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?

So I just signed up and I've been reading through the other solutions - namely the popular Daniel killed Arlene. Lots of different ways to get it but I got something different...which is that Cheryl killed Farley.

Basically, my first step was to determine all of the pairs that applied to all the rules. (order isn't important)

3) AE, BD, BF, BE, CF, CE*, DB*, EA, EB**, EC, FB, FC**
4) EC, DB, AF
5) FC, EB, AD

*- Rules 3+4 both apply
**- Rules 3+5 both apply

So we're left with CE, DB, EB, or FC as possible outcomes that meet 2/3 of the rules. Of those 4 combinations, only Farley can possibly be a victim. Therefore, Cherl kills Farley.

Posted by chris on 2005-08-17 06:55:27