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:
A: Do more natives speak language A than language B?
B: Are all knights language B speakers?
A:Are there more liars than language A speakers?
B:Would any of the other natives tell me the truth?
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?
Using a spreadsheet of truth tables, I was able to eliminate all but one possible combination, thus....
The correct path to follow is the left path.
Native 1 is a Knight who speaks language B.
Native 2 is a Knight who speaks language A.
Native 3 is a Liar who speaks language A.
Native 4 is a Knight who speaks language B.
As we are really only concerned with the answer to "Uf?" in language A, we can derive the truth from the lie of Native 3's response. His answer "NO" to the question "Can I reach the treasure by taking the left path?" tells us the left path is the correct path. The other language A speaker, Native 2, in answer, seemed to agree with this assessment even though he may have been actually repeating his answer to the question "Wuf?"
Of course, if the treasure hunter finds hisself facing the deadly sphinx, we can guess we incorrectly translated the Uwalahooloon words YES and NO.
Posted by Dej Mar
on 2008-02-21 22:00:51