Alex, Bert and Carl are all different types. One is a knave, one is either a knight or liar, and one is a doubleton. A doubleton is a type similar to a knave, except that a doubleton's truth pattern is two true statements followed by two false statements repeatedly.

From the statements below, determine who is the doubleton.

Alex:
1. I am a knight.
2. Bert is the doubleton.
3. Carl is the knave.

Bert:
1. I am the knave.
2. Carl is the doubleton.
3. Alex is a liar.

Carl:
1. I am a liar.
2. Alex is the doubleton.
3. Bert is a knight.

Alex is the doubleton.
Bert is the liar.
Carl is the knave.

The only two true statements are Alex's last and Carl's second.

DECLARE SUB permute (a$)
FOR kv = 1 TO 2 ' truth first or lie first
 FOR cons = 3 TO 4 ' knight or liar
  FOR db = 5 TO 8 ' start w/ 1st of 2 truths, 2nd of 2 truths, 1st of 2 lies, 2nd of 2 lies
    s$ = LTRIM$(STR$(kv)) + LTRIM$(STR$(cons)) + LTRIM$(STR$(db))
    h$ = s$
    DO
      good = 1
      a = VAL(LEFT$(s$, 1)): b = VAL(MID$(s$, 2, 1)): c = VAL(RIGHT$(s$, 1))
      IF a = 1 OR a = 5 OR a = 6 THEN good = 0
      SELECT CASE a
        CASE 2, 3, 5, 8
         IF b < 5 THEN good = 0
        CASE ELSE
         IF b >= 5 THEN good = 0
      END SELECT
      SELECT CASE a
        CASE 1, 3, 7, 8
         IF c > 2 THEN good = 0
        CASE ELSE
         IF c <= 2 THEN good = 0
      END SELECT

      IF b = 2 OR b = 3 OR b = 5 OR b = 6 THEN good = 0
      SELECT CASE b
        CASE 2, 3, 5, 8
         IF c < 5 THEN good = 0
        CASE ELSE
         IF c >= 5 THEN good = 0
      END SELECT
      SELECT CASE b
        CASE 1, 3, 7, 8
         IF a <> 4 THEN good = 0
        CASE ELSE
         IF a = 4 THEN good = 0
      END SELECT

      IF c = 1 OR c = 3 OR c = 5 OR c = 6 THEN good = 0
      SELECT CASE c
        CASE 2, 3, 5, 8
         IF a < 5 THEN good = 0
        CASE ELSE
         IF a >= 5 THEN good = 0
      END SELECT
      SELECT CASE c
        CASE 1, 3, 7, 8
         IF b <> 3 THEN good = 0
        CASE ELSE
         IF b = 3 THEN good = 0
      END SELECT

      IF good THEN PRINT s$

      permute s$
    LOOP UNTIL h$ = s$
  NEXT
 NEXT
NEXT

The output is 742, which in the code expressed in the comments (after the apostrophes), represents:

7: doubleton who starts with the first of two lies
4: liar
2: knave who starts out with a lie

Edited on September 20, 2007, 10:34 am

Posted by Charlie on 2007-09-20 10:27:06