The owner of the mansion has been murdered. The visitors to the mansion were Allen, Bixby, and Crain.

1. The murderer, who was one of the three visitors, arrived at the mansion later than at least one of the other two visitors.
2. A detective, who was one of the three visitors, arrived at the mansion earlier than at least one of the other two visitors.
3. The detective arrived at the mansion at midnight.
4. Neither Allen nor Bixby arrived at the mansion after midnight.
5. The earlier arriver of Bixby and Crain was not the detective.
6. The later arriver of Allen and Crain was not the murderer.

Who was the murderer?

DECLARE SUB permute (a$)
CLS
arr$ = "abc": h$ = arr$
DO
  FOR murd = 2 TO 3 'order of arrival
    FOR det = 1 TO 2
      bm$ = LEFT$(arr$, det - 1)
      am$ = MID$(arr$, det + 1)
      good = 1
      IF INSTR(am$, "a") > 0 OR INSTR(am$, "b") > 0 THEN good = 0
      b = INSTR(arr$, "b")
      c = INSTR(arr$, "c")
      IF b < c THEN early = b:  ELSE early = c
      IF early = det THEN good = 0
      a = INSTR(arr$, "a")
      IF a > c THEN late = a:  ELSE late = c
      IF late = murd THEN good = 0
      IF good THEN PRINT arr$, murd; det
    NEXT det
  NEXT murd

  permute arr$
LOOP UNTIL arr$ = h$

finds

bac            2  2

meaning they arrived in the order Bixby, Allen, Crain, and that both the murderer and the detective were (was) the second to arrive: Allen.

So Allen was the murderer (and also the detective).

Posted by Charlie on 2013-01-24 13:33:52