Iso More Riddles? - Topic

tomasalot3

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#131

Jul 1 2009 06:18pm

Quote (ukitus @ Wed, Jul 1 2009, 07:13pm)

the gaurd can pick the same person 25 times in a row it doesnt matter.

There is a way.

it doesnt go, exm: he picks 25 people the its over.

people can go in the room over 600 times.

it actually doesnt matter, you can say 60 people or 1000 people

the formula works for any number over 20 I think.

in other words the number of people doesnt matter 20+

and what do you mean the light switches every 2 people? They dont have to flick the switch at all.

lold read before posting ^^

i dont really understand, basically... thegaurd explains to them the scenario that the light switch is only way of communicating, then gives them time to form a plan, and he can only call 25 people into the room, but you can call the same person over and over,( unlikely but can happen) and then they succeed and escape, and im spose to figure out how?

TkM

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#132

Jul 1 2009 06:20pm

Quote (ukitus @ Wed, Jul 1 2009, 08:13pm)

Elect a spokesman.

Each prisoner other than the spokesman maintains a counter with initial value 0. When he enters the switch room, if switch "A" is "off" and his counter is 0 or 1, then he switches "A" to "on" and increments his counter. Otherwise (switch "A" is already "on" or his counter is 2) he switches "B".

The spokesman also has a counter with initial value 0. When he enters the switch room, if switch "A" is "on", he switches "A" to "off" and increments his counter. Otherwise (switch "A" is already "off") he switches "B". When the spokesman's counter reaches 44, he declares to the warden "We have all visited the switch room."

He is safe in making this declaration: among the 44 times that the switch had been "on", at most once was because the switch might have started out in the "on" position at the beginning of time. At most two were due to each prisoner (other than the spokesman himself) turning it on. If not everyone had visited the switch room, then it could have been turned "on" at most 2*21=42 times, and his counter would not exceed 42+1=43.

Further, given enough time, each prisoner will have two opportunities to turn "on" the switch, so that the spokesman's counter will eventually reach or exceed 44.

Switch "B" is only used so that the prisoner has something to flip when the protocol says he should not flip switch "A".

The non-spokeman prisoners turn the switch on twice instead of just once, because of the uncertainty about its initial position.

Sorry if it's confusing

This post was edited by TkM on Jul 1 2009 06:21pm

Bail

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#133

Jul 1 2009 06:21pm

Certainty is the key. There is no way you can be certain, because if one of the prisoners does not go along with the plan, what certainty do you have?

2003

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#134

Jul 1 2009 06:25pm

Quote (TkM @ Thu, 2 Jul 2009, 01:20)

u cheated.

copy and paste from google search.

But yea I almost figured this out myself.

I came to the conclusion u need to elect 1 person to set aside and then other shit
\but iwas awhile ago

2003

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#135

Jul 1 2009 06:26pm

Quote (tomasalot3 @ Thu, 2 Jul 2009, 01:18)

The warden meets with the 23 prisoners when they arrive. He tells them:

You may meet together today and plan a strategy, but after today you will be in isolated cells and have no communication with one another.

There is in this prison a "switch room" which contains two light switches, labelled "A" and "B", each of which can be in the "on" or "off" position. I am not telling you their present positions. The switches are not connected to any appliance. 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", and this prisoner will select one of the two switches and reverse its position (e.g. if it was "on", he will turn it "off"); the prisoner will then be led back to his cell. Nobody else will ever enter the "switch room".

Each prisoner will visit the switch room aribtrarily often. That is, for any N it is true that eventually each of you will visit the switch room at least N times.)

At any time, any of you may declare to me: "We have all visited the switch room." If it is true (each of the 23 prisoners has visited the switch room at least once), then you will all be set free. If it is false (someone has not yet visited the switch room), you will all remain here forever, with no chance of parole.

Devise for the prisoners a strategy which will guarantee their release.

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