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?

According to (3), the murderer and the victim were in adjoining rooms, and/or A or F was the victim. This allows the following (killer/victim) pairs: AB, AC, AD, AF, BA, BC, BF, CA, CB, CD, CF, DA, DC, DE, DF, EA, ED, EF, FA, FD, FE.

According to (4), the murderer and the victim were on rooms that bordered the same number of rooms, and/or B or C was the murderer: the possible pairs are AD, BA, BC, BD, BE, BF, CA, CB, CD, CE, CF, DA, EB, FC.

Finally, according to (5), the murderer and the victim were on rooms of the same size, and/or D or E was the murderer, allowing AD, BD, CE, DA, DB, DC, DD, DE, EA, EB, EC, ED, EF, FC.

The only pair that appears three times is DA, meaning that Daniel killed Arlene.

Posted by Federico Kereki on 2005-08-11 13:15:33