I cant see a paradox here.
He could be standing with a noose around his neck until 1 sec before midnight, and STILL not know if that will be his day to die.
By the time he knows he cannot be killed on the current day, the NEXT day has arrived and he can be told and executed.
Ok, seems I’ve misssed the last hald dozen posts or so.
If you start changing the conditions, with ‘executioner going home times’ and ‘he has to be told by a particular time of day’, then that makes a difference.
I think the 1-minute-to-midnight version, or even Joe Randoms ‘not until it’s tomorrow’ versions are exploiting a boundry condition a little. Which is worth a crack.
if we grant the traditional 1-valid-time per day (which should have been stated) Then maybe we are just left with a contradiction.
So the OP answer is - it’s just a confusing bureucratic snarl-up.
I’ve heard this one before - I think it’s usually called the “Surprise Inspection Paradox” or the like - wherein an army unit knows there’ll be aninspection during the week, but not which day. (I just reloaded, and read the stuff about midnight/1second thing. Stop being so pedantic! It’s irrelevant to the paradox trying to be conveyed here.)
I had a file that described this in detail, but it appears to be lost. 
Here’s the only thing I can find that relates to it.
IIRC, the statement hinges on the “surprise inspection” “next week” thing. Friday is part of next week, but (as you note), you can’t have a surprise inspection on that day. Thus the original statement becomes a lie, and you shouldn’t be trying to extract info from it, at least for logical analysis.
(Note that if your commander shows up on Wednesday, you’d be surprised, so it’s only Friday that isn’t a “surprise” day.)
No, it’s not irrelevant.
—if we grant the traditional 1-valid-time per day (which should have been stated) —
—He could be standing with a noose around his neck until 1 sec before midnight, and STILL not know if that will be his day to die.—
Well, I think within the bounds of reality, it doesn’t much matter, though I should have clarified. If we assume that executions are not instantaneous decisions, and take some amount of time to perform, then the man always has time before midnight to think “oh, there’s no time left to strap me in to the chair, so tommorow must be the day.”
But, let’s forget that quibble, and think of it in periods per day.
Stage 1
Every day, the man wakes up.
Stage 2
He finds out whether he’s being executed today
Stage 3
If he isn’t being executed that day, he now has time to think about future days before he goes to sleep that night.
Yes, we can escape the paradox (I gave a perfectly good example in my OP) but that’s not quite the point: the point is whether the paradox can be somehow resolved on its own terms: whether it’s a true paradox or a psuedo-paradox.
Too many assumptions and changes to the OP conditions are creeping in now.
I still dont see how this is a paradox, with these changes.
The guard can walk in on Monday and tell him he’s gonna get hung. Then he gets hung. That’s it.
p.s. Whats the deal with him being ‘very intelligent’ ?
—Too many assumptions and changes to the OP conditions are creeping in now.—
To be fair to my own OP, those “assumptions or changes” are still the plain read of the problem, and your stipulations about spending the days with his neck in a noose are bending reality more than anything else. But to be clear, I should have done what ultrafilter said: that is the traditional telling of the paradox.
—The guard can walk in on Monday and tell him he’s gonna get hung. Then he gets hung. That’s it.—
No, because to do this, he’d have already have known by Sunday. The logic works backwards all the way through the week. You can even think about it forwards: if this is the single “solution” of how he can be executed, then it is, by definition, wrong… because he’d figure out this solution as well.
That’s also why W_A and dmans solution don’t work either: “As William_Ashbless re-iterated - the smarty-pants has convinced himself internally that he cannot be executed on Friday. Hence, he cannot be expecting it, much less ‘know about it beforehand’, as he wouldn’t believe you even if you told him!”
This would be true if we were only looking at smartypants reasoning about what would happen on Friday from Sunday. But that’s not what’s going on: smartypants is reasoning about how we would reason on an execution-free Thursday. Whatever else he’s convinced himself in the meantime in any of the other days, come an execution-free Thursday, he knows that he’ll know for sure when the execution is. Which means it can’t happen then.
While these don’t prove to me that there is no solution, they do prove that there is no single solution to the problem: if there was, the prisoner would know that. If there were two possible solutions for picking days, however, and there were some way prisoner didn’t know which one was picked until the day of his execution, it could work. But I’m not sure such a thing is possible.
—p.s. Whats the deal with him being ‘very intelligent’ ?—
That’s part of the potential paradox. If he was so stupid that he couldn’t figure out on Thursday that he would be killed on Friday, they COULD kill him on Friday (likewise if they knocked him unconcious so he couldn’t think at all).
—I still dont see how this is a paradox, with these changes.—
It’s paradoxical AND ironic. It is the very desire to have the prisoner not know about his execution date that potentially makes him able to predict it. If you never told the prisoner that you cared about whether he knows or not, and if you didn’t really care then you could easily surprise him.
The “surprise exam” telling might be clearer.
I can’t actually see it as a paradox but rather a set of conditions that are impossible.
I had also rewritten this in a more happier terms with rewards. I just like it that way and didn’t feel like letting it die.
On sunday a husband says to his wife “I’m going to make you eggs for breakfast sometime this week, monday through friday. If you can guess which day that will be I will clean the dishes for the rest of the month. But if you fail to guess then you will clean the dishes for the rest of the month.” The wife agrees.
For four days the husband woke up and asked his wife if she thought that he’d be making her eggs for breakfast and each time she said yes. And each time he heard that he thought “Damn it! I guess I can’t make them today.” And went down to the kitchen to make her something else.
And so friday came and he awoke and he asked her and she said yes and he moped on into the kitchen in a quandry. If he made the eggs that day he’d have made a liar of himself since he had stated that she wouldn’t know which day she would have eggs. And if he didn’t make the eggs then he’d have made a liar out of himself because he had told her that he would make her eggs for breakfast. So he was damned if he did and damned if he didn’t. He cursed himself for giving her 5 opportunities to pick one of the 5 days and for making statements that forced him into the situation he was in.
Well the husband sighed a deep sigh, made his wife the eggs he promised her and for the rest of month he did all the dishes and never once complained.
If the first day on which he can be executed is the Monday, how the hell can he know on Sunday if he’s gonna die the next day ?
He sits in his cell, waiting for Monday to come round. He gets woken up for his breakfast on Monday morning. The guard can either tell him he’s gonna hang, or not.
I dont see where any days before the Monday come into this.
I missed this
Sure: you CAN just pick any day you’d like for the clobbering. Er, as long as it’s not Friday… and that rules out Thursday… and…
Sure he does: because rule one states that he will be killed on one of the days M-F of the next week. The problem on Thursday is that he both MUST be executed on that day (since there are no more days left), and also, since he knows that he must, he also MUST NOT be executed on that day.
If the problem were simply a logical contradiction in the two rules, it wouldn’t be as interesting as it is. The interest comes from the fact that 1) one of the rules is ironically self-defeating 2) no matter what logic concludes, it still FEELS like it could be a surprise, that we could just pick, say, Tuesday on a whim, and he wouldn’t know beforehand.
He can think on Sunday (or any day before “the next week”) whether or not he will be executed on Monday.
Okay, let’s consider the following:
The prisoner can’t be executed on Friday, because he would know after a certain time on Thursday that he must be executed on Friday. Thus, we remove Friday as a valid execution day.
Now, we repeat for Thursday. Since Friday is no longer a valid execution day (because the prisoner would know about it) then Thursday becomes the new “Friday” (so to speak). Following the same logic, Thursday is not a valid execution day.
Now, lets stop here for a moment and not follow the same procedure for the rest of the week. What happens when Tuesday’s execution time comes around and the prisoner is left alive? He thinks to himself “Since Thursday and Friday are not valid for executions, then they must be gong to execute me tomorrow (Wednesday)”. So now he knows the day of execution before it has arrived. Or does he?
According to the original conditons, Thursday and Friday are still valid days to be executed on. When Wednesday passes without the prisoner being executed, what happens to the “knowledge” he had about the day of his execution?
The answer is that the prisoner cannot actually know when his execution day is. Even on Thurdsay, after the scheduled execution time, the prisoner simply assumes that he will be executed on Friday. The whole paradox boils down to the fact that the prisoner will always assume that the next day will be the day that he is to be executed, and one of those assumptions must eventually be correct.
In fact, they might let him go and not execution him at all, since they would be forgiven for assuming that the whole situation was an unresolvable paradox. That means that the prisoner can never actually know that the next day will be the day that he is to be executed, since the possibility of not being executed exists.
It’s the very concept that this might be a paradox which prevents it from becoming a paradox.
Your backwards logic theory is based on the assumption “IF he lives through thursday”.
Only IF he lives through thursday, does your reasoning work.
What if he gets hung on Tuesday ?
My previous post was to Apos obviously.
Ok, its 4:30 AM here, wrong time of the night to be doin this kinda thing.
I give up.
The important factor here is that he’s not just reasoning: he’s reasoning ABOUT how he’d reason.
There are some great riddles that involve crazy iterations of reasoning about how others reason.
For instance, let’s say there are three men all with dots on their foreheads. They don’t know what’s on their own foreheads, but they can see the dots on the other two men. That means that they can each see that the other two men have dots on their foreheads.
Now, an outside party comes in, and says “At least one of you has a dot on his head. If you are sure that you do, then stand up now.” No one stands up just then.
However, after thinking through it a bit, all three men realize that they can now know for sure that they have dots on their foreheads.
The thing that seems so odd here is why the announcement of the outside party was so important. If every single man can see at least TWO dots, why would the information that at least ONE man has a dot make any difference?
Basically, the answer to the riddle involves man A first reasoning about how man B would reason about what man C is reasoning, based on the fact that man C does not immediately get up, and then reasoning about how man C would reason about what man B is reasoning, given that B did not immediately get up.
I can explain the exact chain of reasoning if anyone needs it, but it’s definately fun to try and write it out on your own.
If you’ve solved the riddle (without peeking!) then you can see how the thinking involved is very similar: it seems to build logical conclusions out of thin air, using information that seems redundant and useless, but is actually key (in this case, key making the conclusion work, in the hangman’s case, the key to destroying the system). Hopefully that makes what we’re dealing with in the hangman/surprise case clearer.
No, it’s only based on the assumption that “this is how I would reason IF I were alive on Thursday”
Then he’d know on Monday.
He does not have to assume it: it was one of the stated rules that he WOULD be executed on M, Tu, W, Th, or F. Not being executed on Friday would violate rule 1
If this were true, then the prisoner wouldn’t really KNOW, he’d just be guessing, and everything would be okay. But it’s not okay!
Only if the rules are broken. You might as well just break the rule about him not knowing the day before, and kill him on Friday whether he knows or not. Once you play by different rules, you’re not considering the internal logic of the paradox anymore.
But I see what you mean. GIVEN that the rules form a paradox, the prisoner could conclude that one of the rules would HAVE to be broken: and thus he could be executed even on Friday.
However, there might be a small hitch in even that…
No. He wouldn’t.
He’d assume on Monday. The only day where it’s possible for him to know is on Thursday, when he’s guaranteed to be executed on Friday (since there are no days left).
Let’s assume it’s Sunday before Execution Week. The prisoner says, “I know that I will be executed on Monday.” Except, the prisoner isn’t executed on Monday. So of course, he now says, “I know that I will be executed on Tuesday.”
To which his captors reply “You knew you would be executed on Monday, and yet you weren’t. That means that you simply assumed. We will no longer believe you when you say that you know your execution date, because it’s obvious that you’re just guessing.”
Then they’d hang him on Tuesday.
Ok, I’ll bite.
Why assume that he always thinks he’s gonna die the following day ? ? ?
Also, I dont see how what he THINKS affects any outcomes.