perplexus.info :: Liars and Knights : South Sea Treasure Hunt

South Sea Treasure Hunt (Posted on 2008-02-21)

After building your mental muscles on Perplexus logic problems, you feel ready to embark on the south sea logic treasure hunt. You travel to remote Uwalahooloo and are initially delighted to discover that you are the first treasure hunter to arrive. Or so you think. It turns out that the other hunters gave up long ago and departed with the natives, having despaired of ever working out which of the two paths through the jungle leads to the treasure and which leads to the deadly sphinx.

Not being someone to give up easily, you search the island and come upon the journal of a previous treasure hunter. You read:

"I've been here for months, but I’ve still reached no clear conclusion as to which path to take. I’ve recorded my findings in the hopes that someone may yet succeed where I have failed.

I have interviewed four natives and know each to be either a knight or a liar. However, as the island is part of an archipelago occupied by two different tribes, I am at a loss to say which language each native speaks (although I have determined that each native is monolingual). I have been able to learn a few interrogatives in both languages, but the confounded thing is that each question has a distinct, valid meaning in each language.

There is also one further complication: one of the natives has a hearing impairment and can't detect a “w” sound at the start of a word.

I list for you the questions and their variant translations in languages A and B:

Wuf?

A: Do more natives speak language A than language B?

B: Are all knights language B speakers?

Hacha?

A:Are there more liars than language A speakers?

B:Would any of the other natives tell me the truth?

Uf?

A:Can I reach the treasure by taking the left path?

B:Is the native with the hearing problem a knight?

The natives' responses (in uppercase letters) to each question were:

Native 1: Wuf? NO Hacha? YES Uf? YES

Native 2: Wuf? YES Hacha? NO Uf? YES

Native 3: Wuf? YES Hacha? YES Uf? NO

Native 4: Wuf? NO Hacha? YES Uf? YES"

(Note that the native with the hearing disability will have misinterpreted the question "Wuf?" as "Uf?")

Can you reason how to choose the correct path?

Submitted by FrankM

No Rating

Solution: (Hide)

Since native 2 is the only one to answer Uf? and Wuf? consistently, he must be hard of hearing.
Suppose that natives 1 and 3 spoke the same language. Then they would either have to consistently agree (if they had the same truth type) or consistently disagree (if they had divergent truth types). This is not given, hence the natives 1 and 3 speak different languages.
By the same reasoning natives 4 and 3 speak different languages. Hence natives 1 & 4 speak one language and are of the same truth type; natives 2 & 3 speak the other language and are of different truth types. That is: language speakers are split 2-2 and truth types are split 3-1.
Suppose that there were 3 liars. Then each liar would respond “no” to Hacha? (regardless of language). But there is only one “no” answer to Hacha?. Hence, there are three knights.
Now a knight would answer Wuf? with “no” (unless he were hard of hearing). It follows that native 3 is the liar and, in consideration of his response to Hacha?, must be a language A speaker. We therefore negate his response to Uf? and take the left path.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
No Subject	K Sengupta	2008-02-26 05:25:32
re: Eh?	Charlie	2008-02-21 22:42:19
Solution	Dej Mar	2008-02-21 22:00:51
Eh?	FrankM	2008-02-21 16:24:28
computer solution (spoiler)	Charlie	2008-02-21 15:42:21

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