Arlene(A), Brenda(B), Cheryl(C), Daniel(D), Emmett(E) and Farley(F) stayed in a hotel.
1) Each stayed in a different one of six rooms as shown here, identified by his initials :
+----+----+----+----+
| | C | | E |
| B +----+ D +----+
| | | | |
+----+ +----+ +
| A | F |
+---------+---------+2) One of the six murdered one of the other five.
3) If the murderer and the victim stayed in rooms that did not border on each other, then Arlene or Farley was the victim.
4) If the murderer and the victim stayed in rooms that bordered on different numbers of rooms, then Brenda or Cheryl was the murderer.
5) If the murderer and the victim stayed in rooms that were different in size, then Daniel or Emmett was the murderer.
Who was the murderer? Who was the victim?
Assume the premise of (3): the murderer and victim stayed in rooms that did not border each other. Then we know the victim is A or F. That means B killed F or E killed A. In both cases the premise of (4) is true, so the murderer would be B or C. That's a contradiction, so the the premise of (3) must be false, and the murderer and victim DID border each other.
Assume the premise of (4): the murderer and the victim bordered on a different number of rooms. That means B or C was the murderer, which in turn means B killed A or C, or C killed B or A or D. Under this assumption the premise of (5) must be false because its consequence (D or E is the murderer) would contradict the fact that B or C is the murderer, so the murderer and victim must be in the same sized room. But that's a contradiction too, since none of the possibilities above have them both in the same sized room. So the premise of 4 must be false, and the murderer and victim border the same number of rooms.
The rooms and their bordering room count are: A-4, B-2, C-3, D-4, E-2, and F-3. So, combining the two conclusions of the previous 2 paragraphs (the murderer borders the victim, and the 2 rooms border the same number of other rooms), the only possibilities are : A killed D or D killed A. In both cases the rooms are of differing sizes, so (5) tells us D is the murderer.
So, Daniel killed Arlene.
Edited on August 11, 2005, 11:30 am
Edited on August 11, 2005, 11:31 am
Solution
