wrote:

If I understand your solution it is that the reduced problem is different from the original problem. i think that must be the case, but there is still the problem of explicitly identifying why the process of elimination didn't work for the murderer.

I think it's straightforward, on Thursday all days but Friday have been ruled out, so it won't be a surprise because we know what day, earlier in the week we don't know what day it will be because there are multiple days that haven't been ruled out.

When he was arrested it was because the other suspects were eliminated by the enquiry one and we often work by elimination to arrive at a conclusion.

Yes, but if they began with five suspects, they didn't know who did it after eliminating one or two suspects,

It is one thing to deduce the validity of the sentence using different logic - but whuc step in the murders logic breaks which a law of logic - I think that is still outstanding.

I don't think it is, it's a simple math problem, 5 minus 4 tells you what day, five minus two doesn't.

It reminds me of the logic problem where three guys check into a hotel to share a room, they pay $30 but it's a mistake so they should get $5 back, and a dollar goes missing. Have you ever heard that one and tried to logically unpack it?

I do recall it one versino copied off the net:
"Three students checked into a hotel and paid the clerk $30 for a room ($10 each). When the hotel manager returned, he noticed that the clerk had incorrectly charged $30 instead of $25 for the room. The manager told the clerk to return $5 to the students. The clerk, knowing that the students would not be able to divide $5 evenly, decided to keep $2 and to give them only $3.

I see that as a bit different because it's down to an easily spotted (once its been pointed out) bit of misdirection in the way the punchline is constructed, ie

I think this problem is similar because it's also a matter of simple math that uses the same kind of misdirection, we are trying to solve for what day he will be executed, the logic that provides a solution on Thursday, doesn't provide a solution on Wednesday.

Student pay 3*9, clerk 'keeps 2', that makes 29 so where is the other dollar? The sum of what the students pay and what the clerk keeps is indeed 29. The question lures us into thinking that should add up to 30, but the sum of what the students pay and what the clerk keeps is just what it says on the tin ie 'the sum of what the students pay and what the clerk keeps'. It takes a few moment to realise that it is an almost meaningless number. It doesn't threaten the laws of arithmetic the way the surprisue hanging seems to threaten plain logic.

And of course There's the famous 'Monty Hall' problem as well, where intuition is very misleading but logic and arithmetic come to our rescue, so things seem to run the full range from intution being king to logic ruling...

I think arithmetic comes to the rescue on both, if we have the set a,b,c,d,e and want to know which will be left after randomly eliminating one at a time, you will know after four have been removed, but not before, after b and d have been removed you still don't know whether it is going to be a,c, or e.
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
GrimlyF
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1/11/2017 8:50:15 PM
Posted: 3 months ago
The man will be taken to the gallows at dawn on Tuesday and prepared for hanging. He will then be hung on Wednesday or Thursday. He will not know on which of the days he will be hung.
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keithprosser
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1/11/2017 11:38:18 PM
Posted: 3 months ago
At 1/11/2017 1:55:49 PM, Sidewalker wrote:
I think arithmetic comes to the rescue on both, if we have the set a,b,c,d,e and want to know which will be left after randomly eliminating one at a time, you will know after four have been removed, but not before, after b and d have been removed you still don't know whether it is going to be a,c, or e.

I'm not sure if this reduces to the same thing but I've just thought of something. The man back in his cell soon works out that he can't be hanged on friday, because if he is stlil alive on thursday after dawn then the judge's order can't be carried out to the letter and he could appeal it(which we will suppose is the law of that land!).
That is just the same reasoning as before, and I think it does rule out Friday.
But there is a hidden assumption - that he is still alive at that point, ie just after dawn on Thursday.
Thinking in his cell on monday the man only considered one scenario for after dawn on Thurdsay, the 'best case' where he is still alive. He hasn't taken into account the case when he has already been hanged by then. If he did consider that case it could be because was killed on tues, wed or even just a few minutes before on thursday!

The iteration trick for eliminating each day in turn doesn't work if you take 'non-best scenarios' into account. Basically, he can be sure he will be dead just after dawn on Thursday, but he wouldn't know on which day it would happen.
Taust
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2/5/2017 5:00:59 AM
Posted: 2 months ago
One solution would just be that the judge's sentence was self-contradictory.
"Only two things are infinite, the universe and human stupidity, and I'm not sure about the former" -Einstein
skipsaweirdo
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2/5/2017 9:29:36 AM
Posted: 2 months ago
At 1/10/2017 9:30:48 AM, keithprosser wrote:
An oldy but still a goody.

On Monday a man is sentenced for murder by the judge in the following way:
"You will be hanged at dawn, on one day this week on or by Friday at the latest. However you will not know which day until it arrives'.

The criminal reasons that he can't be hung on Friday morning because he would know when it was going to happen (ie on Friday) once dawn had passed on Thursday, contrary to the terms of the sentence. But if it can't be Friday, it can't be Thursday either, because he'd know it was Thursday after dawn on Wednesay, as Friday was already ruled out.

Similarly, by the same logic he can rule out Wednesday and even Tuesday.

It seems like the hanging cannot be carried out in accordance with the sentence, so he is safe. But on, say, Wednesday he was hanged at dawn, with the hangman pointing out that despite the murderer's argument, the murderer did not know he was about to be hanged that day (having 'proven' it couldn't happen at all) so the sentence was indeed being carried out correctly.
He was told his sentence at 3 am. that Monday and was hung at dawn the very same Monday. The sentencing didn't specify when on monday he was sentenced. He could not have reasoned he would be hung on Monday that very same day. But I still say solitary confinement and sensory deprivation would cause him to lose track of time and no where does it say that a judge cannot lie to a prisoner.
What is wrong with the murderer's argument? It must be wrong because it gets the wrong answer, but I have never been able to work out what is wrong.
Obviously the hanging didn't have to be on the wednesday - tuesday or thursday would work just as well. I am not so sure about Friday though...
matt8800
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2/5/2017 4:34:41 PM
Posted: 2 months ago
At 1/10/2017 9:30:48 AM, keithprosser wrote:
An oldy but still a goody.

On Monday a man is sentenced for murder by the judge in the following way:
"You will be hanged at dawn, on one day this week on or by Friday at the latest. However you will not know which day until it arrives'.

The criminal reasons that he can't be hung on Friday morning because he would know when it was going to happen (ie on Friday) once dawn had passed on Thursday, contrary to the terms of the sentence. But if it can't be Friday, it can't be Thursday either, because he'd know it was Thursday after dawn on Wednesay, as Friday was already ruled out.

Similarly, by the same logic he can rule out Wednesday and even Tuesday.

It seems like the hanging cannot be carried out in accordance with the sentence, so he is safe. But on, say, Wednesday he was hanged at dawn, with the hangman pointing out that despite the murderer's argument, the murderer did not know he was about to be hanged that day (having 'proven' it couldn't happen at all) so the sentence was indeed being carried out correctly.

What is wrong with the murderer's argument? It must be wrong because it gets the wrong answer, but I have never been able to work out what is wrong.
Obviously the hanging didn't have to be on the wednesday - tuesday or thursday would work just as well. I am not so sure about Friday though...

I agree it couldn't be Friday.

I think it could be any other day because, due to his reasoning, he ruled out every other day. Because the day of his hanging was contrary to his prediction, he did not know it was going to be Wednesday.
keithprosser
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2/5/2017 4:42:56 PM
Posted: 2 months ago
At 2/5/2017 4:34:41 PM, matt8800 wrote:
At 1/10/2017 9:30:48 AM, keithprosser wrote:
An oldy but still a goody.

On Monday a man is sentenced for murder by the judge in the following way:
"You will be hanged at dawn, on one day this week on or by Friday at the latest. However you will not know which day until it arrives'.

The criminal reasons that he can't be hung on Friday morning because he would know when it was going to happen (ie on Friday) once dawn had passed on Thursday, contrary to the terms of the sentence. But if it can't be Friday, it can't be Thursday either, because he'd know it was Thursday after dawn on Wednesay, as Friday was already ruled out.

Similarly, by the same logic he can rule out Wednesday and even Tuesday.

It seems like the hanging cannot be carried out in accordance with the sentence, so he is safe. But on, say, Wednesday he was hanged at dawn, with the hangman pointing out that despite the murderer's argument, the murderer did not know he was about to be hanged that day (having 'proven' it couldn't happen at all) so the sentence was indeed being carried out correctly.

What is wrong with the murderer's argument? It must be wrong because it gets the wrong answer, but I have never been able to work out what is wrong.
Obviously the hanging didn't have to be on the wednesday - tuesday or thursday would work just as well. I am not so sure about Friday though...

I agree it couldn't be Friday.

I think it could be any other day because, due to his reasoning, he ruled out every other day. Because the day of his hanging was contrary to his prediction, he did not know it was going to be Wednesday.

That true, but what is wrong with his argument? He seems to have proved he coudn't be hanged according to the sentence, but obviously that conclusion was false because he could be! So what mis-step is there in his logic? It is hard to put you finger on, which is a serious problem because if we can't identify the mistake how can we be sure to avoid it in future? Indeeed, what other things might we have 'proved' that aren't true?
matt8800
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2/5/2017 4:55:58 PM
Posted: 2 months ago
At 2/5/2017 4:42:56 PM, keithprosser wrote:
At 2/5/2017 4:34:41 PM, matt8800 wrote:
At 1/10/2017 9:30:48 AM, keithprosser wrote:
An oldy but still a goody.

On Monday a man is sentenced for murder by the judge in the following way:
"You will be hanged at dawn, on one day this week on or by Friday at the latest. However you will not know which day until it arrives'.

The criminal reasons that he can't be hung on Friday morning because he would know when it was going to happen (ie on Friday) once dawn had passed on Thursday, contrary to the terms of the sentence. But if it can't be Friday, it can't be Thursday either, because he'd know it was Thursday after dawn on Wednesay, as Friday was already ruled out.

Similarly, by the same logic he can rule out Wednesday and even Tuesday.

It seems like the hanging cannot be carried out in accordance with the sentence, so he is safe. But on, say, Wednesday he was hanged at dawn, with the hangman pointing out that despite the murderer's argument, the murderer did not know he was about to be hanged that day (having 'proven' it couldn't happen at all) so the sentence was indeed being carried out correctly.

What is wrong with the murderer's argument? It must be wrong because it gets the wrong answer, but I have never been able to work out what is wrong.
Obviously the hanging didn't have to be on the wednesday - tuesday or thursday would work just as well. I am not so sure about Friday though...

I agree it couldn't be Friday.

I think it could be any other day because, due to his reasoning, he ruled out every other day. Because the day of his hanging was contrary to his prediction, he did not know it was going to be Wednesday.

That true, but what is wrong with his argument? He seems to have proved he coudn't be hanged according to the sentence, but obviously that conclusion was false because he could be! So what mis-step is there in his logic? It is hard to put you finger on, which is a serious problem because if we can't identify the mistake how can we be sure to avoid it in future? Indeeed, what other things might we have 'proved' that aren't true?

The hangman said he could not know the day. By ruling out Wednesday automatically made Wednesday a candidate. The only day that could be effectively ruled out was Friday for the reasons given IMHO.
keithprosser
Posts: 3,339
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2/5/2017 5:01:06 PM
Posted: 2 months ago
At 2/5/2017 4:55:58 PM, matt8800 wrote:
At 2/5/2017 4:42:56 PM, keithprosser wrote:
At 2/5/2017 4:34:41 PM, matt8800 wrote:
At 1/10/2017 9:30:48 AM, keithprosser wrote:
An oldy but still a goody.

On Monday a man is sentenced for murder by the judge in the following way:
"You will be hanged at dawn, on one day this week on or by Friday at the latest. However you will not know which day until it arrives'.

The criminal reasons that he can't be hung on Friday morning because he would know when it was going to happen (ie on Friday) once dawn had passed on Thursday, contrary to the terms of the sentence. But if it can't be Friday, it can't be Thursday either, because he'd know it was Thursday after dawn on Wednesay, as Friday was already ruled out.

Similarly, by the same logic he can rule out Wednesday and even Tuesday.

It seems like the hanging cannot be carried out in accordance with the sentence, so he is safe. But on, say, Wednesday he was hanged at dawn, with the hangman pointing out that despite the murderer's argument, the murderer did not know he was about to be hanged that day (having 'proven' it couldn't happen at all) so the sentence was indeed being carried out correctly.

What is wrong with the murderer's argument? It must be wrong because it gets the wrong answer, but I have never been able to work out what is wrong.
Obviously the hanging didn't have to be on the wednesday - tuesday or thursday would work just as well. I am not so sure about Friday though...

I agree it couldn't be Friday.

I think it could be any other day because, due to his reasoning, he ruled out every other day. Because the day of his hanging was contrary to his prediction, he did not know it was going to be Wednesday.

That true, but what is wrong with his argument? He seems to have proved he coudn't be hanged according to the sentence, but obviously that conclusion was false because he could be! So what mis-step is there in his logic? It is hard to put you finger on, which is a serious problem because if we can't identify the mistake how can we be sure to avoid it in future? Indeeed, what other things might we have 'proved' that aren't true?

The hangman said he could not know the day. By ruling out Wednesday automatically made Wednesday a candidate. The only day that could be effectively ruled out was Friday for the reasons given IMHO.

I don't see what you are pointing out as the specific error.