A stand up Logician

[BMAD]

Recently a self-proclaimed stand-up logician held a show with thirty people. here is his opening dialogue:

Hello folks. It's an honor to be on Amateur Logician Night, here on the Internet. How many of you are from out-of-town? Let's see a show of hands.

Now, the people who raised their hands may be truth-tellers who are from out-of-town, or you may be liars who are from in-town. As the amateur logician, it is my job to determine who is really from out-of-town, and who is not. This is not an easy job, as you can well imagine.

If I were to ask how many of you are truth-tellers, then all of you would raise your hands. The liars would have to lie, and claim to be truth-tellers.

Now, let's see a show of hands, all of the people who raised your hands the first time, when I asked how many of you were from out-of-town. Very good. All of you, who now have your hands up, are from out-of-town.

Some of you are truth-tellers who raised your hands both times. You are from out-of-town. Some of you are liars who did not raise your hands last time. You too are from out-of-town. So, all of you who now have your hands up, are from out-of-town.

Thank you. Thank you. What a crowd. Thank you.

Would this approach work in identifying those that always lie and those that always tell the truth? Why or why not?

[bonanova]

[spoiler='Slight change in the process does it']Have them stand in a straight line.

Instead of requesting a show of hands, ask them to take a step forward.

Liars will step forward at one or the other request.

Truth-tellers from out of town will take two steps.

Truth-telling locals wont' move.

The one-steppers comprise all of the liars.

[bhramarraj]

This method may be useful for identifying the number of always truth tellers and number of always liars.

Say first time truth tellers raised their hands are Xo (o stands for out of town), and liars Yi (i stands for in town).
So we know Xo + Yi = A...................................................[1]

And Xi = Yo......................................................................[2]

Then second time hands raised by Xo + Yo = B..............[3]

And Xi + Yo......................................................................[4]

Given Xo + Xi + Yo + Yi = 30............................................[5]
From the above equations equations we may know Yo + Yi; and Xo + Xi.

[BMAD]

Now, let's see a show of hands, all of the people who raised your hands the first time, when I asked how many of you were from out-of-town. Very good. All of you, who now have your hands up, are from out-of-town.

I am curious as to how people interpet this statement. When the logician asked those who raised their hands before to raise their hands again. Would the same liars raise their hands?

[bonanova]

Because that would implicitly state (truthfully) that they had been among those who had raised their hands.

That is the self-referential part of the 2nd question that makes it different from the first question.

[kingofpain]

Depends on if a lie means the person evaluates the statement and then inverts his answer

(For an out of town liar:

You: Are you from out of town?

OOTL: *I am indeed from out of town. So I will lie and say NO*

You: If you raised your hand last time, then raise it again.

OOTL: *I did not raise my hand last time, so this time I should do so*

)

However, a perfect liar would give you the answer that will prevent you from knowing the truth by withholding information. In this case, that would mean telling the truth when it is likely to lead you to misinterpret the truth or at least not know it.

[bonanova]

[spoiler='Slight change in the process does it']Have them stand in a straight line.Instead of requesting a show of hands, ask them to take a step forward. Liars will step forward at one or the other request. Truth-tellers from out of town will take two steps.Truth-telling locals wont' move.The one-steppers comprise all of the liars.

Four groups:

Truthtellers (T) and Liars (L) who are Residents ( R) or from Out of town (O).

"All from out of town take a step forward." (TO and LR step forward one step.)

"All who stepped forward take a step forward." (TO and LO step forward one step.)

Those who took one step are LR and LO: only liars and all the liars.

You have thus used the same method to distinguish the Ls from the Ts.

Q.E.D.

[bhramarraj]

Sorry...! My last reply was posted in a hurry as I was called to attend an urgent meeting. There were mistakes in the post

As far as I know A truth teller always speak or act truthfully, and a liar always speak lie or act untruthfully, i.e. if he raised his hands first time and asked to raise his hands second timeif he raised his hands first time, then he will not raise his hands second time. Because he has to lie or act untruthfully like a robot.

So first time the logician must ask the crowd to raise their hands if they were truth tellers. Whole crowd will raise their hands.
Then second time logician should ask them to raise their hands who first time raised their hands, then only truth tellers will raise their hands.

Hope this time I am correct.

.

Edited May 30, 2013 by bhramarraj