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Another Prisoner Problem 2...


Best Answer plasmid, 09 September 2014 - 06:34 AM

Ok, that's enough dallying around for now. Time for an answer.

Spoiler for might not be optimal but is probably a good start


Edit: correction to the above.
Spoiler for
Go to the full post


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11 replies to this topic

#1 Yoruichi-san

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Posted 23 August 2014 - 05:45 AM

(Elsewhere in Braingate Denitentiary)

 

"Well, we're in a pickle.  There are 9 of us in the special cell block, arranged in a circular fashion and facing outward so that we can't see each other.  And worse, they don't want us 'to get too comfortable' so we are reassigned to different cells randomly each day after the morning walk."

 

"You're right, Mr. Fredege. I eavesdropped the another group talking about toilets but we don't have the comfort of having them in our own cells, so that's out.  The lights in my cell have been acting weird lately, but I don't know what that's about..."

 

"It think I might, Phiddler.  I overheard the guards talking, and it seems there is an issue with the wiring...rats or something of the sort, and now when one of us switches on or off the lights in our cell, the lights of the adjacent cells are also switched."

 

"Hmm...good observation K-croc.  I think we may be able to use that, but we'll have to be careful.  We need to avoid messing with the lights when the guards are walking by our cells, which as far as I can tell is at random intervals, so whatever we do has to be independent of time intervals."

 

"Alright, where do we start?"


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#2 Barcallica

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Posted 28 August 2014 - 02:19 AM

Since the prisoners doesn't appear to be around, 

1. What is the beginning states of the lamps.

2. Can I use off/on then on/off as a signal?

3. How many times can they act a day? (it says they are shuffled each day)


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#3 Yoruichi-san

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Posted 29 August 2014 - 06:41 AM

Since the prisoners doesn't appear to be around,
1. What is the beginning states of the lamps.
2. Can I use off/on then on/off as a signal?
3. How many times can they act a day? (it says they are shuffled each day)


1.Off
2.Sure
3.No limit, just the starting configuration is unknown.
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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page! Episode 3 is finally here!

When life hands me lemons, I make invisible ink.

#4 plasmid

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Posted 29 August 2014 - 08:00 AM

It seems unsolvable, so maybe I don't fully understand the question.

How independent of time intervals do things have to be?
For example, if a prisoner sees four flips of the light and waits say five minutes (or any other period of time that you want) without seeing anything, can he safely assume that the string of flips he was watching has ended?
Or do all the prisoners have to lie low at the same time when guards are about: meaning that if a prisoner has to interrupt a string of flips in the middle because of patrolling, then the other prisoners will also not be able to send flips at the same time?

For most solutions I could imagine, unless one of the above answers allows them to give more info than I think they're allowed to give, we end up facing the problem of a prisoner having to wait indefinitely to know if another flip is going to be sent to him or if a string of flips being sent to him has ended.
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#5 Barcallica

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Posted 29 August 2014 - 08:41 AM

 

Since the prisoners doesn't appear to be around,
1. What is the beginning states of the lamps.
2. Can I use off/on then on/off as a signal?
3. How many times can they act a day? (it says they are shuffled each day)


1.Off
2.Sure
3.No limit, just the starting configuration is unknown.

 

 

(with regard to 2nd answer) Then can't it be solved with similar fashion. Switching once is odd, switching twice is even etc...

Anyway, this is what I was asking with second question.


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#6 plasmid

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Posted 29 August 2014 - 02:32 PM

If a prisoner sees one flip, how does he ever know that he's only going to see just one flip and not eventually a second one if he waits long enough?
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#7 Barcallica

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Posted 30 August 2014 - 02:12 AM

If a prisoner sees one flip, how does he ever know that he's only going to see just one flip and not eventually a second one if he waits long enough?

Second flip is immediately after first one that it actually like one action.

I mean Flif,flip is one continuous action there is no time wasted between them. So one could tell if it is flip or flipflip.

Edited by Barcallica, 30 August 2014 - 02:18 AM.

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#8 Yoruichi-san

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Posted 30 August 2014 - 02:39 AM

Sorry for the confusion, I was in a hurry when I was writing this (packing for Paris...as a female, I think that says it all ;)), and have been in Paris with little reliable internet.  

 

Anyways, Barca is correct, you can assume the instantaneous flipping is distinguishable from leaving the lights on or off, and the prisoners can see a little ways down the hall from their cells so that they'll have a little prior warning to when a guard is coming.  The idea is to minimize the chain of actions so that they run a smaller risk of being caught by a guard.


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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page! Episode 3 is finally here!

When life hands me lemons, I make invisible ink.

#9 bonanova

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Posted 30 August 2014 - 08:56 AM

I hope you weren't counting on any ... sympathy ... for having to pack ... for Paris.  ^_^


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#10 plasmid

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Posted 06 September 2014 - 06:19 AM

Just to make sure: If a prisoner sees his light getting flipped by someone other than himself, does he have any way to know whether the person flipping the lights is clockwise or counterclockwise from him?

If the answer to the above is no, then are the cells in the cell block distinguishable in any way (like being visibly numbered) such that the prisoners can say "Whoever's in cell #1 should start signaling according to this code, and whoever's in cell #2 should do X but whoever's in cell #9 should do Y"? Or will the prisoners be in cells that have no particular identifying features?
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