Esther is engaged. Her fiancé is either Arthur, Barton, Claude, or Dexter.

1. Each of the four men and Esther is a knight or a liar.
2. Arthur says: "Exactly one of us four men is a knight."
3. Barton says: "Exactly one of us four men is a liar."
4. Claude says: "Arthur or Barton is Esther’s fiancé."
5. Esther says: "My fiancé and I are either both knights, or both of us are liars."

Who is Esther's fiancé?

FOR fiance = 1 TO 4
  FOR a = 0 TO 1
  FOR b = 0 TO 1
  FOR c = 0 TO 1
  FOR d = 0 TO 1
  FOR e = 0 TO 1
    totkt = a + b + c + d
    totliar = 4 - totkt
    IF (a = 1) = (totkt = 1) THEN
      IF (b = 1) = (totliar = 1) THEN
        IF (c = 1) = (fiance = 1 OR fiance = 2) THEN
          SELECT CASE fiance
            CASE 1
              f = a
            CASE 2
              f = b
            CASE 3
              f = c
            CASE 4
              f = d
          END SELECT
          IF (e = 1) = (e = f) THEN
            PRINT MID$("ABCD", fiance, 1), a; b; c; d; e
          END IF
        END IF
      END IF
    END IF
  NEXT
  NEXT
  NEXT
  NEXT
  NEXT
NEXT fiance

finds

B              0  1  1  1  0
B              0  1  1  1  1

meaning

Esther's fiance is Barton. Arthur is a liar. Everyone else is a knight, except for Esther, who could be either a liar or a knight.

Posted by Charlie on 2013-03-25 11:29:29