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 Freedom or Aligators using light switches
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westworld
Average Member

USA
19 Posts

Posted - 02/08/2012 :  21:35:07  Show Profile  Reply with Quote
1. Freedom or Alligators
Once upon a time, a prison warden was responsible for 22 prisoners on Death Row. These prisoners were students who had done terrible things: some illegally downloaded movies and music, some texted during classes, some were addicted to Facebook, and some watched Glee.
One day, the warden offers the prisoners one chance at freedom. After a brief discussion period in which they could plan their strategy, each of the prisoners will be placed in solitary confinement (in completely soundproof cells) with absolutely no way to communicate with one another. The warden will arbitrarily take one prisoner at a time to another room containing two light switches side by side. The switches are not connected to anything, but the warden tells the prisoners that at the beginning of the entire process both switches will begin in the “Off” or “Down” position. The rules are that each time one of the prisoners enters the room he or she must flip exactly one of the switches.
The warden tells the prisoners that if one of them ever correctly announces that all 22 prisoners have been in the room that they will all be released. However, if any of the prisoners ever incorrectly claims that all 22 have been in the room, then all 22 will be fed to the warden’s pet alligators.
The warden makes it clear to that prisoners may be returned to the room any number of times, but there is no way for the prisoners to communicate with one another other than by way of the two light switches. The room with the switches will be thoroughly cleaned after each prisoner leaves.
The prisoners are given some time to come up with a plan before they are to be placed in solitary confinement.
How do they ensure their freedom?
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the_hill1962
Advanced Member

USA
1468 Posts

Posted - 02/09/2012 :  11:36:55  Show Profile  Reply with Quote
There is a solution to this!
I don't know how anyone would come up with it but someone named
"solver91311" came up with a solution.
Since we are not supposed to refer anyone to other websites, I will just tell you that if you do a search for the problem on the Internet, you will find it.
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westworld
Average Member

USA
19 Posts

Posted - 02/09/2012 :  12:35:59  Show Profile  Reply with Quote
Here's an answer to this. by solver 91311, thanks solver

If switch B is OFF and this person has never encountered switch B in the OFF position before, turn switch B ON.

If switch B is ON, change the position of switch A.

If switch B is OFF but this person has seen switch B in the OFF position on a previous visit, change the position of switch A.

The Transmitters' job is to wait for that one occasion when they encounter switch B in the OFF position for the first time so that they can turn it on.

When the Scorekeeper enters the room s/he takes one of the following actions:

If switch B is ON, s/he turns it off and adds 1 to the score.

If switch B is OFF, s/he changes the position of switch A and does NOT add to the score.

When the score reaches 21, the Scorekeeper announces that all of the prisoners have visited the room at least once.

I hope the warden takes the students who were convicted of watching Glee and throws them to the alligators anyway.
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the_hill1962
Advanced Member

USA
1468 Posts

Posted - 02/09/2012 :  14:30:06  Show Profile  Reply with Quote
You forgot to mention that one of the prisoners is chosen to be a "scorekeeper" and the other 21 are going to be "transmitters".
I am also adding some notes (see the red):
quote:
Originally posted by westworld

Here's an answer to this. by solver 91311, thanks solver

If switch B is OFF and this person (a transmitter) has never encountered switch B in the OFF position before, turn switch B ON.

If switch B is ON, the transmitter changes the position of switch A.

If switch B is OFF but this person (a transmitter) has seen switch B in the OFF position on a previous visit, change the position of switch A.

Basically,
The Transmitters' job is to wait for that one occasion when they encounter switch B in the OFF position for the first time so that they can turn it on.

When the Scorekeeper enters the room s/he takes one of the following actions:

If switch B is ON, s/he turns it off and adds 1 to the score.

If switch B is OFF, s/he changes the position of switch A and does NOT add to the score.

When the score reaches 21, the Scorekeeper announces that all of the prisoners have visited the room at least once.

I hope the warden takes the students who were convicted of watching Glee and throws them to the alligators anyway.



It took me a while to figure out how this works. Once I thought about how the switch B gets turned on and then no one turns it off except the scorekeeper, it made sense.
If you are having trouble figuring out how this works, let us know and we will explain further.

Edited by - the_hill1962 on 02/09/2012 14:36:58
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westworld
Average Member

USA
19 Posts

Posted - 02/09/2012 :  16:26:23  Show Profile  Reply with Quote
If you dont mind, I am having a bit of trouble wraping my head around this A and B business. How did you know?
Thanks!
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the_hill1962
Advanced Member

USA
1468 Posts

Posted - 02/10/2012 :  18:04:37  Show Profile  Reply with Quote
You can just say the switch on the left is A and the switch on the right is B.
It is a difficult problem and the solution is even difficult to grasp.
I might suggest trying to act out the solution with a group of friends.
I can explain the solution in more detail after you have tried acting out the solution and still have a question.
quote:
Originally posted by westworld

If you dont mind, I am having a bit of trouble wraping my head around this A and B business. How did you know?
Thanks!

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