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?

1) Murderer and victim stayed in rooms that did not border each other then we have the following possibilities ( murderer  victim ) : EA – BF – CF

a) Murderer and victim stayed in rooms that bordered each other then we have the following possibilities:
AB – AC – AD – AF – BA – BC – CA – CB – CD – DA – DC – DE – DF – ED – EF – FD – FE

2) Murderer and victim stayed in rooms that bordered on different numbers of rooms then we have the following possibilities:
BA – BC – BD – BF – CA – CB – CD – CE

b)  Murderer and victim stayed in rooms that bordered on equal numbers of rooms then we have the following possibilities:
AD – DA - BE – EB – CF – FC

3) Murderer and victim stayed in rooms that were different in size then we have the following possibilities:
DA – DC – DE – DF – EA – EB – ED – EF

c)  Murderer and victim stayed in rooms that were equal in size then we have the following possibilities:
CE – EC – AF – FA – BD – DB

We have only 8 choices
                            
123 (rooms did not border each other, bordered by different no. of rooms & different in size)

12c (rooms did not border each other, bordered by different no. of rooms & equal in size)

1b3 (rooms did not border each other, bordered by equal no. of rooms & different in size)

1bc (rooms did not border each other, bordered by equal no. of rooms & equal in size)

a23 (rooms bordered each other, bordered by different no. of rooms & different in size)

ab3 (rooms bordered each other, bordered by equal no. of rooms & different in size)

abc (rooms bordered each other, bordered by equal no. of rooms & equal in size)

a2c (rooms bordered each other, bordered by different no. of rooms & equal in size)

Only ab3 lead to one solution

the only repeated possibility in the three givens was DA (Daniel murdered Arlene)

 

 

Posted by MSS on 2005-08-21 21:25:10