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?
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Submitted by pcbouhid
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Rating: 3.4444 (18 votes)
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Solution:
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From (2), there was only one murderer. So, both hypotheses in (4) and (5) are false (Case I) or either one of the hypothesis of (4) and (5) is false (Cases II and III).
Case I : Both hypotheses in (4) and (5) are false.
Then the murderer and the victim stayed in rooms that bordered on the same number of rooms (from (4)), and that were the same size (from (5)). This situation is impossible, watching the layout.
Case II : The hypothesis in (4) is true and the hypothesis in (5) is false.
Then the murderer and the victim stayed in rooms that bordered on different numbers of rooms (from (4)), and that were the same size (from (5)). Then, from (1), either : a) Arlene or Farley was the victim and the other was the murderer, b) Brenda or Daniel was the victim and the other was the murderer, or c) Cheryl or Emmett was the victim and the other was the murderer. From (4), (a) is impossible and, from (3), (b) and (c) are impossible.
So, Case III is the correct one.
Case III : The hypothesis in (4) is false and the hypothesis in (5) is true.
Then the murderer and the victim stayed in rooms that bordered on the same number of rooms (from (4)) and that were different in size (from (5)). Then, from (1), either : d) Arlene or Daniel was the victim and the other was the murderer, e) Brenda or Emmett was the victim and the other was the murderer, or f) Cheryl or Farley was the victim and the other was the murderer. From (5), f) is impossible and, from (3), e) is impossible. Then d) is correct and, from (5), Daniel was the murderer. So, Arlene was the victim.
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