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?

The program:

DATA ak,al,bk,bl
FOR i = 1 TO 4: READ typ$(i): NEXT
CLS

FOR n1 = 1 TO 4
 SELECT CASE typ$(n1)
   CASE "ak"
    q$(1, 1) = "f": q$(3, 1) = "t": q$(5, 1) = "t"
   CASE "al"
    q$(1, 1) = "t": q$(3, 1) = "f": q$(5, 1) = "f"
   CASE "bk"
    q$(2, 1) = "f": q$(4, 1) = "t": q$(6, 1) = "t"
   CASE "bl"
    q$(2, 1) = "t": q$(4, 1) = "f": q$(6, 1) = "f"
 END SELECT

FOR n2 = 1 TO 4
 SELECT CASE typ$(n2)
   CASE "ak"
     q$(3, 2) = "f": q$(5, 2) = "t"
   CASE "al"
     q$(3, 2) = "t": q$(5, 2) = "f"
   CASE "bk"
     q$(4, 2) = "f": q$(6, 2) = "t"
   CASE "bl"
     q$(4, 2) = "t": q$(6, 2) = "f"
 END SELECT

FOR n3 = 1 TO 4
 SELECT CASE typ$(n3)
   CASE "ak"
    q$(1, 3) = "t": q$(3, 3) = "t": q$(5, 3) = "f"
   CASE "al"
    q$(1, 3) = "f": q$(3, 3) = "f": q$(5, 3) = "t"
   CASE "bk"
    q$(2, 3) = "t": q$(4, 3) = "t": q$(6, 3) = "f"
   CASE "bl"
    q$(2, 3) = "f": q$(4, 3) = "f": q$(6, 3) = "t"
 END SELECT

FOR n4 = 1 TO 4
 SELECT CASE typ$(n4)
   CASE "ak"
    q$(1, 4) = "f": q$(3, 4) = "t": q$(5, 4) = "t"
   CASE "al"
    q$(1, 4) = "t": q$(3, 4) = "f": q$(5, 4) = "f"
   CASE "bk"
    q$(2, 4) = "f": q$(4, 4) = "t": q$(6, 4) = "t"
   CASE "bl"
    q$(2, 4) = "t": q$(4, 4) = "f": q$(6, 4) = "f"
 END SELECT

 good = 1
 REDIM cons$(6)
 FOR i = 1 TO 6
  IF i <> 4 THEN
   FOR spkr = 1 TO 4
     IF q$(i, spkr) > "" THEN
       IF cons$(i) > "" AND cons$(i) <> q$(i, spkr) THEN good = 0: EXIT FOR
       cons$(i) = q$(i, spkr)
     END IF
   NEXT spkr
  END IF
  IF good = 0 THEN EXIT FOR
 NEXT
 IF good THEN
  IF cons$(6) = "t" AND RIGHT$(typ$(n2), 1) <> "k" THEN good = 0
  IF cons$(6) = "f" AND RIGHT$(typ$(n2), 1) = "k" THEN good = 0
  IF cons$(2) = "t" THEN
    IF typ$(n1) = "ak" OR typ$(n2) = "ak" OR typ$(n3) = "ak" OR typ$(n4) = "ak" THEN
      good = 0
    END IF
  END IF
  FOR spkr = 1 TO 4
   IF q$(4, spkr) = "f" THEN
     IF RIGHT$(typ$(n1), 1) = "k" AND spkr <> 1 THEN good = 0
     IF RIGHT$(typ$(n2), 1) = "k" AND spkr <> 2 THEN good = 0
     IF RIGHT$(typ$(n3), 1) = "k" AND spkr <> 3 THEN good = 0
     IF RIGHT$(typ$(n4), 1) = "k" AND spkr <> 4 THEN good = 0
   END IF
  NEXT
  IF good THEN
    FOR spkr = 1 TO 4
     IF q$(4, spkr) = "t" THEN
       good = 0
       IF RIGHT$(typ$(n1), 1) = "k" AND spkr <> 1 THEN good = 1
       IF RIGHT$(typ$(n2), 1) = "k" AND spkr <> 2 THEN good = 1
       IF RIGHT$(typ$(n3), 1) = "k" AND spkr <> 3 THEN good = 1
       IF RIGHT$(typ$(n4), 1) = "k" AND spkr <> 4 THEN good = 1
     END IF
     IF good = 0 THEN EXIT FOR
    NEXT
  END IF

  IF good THEN
    PRINT typ$(n1); " "; typ$(n2); " "; typ$(n3); " "; typ$(n4); "   ";
    FOR i = 1 TO 6
     IF cons$(i) = "" THEN
      PRINT "-";
     ELSE
      PRINT cons$(i);
     END IF
    NEXT
  END IF
 END IF

 FOR i = 1 TO 6
   q$(i, 4) = ""
 NEXT i
NEXT n4

 FOR i = 1 TO 6
   q$(i, 3) = ""
 NEXT i
NEXT n3

 FOR i = 1 TO 6
   q$(i, 2) = ""
 NEXT i
NEXT n2

 FOR i = 1 TO 6
   q$(i, 1) = ""
 NEXT i
NEXT n1

finds:

bk ak al bk   fff-tt

meaning

Native 1 speaks B and is a Knight.
Native 2 speaks A and is a Knight.
Native 3 speaks A and is a Liar.
Native 4 speaks B and is a Knight.

The correct answers to the six questions, in the order presented are:
false
false
false
indeterminate (but in fact true for each speaker)
true
true

Since the penultimate question's correct answer is "true", you can indeed reach the treasure by taking the left path.

Posted by Charlie on 2008-02-21 15:42:21