# Hardest logic problem ever

Suppose you are in a land where orcs only tell lies, and elves only tell the truth. On your way to Gondor, you come across a fork in the path, going two seperate ways. One path leads you to Gondor, while the other leads you to some place else. There is also an orc and an elf standing around to answer any questions. Suppose you are allowed to ask just one question. What question do you ask to know that you take the correct path to Gondor?

Ask the elf what the correct path is... Duh. I think it would be a lot more interesting if the orc and elf were indistinguishable.

If they were indistinguishable, then you would merely ask:

"And which way is the city you live in?"

The answer would be the city of truth (or elves in this case).

The lier would lie, thus saying the city of truth, the truther (pardon the made up word) would point to the city of truth.

mruncleramos said:
Ask the elf what the correct path is... Duh. I think it would be a lot more interesting if the orc and elf were indistinguishable.

If they were indistinguishable what would you ask the orc/elf?

point to a road and ask if the other person would say if it was the road to gondor. This way if you are pointing to the correct road, and the person you are speaking to is the truth person, he would say no. Similiarily, if it was the lying person, then he would also say no. Thus you know to take that road. If the one you are pointing at is not the road, the truth person would say yes and the lying person would say yes as well. Thus you take the opposite road. And the third poster did not answer the question.

In this problem is the person able to distinguish which is the orc and which is the elf??

Mozart said:
In this problem is the person able to distinguish which is the orc and which is the elf??

originally, yes.

But the answer to it is extremely easy, I don't see much hard logic in asking the truth-saying-creature about the truth-path-to-gondor.

I agree with you.

so if we edit the question n suppose that their are in distingush able. is muncleramos correct

he is indeed.

so if we edit the question n suppose that their are in distingush able. is muncleramos correct

It makes sense to me

Along those same lines...

I hope my problem solving prof. never sees this post. I got a worse version on my final for my problem solving class, I am restating the problem, although not as eloquently:

There are 3 types of people living on an island, who look exactly the same, Yohns, Wishi, and Naal. The Naal always lie, the Yohns always tell the truth and the Wishi always alternate between telling the truth and telling lies. You are trying to get to (Insert Town/Street/Destination Name Here), You may ask 3 questions, what are they?

It's not the most DIFFICULT problem ever, but very interesting.

Here is an answer to Vanes63, based on the assumption that I am at a fork in the road, one road leads to Rome, and the other doesn't.

I would pick one guy at random and point to one of the roads and ask "Would a Wishi always say that this is the road to Rome?". Then I would ask the same question a second time.

A Yohn will answer "no" twice.
A Naal will answer "yes" twice.
A Wishi will answer "yes" once and "no" once. The next answer I get from this guy will be true or lie depending on the order in which he said "yes" and "no".

The third question will be "Is this the road to Rome?" and based on the answers to the first two questions, I will know if the answer I get is true.

I have been given the same problem (although the characters and setting are different) and was able to figure out what question to ask. A perhaps important point that hasn't been mentioned but is considered in mruncleramos's answer is that the person is only allowed to answer either "Yes" or "No".

Like I said, the problem is the same, but another prerequisite is that (this is freely translated from Japanese so it may sound slightly weird):

"A person was asked and answered Yes. Hence, the traveler knew that the left road was the correct one".

Accordingly, I figured out the question to be

"Would the other kind of person say that the left road is incorrect?"

However, the problem I am working on has a second part.

"Using the below assignments, write the question's logical expression
p = {The person is an honest person}
q = {The left road is correct}
"

This is actually part one of the problem which is even more perplexing as I'm having a much harder time to figure it out. I haven't made any progress in approx. three hours and would greatly appreciate any help. The deadline is tomorrow...

I thought this was the "Hardest Logical Puzzle Ever":

Three gods, A, B, and C, are called True, False, and Random (in some order you do not know.)
True always speaks truly. False always lies. And Random always speaks truly or lies in a completely random manner. Furthermore, they speak their own language. They will respond "da" or "ja" (one means Yes and the other means No but you do not know which is which.)

You may ask three questions in total. Each time you ask one of your questions, it can only be directed at one god. (You can repeat a question to another god but that counts as 2.)

Determine the identities of A, B, and C (i.e. which is True, which is False, and which is Random.)