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Can u help prisoners to get free ?


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15 replies to this topic

#1 ujjagrawal

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Posted 28 June 2012 - 11:45 AM

The warden meets with 23 new prisoners when they arrive. He tells them, "You may meet today and plan a strategy. But after today, you will be in isolated cells and will have no communication with one another.

"In the prison is a switch room, which contains two light switches labeled 1 and 2, each of which can be in either up or the down position. I am not telling you their present positions. The switches are not connected to anything.

"After today, from time to time whenever I feel so inclined, I will select one prisoner at random and escort him to the switch room. This prisoner will select one of the two switches and reverse its position. He must flip one switch when he visits the switch room, and may only flip one of the switches. Then he'll be led back to his cell.

"No one else will be allowed to alter the switches until I lead the next prisoner into the switch room. I'm going to choose prisoners at random. I may choose the same guy three times in a row, or I may jump around and come back. I will not touch the switches, if I wanted you dead you would already be dead.

"Given enough time, everyone will eventually visit the switch room the same number of times as everyone else. At any time, anyone may declare to me, 'We have all visited the switch room.'

"If it is true, then you will all be set free. If it is false, and somebody has not yet visited the switch room, you will all die horribly. You will be carefully monitored, and any attempt to break any of these rules will result in instant death to all of you"

What is the strategy they come up with so that they can be free?
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#2 bonanova

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Posted 28 June 2012 - 03:33 PM

Spoiler for looks like

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#3 psykomakia

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Posted 28 June 2012 - 03:44 PM

Spoiler for not quite, bonanova

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#4 TripleOption

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Posted 28 June 2012 - 04:08 PM

Spoiler for not quite, bonanova

Spoiler for wouldn't that be ok?

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#5 psykomakia

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Posted 28 June 2012 - 04:10 PM

Yes of course. You're both right.
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#6 phil1882

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Posted 28 June 2012 - 04:31 PM

Spoiler for garanteed

Spoiler for a little faster less certain

Spoiler for even faster even less certain

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#7 psykomakia

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Posted 28 June 2012 - 04:38 PM

Spoiler for garanteed

But he can't switch both switches at once.

Spoiler for a little faster less certain

But all 23 "changed states" could be due to the same single prisoner!

Spoiler for even faster even less certain

But all of the "changed states" could be due to the same single prisoner!
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#8 phil1882

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Posted 28 June 2012 - 05:01 PM

agreed on 2 and 3, its extreamely unlikely, but possible. i didnt realize that about my garenteed solution.
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#9 psykomakia

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Posted 28 June 2012 - 05:38 PM

agreed on 2 and 3, its extreamely unlikely, but possible. i didnt realize that about my garenteed solution.


My point wasn't that the 23 state changes might possibly be the same single prisoner, but that it is LIKELY that some of the 23 state changes would be from the same prisoner, and so is not a viable solution.
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#10 EventHorizon

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Posted 28 June 2012 - 08:10 PM

Spoiler for Agreement with bonanova

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