The inhabitants of the planet Realmazure are Knights, Pretenders, Prevaricators or Liars. All the statements by a Knight are true, a Pretender will tell precisely one true statement, a Prevaricator will tell precisely two true statements, and all the statements made by a Liar will be false.

Four inhabitants J, K, L and M of Realmazure were busy in a conversation, when another visitor from a neighboring planet stopped by and asked each of them their identity. They said:

Inhabitant J

1. M is a Pretender.
2. K’s first statement is true.
3. M’s third statement is true.

Inhabitant K

1. J is a not a Knight.
2. J’s first statement is true.
3. M is a Prevaricator.

Inhabitant L

1. J is a Prevaricator.
2. M is a Liar.
3. K’s second statement is false.

Inhabitant M

1. L’s third statement is true.
2. I am a Pretender.
3. J is a Knight.

Determine the type of each of the four inhabitants in terms of the above statements.

(In reply to solution by Daniel)

But K1 and K2 are both true, so K is a Prevaricator rather than a Pretender.

Truth values and speaker types:

   J             K             L             M
1  1  0       1  1  0       1  0  0       0  1  0
   2             2             1             1

where 1 is true and 0 false on the first line and 2 indicates prevaricator and 1 is pretender on the second line.

DECLARE SUB choose (s!)
DIM SHARED stmt(12), typ(4)

choose 1

SUB choose (s)
 FOR tr = -1 TO 0  ' -1 is true
   stmt(s) = tr
   SELECT CASE s
     CASE 3
      typ(1) = 0
      FOR i = 1 TO 3
        typ(1) = typ(1) + ABS(stmt(i))
      NEXT
      choose s + 1
     CASE 6
      typ(2) = 0
      FOR i = 4 TO 6
        typ(2) = typ(2) + ABS(stmt(i))
      NEXT
      choose s + 1
     CASE 9
      typ(3) = 0
      FOR i = 7 TO 9
        typ(3) = typ(3) + ABS(stmt(i))
      NEXT
      choose s + 1
     CASE 12
      typ(4) = 0
      FOR i = 10 TO 12
        typ(4) = typ(4) + ABS(stmt(i))
      NEXT
      good = 1
      FOR j = 1 TO 1
        IF stmt(1) <> (typ(4) = 1) THEN good = 0: EXIT FOR
        IF stmt(2) <> (stmt(4) = -1) THEN good = 0: EXIT FOR
        IF stmt(3) <> (stmt(12) = -1) THEN good = 0: EXIT FOR
      
        IF stmt(4) <> (typ(1) <> 3) THEN good = 0: EXIT FOR
        IF stmt(5) <> (stmt(1) = -1) THEN good = 0: EXIT FOR
        IF stmt(6) <> (typ(4) = 2) THEN good = 0: EXIT FOR

        IF stmt(7) <> (typ(1) = 2) THEN good = 0: EXIT FOR
        IF stmt(8) <> (typ(4) = 0) THEN good = 0: EXIT FOR
        IF stmt(9) <> (stmt(5) = 0) THEN good = 0: EXIT FOR

        IF stmt(10) <> (stmt(9) = -1) THEN good = 0: EXIT FOR
        IF stmt(11) <> (typ(4) = 1) THEN good = 0: EXIT FOR
        IF stmt(12) <> (typ(1) = 3) THEN good = 0: EXIT FOR
      NEXT
      IF good THEN
        FOR j = 1 TO 12
          PRINT -stmt(j);
          IF j MOD 3 = 0 THEN PRINT "     ";
        NEXT: PRINT
        FOR j = 1 TO 4: PRINT typ(j); : NEXT: PRINT
        PRINT
      END IF

     CASE ELSE
      choose s + 1
   END SELECT
 NEXT
END SUB

 

Posted by Charlie on 2009-09-23 12:53:47