Tuesday Puzzle 2 -- for after you get #1

Re: Tuesday Puzzle 2 -- for after you get #1

This is an application for 'digital communication' technology.

Ask either one to point out the direction the other one would send you, then go the other way.

Two problems with that answer

There is only one person at the fork in this version.

You need to ask a question, not make a request. And I intended, but failed to specify, that it was a yes/no question that could be answered with "Bal" or "Da".

Re: Two problems with that answer

And what happens if I ask a yes/no question that cannot be answered in a manner consistent with his programming?

Re: Two problems with that answer

He'd probably respond with native-speak for "I don't understand the question". But of course, you won't understand him, and just hope he isn't saying "I can't decide if you would be better boiled over a bed of rice, or roasted with barbecue sauce and a side of fries."

Re: Two problems with that answer

But that would be the most meaningful (to me) answer he could give.

Hint (for both)

In Dan's problem, when you receive the answer to your question, you will know which path to take, but you still will not know whether the person you asked it of is a truth teller or liar.

Same is true of the problem I posted, and in addition, while the response you received will have been "bal" or "da", you still will not know what that word means.

The fascinating thing about these puzzles is that information is conveyed reliably, even though you don't know if the person is telling the truth, and in the second case, even what the words they say mean!

Think I have a solution

Will wait to see if anyone else chimes in. This answer could also be used for the question that I asked.

To get to the truth

Which way to the truth. If I understand correctly, either way you get the answer to the truth road.

Re: To get to the truth

You do get the answer, but not with that question ;-) (must be yes or no question and you do not know the meaning of bal or da, nor the village of the person at the fork. )

An indirect solution

BRIDGEKEEPER:

What... is the air-speed velocity of an unladen swallow?

ARTHUR:

What do you mean? An African or European swallow?

BRIDGEKEEPER:

Huh? I-- I don't know that. Auuuuuuuugh!

My question would be:

"Will you answer this question with the word that represents the true answer to the question 'Are you from the village at the end of the left fork?'"

If he screams 'Auuuuuuuugh!' and is hurled into the gorge, then I can proceed with confidence down the right fork.

If there is any answer ('Bal' or 'Da', I don't care which), then I can proceed with confidence down the left fork, having also learned the local word for 'Yes'.

Funny

And closer than you may think!

Let's see it

Re: Think I have a solution

Pick a direction and ask:

"If I were to ask you if this is the direction to the truth-telling village, would you say "da"?" If the answer is "da" then that is the right way, if not, go the other way. Don't care which (yes or no) "da" means.

The logic of this is left as an exercise for the student ;-))

Re: An indirect solution *LINK*

Here is a link for part of the answer that you gave ;-))


Airspeed of unladen swallow

Exactly!

I'm impressed; I gave up and read the solution.

BTW, I have a whole book of these, with lots of twists on the "knights and knaves" puzzles such as yours. One set has three tribes -- knights who always tell the truth, knaves who always lie, and normals who sometimes tell the truth and sometimes lie. Some pretty mind-bending puzzles. _What Is the Name of This Book_ by Smullyan. Out of print, but he has some others that might contain the same material.

Funny and correct too!

Professors were always reluctant to give full credit for my non-textbook proofs. But propositional calculus applied sideways is still logical, and I like to have fun with it.

My approach here was to take advantage of the native�s simple-minded logic and attempt to force a contradiction.

For example: If you ask a truth teller: �Will you answer �no� to this question�. He cannot answer truthfully and therefore cannot answer at all.

Similar logic applies if you ask a liar �Will you answer �yes� to this question�. He cannot give you an answer that is false, so he cannot answer at all.

Much like Dan�s solution, the trick was to construct a question that:

a) Had to be answered the same way by either truth-tellers or liars.

b) Would reveal information sufficient to deduce the correct path.

Also like Dan�s solution, the word (if any) used in the answer was unimportant. The difference here is that I took advantage of the fact that a non-answer can also convey information.

If you work through all the possible cases, you will see that the solution is correct.

Rabern and Rabern used a similar technique to solve another of Smullyan's puzzles. They postulated that if you asked a god a question that could not be answered logically that the god's head would explode.

You're right

I didn't think long and hard enough about your answer, but it certainly does work, as you describe.

My apologies for not giving credit where due!

Slowly, it dawns on me

the meaning of your question!

God thinking.