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I have another puzzle to hopefully satisfy the intellectual appetite of the Team Liquid community. There are actually two versions of this puzzle, the easier one and the harder one. You could jump to the harder one if you don't want any hints, but for most people I think solving the easier one first is better.
+ Show Spoiler [Easier Version] +
There are 2 prisoners who have both been sentenced to life in prison. They are each going to be placed in solitary confinement(separate cells, they cannot communicate or see each other at all).
There are 100 guards working at this prison. Every day, each cell is guarded by one of the guards. If possible, both cells must be guarded. Also, a guard would prefer not to guard the same cell on consecutive days.
Lucky for the prisoners, there is a way for them to be released from prison.
Each prison cell's walls are painted either white or black. If either prisoner can successfully guess the color of the other prisoner's cell, then both will be freed. If either guesses wrong, they both die.
Every single day, the prisoners can do one of three things:
1) Talk to the guard. If the prisoner does this, the guard will be very offended and will never guard this prisoner's cell again.
2) Tell the guard what he thinks the color of the other prisoner's cell is. If the prisoner guesses correct, they both go free. Otherwise, they both die.
3) Do nothing.
As is usual with these kinds of problems, the prisoners have time beforehand to discuss their strategy. Can you think of a strategy that the prisoners can use to guarantee their freedom?
Clarifications
1) The priority of rules for the guards is as follows (first being highest priority):
----If a guard has been talked to, he will never guard that cell again
----If there is no other guard available to guard a cell, he will guard it.
----If the guard has guarded that cell the day before, he will not guard it today.
2) It is possible for a prisoner's cell to be completely unguarded on a day. For example, if the prisoner has talked to all 100 guards, then there will be no more guards left who are willing to guard him. This also means that the prisoner can no longer guess because there are no guards available to listen to him.
+ Show Spoiler [Harder Version] +
There are 2 prisoners who have both been sentenced to life in prison. They are each going to be placed in solitary confinement(separate cells, they cannot communicate or see each other at all).
There are 100 guards working at this prison. Every day, each cell is guarded by one of the guards. If possible, both cells must be guarded. Also, a guard would prefer not to guard the same cell on consecutive days.
Lucky for the prisoners, there is a way for them to be released from prison.
Each guard has an astrological sign (there are 12 astrological signs). If either prisoner can successfully guess the sign of the guard that is currently guarding them, then both will be freed. If either guesses wrong, they both die.
Every single day, the prisoners can do one of three things:
1) Ask the guard what his sign is. If the prisoner does this, the guard will tell you, but will also become very offended and will never guard this prisoner's cell again.
2) Guess the guard's astrological sign. If the prisoner guesses correct, they both go free. Otherwise, they both die.
3) Do nothing.
As is usual with these kinds of problems, the prisoners have time beforehand to discuss their strategy. Can you think of a strategy that the prisoners can use to guarantee their freedom?
Clarifications
1) The priority of rules for the guards is as follows (first being highest priority):
----If a guard has been asked his sign by a prisoner, he will never guard that prisoner's cell again.
----If there is no other guard available to guard a cell, he will guard it.
----If the guard has guarded that cell the day before, he will not guard it today.
2) It is possible for a prisoner's cell to be completely unguarded on a day. For example, if the prisoner has talked to all 100 guards, then there will be no more guards left who are willing to guard him. This also means that the prisoner can no longer guess because there are no guards available to listen to him.
3) A prisoner is only allowed to guess the sign of the guard that is currently guarding him.
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<3 puzzles! Have to skip sc2 for a bit now tho ;(
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I am assuming the prisoners can differentiate between the different guards?
+ Show Spoiler [Easier version] +Both prisoners talk to the guards for 49 days, thus chasing away 98 of the guards and leaving 2 of them.
On the 50th day, prisoner A will talk to the guard if his wall is white, but not talk if his wall is black. Prisoner B will do nothing.
On the 51st day, if prisoner B has no guard, he knows that A's wall is white, since A's guard on the 50th day will have ran off, and B's guard will go to A. If the guards changed, prisoner A's wall is black and B will know, thus freeing them.
If A's wall is white, B will tell the guard on the 52nd day.
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Harder version is so difficult. I think I'm going to have to try working out the easier version first.
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On October 08 2010 18:07 Vinnesta wrote:I am assuming the prisoners can differentiate between the different guards? + Show Spoiler [Easier version] +Both prisoners talk to the guards for 49 days, thus chasing away 98 of the guards and leaving 2 of them. On the 50th day, prisoner A will talk to the guard if his wall is white, but not talk if his wall is black. Prisoner B will do nothing. On the 51st day, if prisoner B has no guard, he knows that A's wall is white, since A's guard on the 50th day will have ran off, and B's guard will go to A. If the guards changed, prisoner A's wall is black, and B will know.
If A's wall is white, B will tell the guard on the 52nd day.
If a prisoner talks to a guard, that guard will only stop guarding that one prisoner, not both prisoners.
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Vatican City State1176 Posts
in the hard version, under clarification 1), what do you mean with
"----If there is no other guard available to guard a cell, he will guard it."
most likely not important, but still
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On October 08 2010 18:07 Vinnesta wrote:I am assuming the prisoners can differentiate between the different guards? + Show Spoiler [Easier version] +Both prisoners talk to the guards for 49 days, thus chasing away 98 of the guards and leaving 2 of them.
On the 50th day, prisoner A will talk to the guard if his wall is white, but not talk if his wall is black. Prisoner B will do nothing.
On the 51st day, if prisoner B has no guard, he knows that A's wall is white, since A's guard on the 50th day will have ran off, and B's guard will go to A. If the guards changed, prisoner A's wall is black and B will know, thus freeing them.
If A's wall is white, B will tell the guard on the 52nd day.
But I thought the prisoner's can't talk to each other?
+ Show Spoiler +If I was the prisoner, I'll just randomly guess the other guy's colour because I really can't find a solution.
50% chance of being freed! :D
Edit: Nevermind, didn't really read the questions carefully XD
I think the dude go it though
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On October 08 2010 18:11 Sadir wrote:
in the hard version, under clarification 1), what do you mean with
"----If there is no other guard available to guard a cell, he will guard it."
most likely not important, but still
Suppose there's only 1 guard willing to guard prisoner A, while there are plenty of guards willing to guard prisoner B. In this scenario, the same guard will keep guarding prisoner A, even though he would prefer to switch.
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+ Show Spoiler +so he could do nothing until he noticed a guard missing
one if by land (white!)
two if by sea (black!)
if he noticed two missing from his rotation, it's black
if he noticed one missing from his rotation, it's white
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no idea on the harder version whatsoever
please dont keep me up for hours
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On October 08 2010 18:07 Vinnesta wrote:I am assuming the prisoners can differentiate between the different guards? + Show Spoiler [Easier version] +Both prisoners talk to the guards for 49 days, thus chasing away 98 of the guards and leaving 2 of them.
On the 50th day, prisoner A will talk to the guard if his wall is white, but not talk if his wall is black. Prisoner B will do nothing.
On the 51st day, if prisoner B has no guard, he knows that A's wall is white, since A's guard on the 50th day will have ran off, and B's guard will go to A. If the guards changed, prisoner A's wall is black and B will know, thus freeing them.
If A's wall is white, B will tell the guard on the 52nd day.
this is assuming that they go in order
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+ Show Spoiler + easy version: the cellmates before going in (assuming they know all the rules) decide that one of them is the 'talker' whilst the other is the 'thinker'.
The talkers job is simple, he talks to 99 of the guards if his cell is white, if it is black he doesnt talk at all, the thinkers job is pretty easy too, he waits 100 days, and then talks to 99 guards.
What this accomplishes is that the 'talker' prisoner always has that 1 guard left if he's in a white room, and due to the 'rules' that one guard must always guard him despite his preferences, so after 'thinker' gets rid of his 99 after 200 days or w/e, this one guard begins swapping back and forth if 'talker' is in a white room, at which point thinker knows the colour of both rooms and gets them free.
If however 'talker' is in a black room, and has never talked, the one guard 'thinker' didnt talk to is always stationed at his room, allowing 'thinker' to realize that 'talker' must be in a black room, at which point he knows the colour of both rooms.
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i was just assuming that you could 98 or 99 it and then follow by the other guy talking to all 100
your method is pretty good, i didn't think about having to get two right
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On October 08 2010 18:17 Bill Murray wrote:+ Show Spoiler +so he could do nothing until he noticed a guard missing
one if by land (white!)
two if by sea (black!)
if he noticed two missing from his rotation, it's black
if he noticed one missing from his rotation, it's white
Clarification: You cannot assume anything about the order of the guards. For example, if there are 3 guards available to guard prisoner A, he could very easily see the following:
1 2 1 2 1 2 ....
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On October 08 2010 18:19 Ftrunkz wrote:+ Show Spoiler + easy version: the cellmates before going in (assuming they know all the rules) decide that one of them is the 'talker' whilst the other is the 'thinker'.
The talkers job is simple, he talks to 99 of the guards if his cell is white, if it is black he doesnt talk at all, the thinkers job is pretty easy too, he waits 100 days, and then talks to 99 guards.
What this accomplishes is that the 'talker' prisoner always has that 1 guard left if he's in a white room, and due to the 'rules' that one guard must always guard him despite his preferences, so after 'thinker' gets rid of his 99 after 200 days or w/e, this one guard begins swapping back and forth if 'talker' is in a white room, at which point thinker knows the colour of both rooms and gets them free.
If however 'talker' is in a black room, and has never talked, the one guard 'thinker' didnt talk to is always stationed at his room, allowing 'thinker' to realize that 'talker' must be in a black room, at which point he knows the colour of both rooms.
Congratulations. You have solved the easy version.
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I'm going to sleep. Good luck with the hard version. I'll give clarifications when I wake up if necessary.
Edit: lol accidentally tripled posted.
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omfg at hard version, braintstorming some ideas right now and not getting very far haha.
edit 1:OMG MY 2000TH POST NOOOOOOOO.
atleast im a sexy dt now.
edit 2: joke answer: if the a guard says leo he throws his show at their face hard enough to leave a bruise, allowing the other guy to say leo when he comes around.
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argggggggggggggggggghhhhhh hard version.
nuts,
seems impossible cuz its 1 out of 12, and noway of knowing the guard's sign without asking.
going to think while sleep.
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yeah, going completely round in circles and getting nowhere on hard, this is doing my head in, not enough IQ...
edit: I give up, im getting to that "its impossible fuck it" point in my head, haha. The thinking im up to is that one guy has to stop talking to guards at some point because a guard gives a certain answer, however I'm unsure as to how that helps the other guy, but its the only way of conveying any sort of information between the 2, which is what the problems all about... I just have no idea at what point logically makes sense for him to stop talking and to have the other guy figure it out based off that.
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EPT
