# Neverneverland and the three old men

1. Oct 28, 2004

### Aphex_Twin

One problem I'd been wondering how to solve:

We want to enter Neverneverland and at the gates we are confronted with three old men. A sign next to them reads in English:

"You can only pass if you identify who are the three before you. One, the Knight always tells the truth, one, the Knave always lies and, one, the Knexus nods his head as a yes if both others would answer the same way and as a no if one of the other men would not answer in the same way as the other. Theese wise men know all the languages in the world, they can understand you, but ah, they will not speak in YOUR language".

In short:
A is a liar
B tells the truth
C tells the result between A XOR B

You do not know the language, therefore you do not know the sound of the words "yes" and "no" in their language. You must either do without the meaning or you must infere it.

Come up with three questions you should ask the three men as to identify them.

I have already worked up an entire theory, which I will submit if the problem is not a case of "incredibly simple/something I overlooked and will kick muself for".

2. Oct 29, 2004

### Mk

Can you command them to do something that will not break the rules?

3. Oct 29, 2004

### Cosmo16

Here's 3 that will do it.

"Are you the one who always lies?" -- The 1st 2 will both say no, so you know what the sound for no is.

"Are you the one that always tells the truth" The 1st 2 will both say yes, so you know the sound for yes.

Finally ask a known somthing with a true truth value. (2+2=4) The one who tells the truth will make the sound for yes, the one that makes the sound for no will always lies.

4. Oct 30, 2004

### Aphex_Twin

@Cosmo16

"Are you the one who always lies?"

Both the liar (knave) and the one who tells the truth (knight) will say no, but the knexus will say yes because no xor no is yes.

It is possible to ask a question all men will answer the same. For instance: "Are you not the knave?". The knight will say yes and the knave will also say yes because he lies. Yes xor yes is yes. And you know the word for yes. But now you only have 2 questions left and you still haven't identified the men before you.

I think the problem has no sollution after all, but I need a way to prove it.

We will note yes with 1 and no with 0. The three men are: the knight - A, the knave - B, the knexus - C

All the possible answers to a presumptive question are:

A B C
0 0 1 ("Are you the knave?")
0 1 0 ("If you were the knight, would you lie?")
1 0 0 ("If you were the knave, would you lie?")
1 1 1 ("Are you not the knave?")

We define a question as a (x, y, z) or xyz sequence, where x,y,z are either 0 or 1 and x is and answer of A, y the answer of B and z the answer of C.

So "Are you the knave" is a (0, 0, 1) or 0 0 1 question because A would answer no, B would answer no and C would answer yes.

There are 6 possible permutations of A B C:

ABC
ACB
BAC
BCA
CAB
CBA

After three questions (asked to one individual at a time) you have to find out the correct permutation of the men before you. This can be performed easily if you know the words for yes and no, but if you don't...

5. Oct 31, 2004

### Cosmo16

I still think I'm right

"Are you the one who always lies?"

A=F
B=F
Know you know the word for no because A and B will have both said it
C=T
Know you know C=C.

"Are you the one who always tells the truth?"
A=T
B=T
Know you know the word for for true
C=T
It doesn't matter he agrees because you already know which one he is.

"Is my name ______"
A=T
Now you know that A=A
B=F
Know you know that B=B

Unless I missed somthing I think this is right.

6. Nov 1, 2004

### Aphex_Twin

If you get an answer of YES, another answer of YES and an answer of NO, you will have asked three questions. A question is defined as something asked to a SINGLE man at a time. Ask the same question to two diferent men and you will have asked two questions.

7. Nov 3, 2004

### Cosmo16

Oh, I read the riddle as you could ask one question and each of them would answer it.

8. Nov 7, 2004

### Myclicheisbetter

Wouldn't simply watching who nods thier head at the first question show who the Knexus was? The riddle states that he will only nod while the other two will use an audible response. Then ask the two remaining at random if the one nodding is the Knexus. The one who answers yes is Knight and you have your solution by only asking 2 questions.

9. Nov 8, 2004

### Cosmo16

We don't know the words for yes or no

10. Nov 8, 2004

### Myclicheisbetter

use that translate feature on altavista

11. Nov 16, 2004

### nnnnnnnn

Q1: Ask any of three: do you always lie?
->Case 1 If spoken answer, you know what no is, you know this is truth teller or liar.
Case 2 If nod, you know who knexus is.

Q2: case 1) Ask the same one: will you speak my language?
-> If same answer (no), then you are talking to truth teller.
If different answer, you are talking to liar.

Q3: case 1) Ask a different person a yes/no question.
-> If spoken answer you are talking to liar/truth teller (depending on ans to prev quest), if nod, you are talking to knexus... you know 2 of 3 ---> you know all 3...

Q2: case 2) Ask someone else: do you always lie?
->You know what no is.

Q3: case 2) Ask same one: does he ever lie? (while pointing at knexus)
->If yes, person asked is truth teller, if no, person asked is liar.... you know 2 of 3 ---> you know all 3...

Last edited: Nov 16, 2004
12. Nov 16, 2004

### Jake

quite a toughy, But I don't get the full riddle. Do you know who the Knexus is? And if you ask the Knexus, is it so that no matter what, hell just shake his head yes/no depending on the question? Or what.

Last edited: Nov 16, 2004
13. Nov 17, 2004

### nnnnnnnn

Thats how I understood it, that he will nod and the others will speak.

14. Nov 23, 2004

### Aphex_Twin

The Knexus will say either "yes" or "no", just like the other two men, he will not nod, nor do anything else. The deal is that you can't ask questions like "what would the knexus say?".

15. May 13, 2011

### slyuncle

Here's how:

Step 1. Ask person 1: Are you the Knexus? (Question 1) If he nods, then you know he's the liar. Why? Because the truth-teller will shake his head, while the Knexus himself will also shake his head because the truth-teller and the liar give different responses to the question.

Step 1B. In the case that person 1 nods, then for person 2, ask (Question 2): Are you the Knave (truth-teller)? The Knight will shake his head, but the Knexus will nod, because both the Knight and the Knave will give the same answer to this question. Solved.

Step 2. In the case that person 1 shakes his head to the question of whether he is the Knexus, you know he is either the Knexus or the Knight. Then ask person 2 if he is the Knexus (Question 2). If he nods, then you know person 2 is the Knave. Then ask person 1 or person 2 if they're the Knave (Question 3). You know that the Knight will shake his head while the Knexus will nod. Solved.

Step 2B: If person 2 shakes his head to the Knexus question, then you know person 3 is the Knave. So then ask either person 1 or 2 if they're the Knave (Question 3). That will determine which is the Knight and which is the Knexus. Solved.