Alex, Bert, and Carl are each a knight, knave or a liar. Three people asked them what their types were.

The first person got the following responses:
Alex:Carl is a liar.
Bert:Alex is a knight.
Carl:Bert is a knave.

The second person got the following responses but forgot who made which ones:
Exactly one of us is a knight.
Exactly one of us is a knave.
Exactly one of us is a liar.
(Alex, Bert, and Carl each made one of the statements.)

The third person got the following responses:
Alex:Bert is a knave.
Bert:Carl is a liar.
Carl:Alex is a knight.

What types are Alex, Bert, and Carl?

The computer program I used was:

DECLARE SUB permute (a$)
'1=Kt 2=Kv truth first 3=Kv lie first 4=L
FOR a = 1 TO 4
 SELECT CASE a
  CASE 1
   kt = 1
  CASE 2, 3
   kv = 1
  CASE 4
   l = 1
 END SELECT
 FOR b = 1 TO 4
  SELECT CASE b
   CASE 1
    kt = kt + 1
   CASE 2, 3
    kv = kv + 1
   CASE 4
    l = l + 1
  END SELECT
  FOR c = 1 TO 4
   SELECT CASE c
    CASE 1
     kt = kt + 1
    CASE 2, 3
     kv = kv + 1
    CASE 4
     l = l + 1
   END SELECT
   s$ = LTRIM$(STR$(a)) + LTRIM$(STR$(b)) + LTRIM$(STR$(c))
   h$ = s$
   DO
     good = 1
     SELECT CASE a
      CASE 1, 2
       IF c <> 4 THEN good = 0
       IF b < 2 OR b > 3 THEN good = 0
      CASE 3, 4
       IF c = 4 THEN good = 0
       IF b > 1 AND b < 4 THEN good = 0
     END SELECT
     SELECT CASE b
      CASE 1, 2
       IF a <> 1 THEN good = 0
       IF c <> 4 THEN good = 0
      CASE 3, 4
       IF a = 1 THEN good = 0
       IF c = 4 THEN good = 0
     END SELECT
     SELECT CASE c
      CASE 1, 2
       IF b < 2 OR b > 3 THEN good = 0
       IF a <> 1 THEN good = 0
      CASE 3, 4
       IF b > 1 AND b < 4 THEN good = 0
       IF a = 1 THEN good = 0
     END SELECT
    
     x = VAL(MID$(s$, 1, 1))
     y = VAL(MID$(s$, 2, 1))
     z = VAL(MID$(s$, 3, 1))

     SELECT CASE x
      CASE 1, 3
       IF kt <> 1 THEN good = 0
      CASE 2, 4
       IF kt = 1 THEN good = 0
     END SELECT
     SELECT CASE y
      CASE 1, 3
       IF kv <> 1 THEN good = 0
      CASE 2, 4
       IF kv = 1 THEN good = 0
     END SELECT
     SELECT CASE z
      CASE 1, 3
       IF l <> 1 THEN good = 0
      CASE 2, 4
       IF l = 1 THEN good = 0
     END SELECT

     IF good THEN PRINT a, b, c: PRINT s$

     permute s$
   LOOP UNTIL s$ = h$
   SELECT CASE c
    CASE 1
     kt = kt - 1
    CASE 2, 3
     kv = kv - 1
    CASE 4
     l = l - 1
   END SELECT
  NEXT c
  SELECT CASE b
   CASE 1
    kt = kt - 1
   CASE 2, 3
    kv = kv - 1
   CASE 4
    l = l - 1
  END SELECT
 NEXT b
 kt = 0: kv = 0: l = 0
NEXT a

END



with the output

 4             4             3
434

the key having been given in a comment in the program:

'1=Kt 2=Kv truth first 3=Kv lie first 4=L

A, B and C were liar, liar, knave respectively, and the sequence of speaking for the middle question was liar, truth-telling knave (as he lied in the first and third questions), liar. So the only truth that was told was by Carl the Knave, to the middle question, saying that only one was a liar.

Posted by Charlie on 2007-09-29 16:19:40