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## #1 2008-05-29 06:37:46

Chilli the Cow
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### The hardest logic puzzle EVER!

Hello, Chilli the Cow here.
Here's a logic puzzle I read about on Wikipedia. It's supposed to be the hardest ever...it's kinda like Knights and Knaves, but with a twist.

You are on a trip to a tropical island. As you find out, the island is inhabited by three tribes. As it turns out, you arrive right when the chiefs of these tribes are all meeting. One chief is wearing a blue headress, one is wearing a green one, and the other is wearing white. One cheif always tells the truth, one always lies, and one can either tell the truth or lie, but you don't know which is which. The chiefs are very busy and only have time to answer one yes-or-no question each, and each question must be directed at one of the chiefs. The chiefs can understand English but they can't speak it, so they answer in their own language. You know that the words "da" and "ja" mean "yes" and "no", but you do not know which word means which. Taking that all into consideration, what questions will you ask to determine which chief is the truth-teller, which lies, and which can do both?

## #2 2008-05-29 18:21:12

Simon
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### Re: The hardest logic puzzle EVER!

This is a twister alright and I'm still working on it.

The first priority for me has been to find a question that establishes the correct meanings of 'da' and 'ja'.

I beleive I've succeeded in formulating the first question to ask a chief.

Ok, so we have three chiefs. Call them "Truthteller", "Liar", and "X" - and we don't know which is which. I'm also assuming that, although we have no idea whether "X" lies or tells the truth in his answer, he fully understands the question and knowingly must do one or the other. In other words, if "X" says 'da' or 'ja', it will definitely be a conciously true or false statement, not a random utterance.

Alright here goes:

Do others agree with this analysis?

Last edited by Simon (2008-05-30 08:05:45)

## #3 2008-05-30 01:58:02

TheDude
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### Re: The hardest logic puzzle EVER!

The only problem I can see is the cheif who can answer truthfully or falsely.  It's possible that he would ansewer "true" if you asked him if 1+1=2, but then he lies to your question, and would answer "no".

Wrap it in bacon

## #4 2008-05-30 02:36:36

Simon
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### Re: The hardest logic puzzle EVER!

That's a point I considered.

Make sense?

Last edited by Simon (2008-05-30 23:44:35)

## #5 2008-05-30 03:16:05

TheDude
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### Re: The hardest logic puzzle EVER!

I see what you're saying, but I think clarification would be needed to ensure that that we can use that type of reasoning.

Wrap it in bacon

## #6 2008-05-30 04:40:14

Chilli the Cow
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### Re: The hardest logic puzzle EVER!

Hmm, that is an interesting way to to determine what "ja" or "da" means. It's not what I was thinking of, but it still works. However, you still need to determine the identities of the cheifs.

I'll give you a hint:

Last edited by Chilli the Cow (2008-05-30 04:46:27)

## #7 2008-05-30 08:02:50

Simon
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### Re: The hardest logic puzzle EVER!

#### Chilli the Cow wrote:

Hmm, that is an interesting way to to determine what "ja" or "da" means. It's not what I was thinking of, but it still works.

What was your way of determining 'da' and 'ja', Chilli?

As for the rest of puzzle, I'm thinking on the same lines you put in hidden text. (I'm now doing the same with all my past and future conclusions).

Last edited by Simon (2008-05-30 08:07:01)

## #8 2008-05-30 08:57:07

Chilli the Cow
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### Re: The hardest logic puzzle EVER!

According to Wikipedia, (remember, I got this off Wikipedia, so I didn't come up with the idea) the answer there is:

but I like yours better, it's a LOT less complicated. There are multiple solutions, so I'm not saying yours is wrong.

Last edited by Chilli the Cow (2008-05-30 08:57:29)

## #9 2008-05-31 00:54:18

Simon
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### Re: The hardest logic puzzle EVER!

Still slightly concerned about the point TheDude raised. I discuss it here.

I think that covers it...

## #10 2008-05-31 01:58:18

integer
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### Re: The hardest logic puzzle EVER!

What if the Hybrid Chief does say "No."
He'd be lying & telling the truth at the same time.

## #11 2008-05-31 04:22:02

Simon
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### Re: The hardest logic puzzle EVER!

If he's allowed to do that, then I'm stuck.

As for your version Chilli that you got from Wikipedia:

## #12 2008-05-31 04:39:20

Chilli the Cow
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### Re: The hardest logic puzzle EVER!

No, it means

But remember, there are multiple solutions for this puzzle.

## #13 2008-05-31 05:22:11

mathsyperson
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### Re: The hardest logic puzzle EVER!

If you're allowed to pose questions such that not answering is an option, then surely it's a yes-or-no-or-silence question? The three options instead of two make it easier, and so such a solution wouldn't necessarily satisify the original puzzle.

Why did the vector cross the road?
It wanted to be normal.

## #14 2008-05-31 05:32:07

Chilli the Cow
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### Re: The hardest logic puzzle EVER!

Okay, maybe I need to rephrase that...

## #15 2008-05-31 05:49:38

mathsyperson
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### Re: The hardest logic puzzle EVER!

Oh, fair enough then. Although I'm not sure how that question would help things.

Why did the vector cross the road?
It wanted to be normal.

## #16 2008-05-31 16:08:39

Simon
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### Re: The hardest logic puzzle EVER!

Yes mathysperson is right.

## #17 2008-06-02 23:39:57

TheDude
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### Re: The hardest logic puzzle EVER!

I can find no loopholes in that question Simon.

Wrap it in bacon

## #18 2008-06-03 02:36:00

mathsyperson
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### Re: The hardest logic puzzle EVER!

It's perfectly correct, but I don't like how it forces the hybrid to be truthful by threatening him with a paradox.

I'd prefer it if we could find a question that wasn't self-referential.

Why did the vector cross the road?
It wanted to be normal.

## #19 2008-06-04 20:09:39

Simon
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### Re: The hardest logic puzzle EVER!

My brother, who says he has the seen the orignal puzzle, confounded me with the following information:

a) the solution does not require that you know the meaning of 'da' and 'ja'

b) the solution doesn't require that the hybrid's responses be anything except random sounds - i.e not deliberately true or false

That throws everything into disarray and my gut response is: impossible. My brother is lying.

#### mathsyperson wrote:

I'd prefer it if we could find a question that wasn't self-referential.

So would I but I don't think there is one. At least, not a question that establishes the meaning of 'da' and 'ja' beyond all doubt from just one chief.

Making the question to one chief not self-referential would tell you the most likely synonyms of 'da' and 'ja'.

## #20 2008-06-06 02:19:07

simron
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### Re: The hardest logic puzzle EVER!

I remember working on a problem like this, except they spoke English, there were two of them, and you needed to get through a certain door that one of them were guarding. The answer was to ask one of them what the other one would say to a certain question. I think that could be adapted to this problem.
By the way, Simon, it's interesting that our user names are one letter off from each other.

Linux FTW

## #21 2008-06-06 08:10:53

Simon
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### Re: The hardest logic puzzle EVER!

#### simron wrote:

I remember working on a problem like this, except they spoke English, there were two of them, and you needed to get through a certain door that one of them were guarding.

Yes, that one is relatively easy compared to this.

Ok, I believe I'm getting very close to a correct solution.
If I'm right, it appears that my brother iwas correct. Finding a logical solution doesn't require you to know what DA and JA means - which sounds impossible.

But my solution does require that the Hybrid chief deliberately tell the truth or lie, even if he has tossed a coin to decide which.

## #22 2008-06-06 20:10:00

Simon
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### Re: The hardest logic puzzle EVER!

Ok I have found a solution and (unless I've miscalculated) it works perfectly.

With this method, you are asking a chief one question while inserting it within another. The result is a guaranteed truthful reply to the question you actually want answered, but as far as the Chief is concerned he has answered the other question.

At the same time, for the purposes of your question, DA and JA can mean YES and NO respectively,, irrespective of what it means to the chiefs.

So in this solution, you could have following situation:
You ask a chief, using the implicit question "Are you the Liar?" inserted within another question.
The chief replies "DA", which will truthfully answer your inserted question reliably as YES. But the Chief is actually responding falsely to the other question and for him DA might mean NO.

Baffled?

Here's the solution.

## #23 2009-04-05 15:04:51

Brian_Corr
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### Re: The hardest logic puzzle EVER!

I had this puzzle in a notebook from a while ago, came across it yesterday and solved it.
The version of the puzzle I was given they don't have feathers they are sitting in a circle in thrones numbered 1, 2 and 3, and you have to ask each Chief the same question (so asking one chief multiple questions is out), it has to be a yes/no question so none of the "answer only if your ...". AND I managed to solve it by asking only two of the three Chiefs.

The version I was given:

You arrive on an island that has three tribes: the Truthies who must always tell the truth, the Falsies who must always lie, and the Unpredictables who can say what ever they want. In order to continue on your quest you need to figure out which tribe is which. You are taken to a tent where the Chief from each tribe is sitting in a circle, we'll say in thrones numbered 1, 2 and 3. They are busy so you only get to ask each Chief one yes/no question, the same yes/no question. AND even though they understand your "pig snout language", as one of the locals put it, they refuse to speak it. So they will answer DA or JA, their words for yes and no BUT you don't know which means which.
What question do you ask to find out which Chief is from which tribe.
Can you do it asking only 2 of the 3 Chiefs?

## #24 2009-05-16 12:28:04

scapeplan
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### Re: The hardest logic puzzle EVER!

i would of just walked away