Three people decide to go out for burgers. They are either Knights, which always tell the truth, Knaves, which tell truths and lies in an alternating pattern, or Liars, which always tell lies.

They each want a burger, and want to get 4 toppings from the list of 7 (ketchup, mustard, onions, relish, tomato, cheese, lettuce) and give their order as follows:

A: I want ketchup, mustard, onions, lettuce, relish.

B: A wants tomato too, and he doesn't want mustard. I want ketchup, tomato, cheese, lettuce.

C: B doesn't want ketchup, and he doesn't want mustard. A doesn't want relish. I want mustard, tomato, cheese, lettuce.

After giving the orders to the burger cooker, he figures out what they want.(as anyone who can cook well must be really intelligent)

If all three people didn't all want a certain topping, what do the three people actually want as their four toppings on their burger?

(Note: I placed commas and periods to remind that each item/statement separated by commas is a separate statement.)

(In reply to A consistent set by Charlie)

The following are the possibilities, each set listing, for each of the buddies, the initials of the four condiments he wanted, plus the number of true odd-numbered statements he made and the number of true even-numbered statements he made:

kort 3 0
ktcl 3 3
kmoc 0 3

kort 3 0
ktcl 3 3
kmrc 0 3

kort 3 0
ktcl 3 3
morc 0 3

In each instance A and C were knaves and B a knight. In each instance A had ketchup, onions, relish and tomato, while B had ketchup, tomato, cheese and lettuce. C does indeed have mustard and cheese in each instance, but could have any pair out of relish, ketchup and onions.

The program to find this is:
DECLARE FUNCTION present! (person!, condi$)
DECLARE SUB vary (person!)
DIM SHARED list$
list$ = "kmortcl"
DIM SHARED st$(3), p1(3), p2(3)

vary 1

FUNCTION present (person, condi$)
  IF INSTR(st$(person), condi$) > 0 THEN present = 1: ELSE present = 0
END FUNCTION

SUB vary (person)
  st$(person) = SPACE$(4)
  FOR i = 1 TO 4
   MID$(st$(person), 1, 1) = MID$(list$, i, 1)
   FOR j = i + 1 TO 5
    MID$(st$(person), 2, 1) = MID$(list$, j, 1)
    FOR k = j + 1 TO 6
     MID$(st$(person), 3, 1) = MID$(list$, k, 1)
     FOR l = k + 1 TO 7
      MID$(st$(person), 4, 1) = MID$(list$, l, 1)
      IF person = 1 THEN
        p1 = present(person, "k") + present(person, "o") + present(person, "r")
        p2 = present(person, "m") + present(person, "l")
        IF p1 <> 0 AND p1 <> 3 OR p2 <> 0 AND p2 <> 2 THEN GOTO notThis
        p1(1) = p1: p2(1) = p2
      END IF
      IF person = 2 THEN
        p1 = present(1, "t") + present(person, "k") + present(person, "c")
        p2 = 1 - present(1, "m") + present(person, "t") + present(person, "l")
        IF p1 <> 0 AND p1 <> 3 OR p2 <> 0 AND p2 <> 3 THEN GOTO notThis
        p1(2) = p1: p2(2) = p2
      END IF
      IF person = 3 THEN
        p1 = 1 - present(2, "k") + 1 - present(1, "r") + present(person, "t") + present(person, "l")
        p2 = 1 - present(2, "m") + present(person, "m") + present(person, "c")
        IF p1 <> 0 AND p1 <> 4 OR p2 <> 0 AND p2 <> 3 THEN GOTO notThis
        p1(3) = p1: p2(3) = p2
      END IF
      IF person < 3 THEN
        vary person + 1
      ELSE
        FOR p = 1 TO 3
          PRINT st$(p), p1(p), p2(p)
        NEXT
        PRINT
      END IF

notThis:
     NEXT
    NEXT
   NEXT
  NEXT
END SUB

Posted by Charlie on 2003-11-28 01:39:27