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Murderous Performer (Posted on 2013-03-22) Difficulty: 3 of 5
+---+-------+---+
| 1 |   2   |   |
+---+---+---| 3 |  
|   4   | 5 |   |
+-------+---+---+
Vera,one of the performers in a play,was murdered in her dressing room. The following facts refers to the dressing rooms shown above. Each of the five performers in the play - Vera, Adam, Babe, Clay and Dawn - had his or her own dressing room.
  1. The killer's dressing room and Vera's dressing room border on the same number of rooms.
  2. Vera's dressing room borders on Adam's dressing room and on Babe's dressing room.
  3. Clay's dressing room and Dawn's dressing room are the same size.
  4. Babe's dressing room does not border on Clay's dressing room.
  5. The five rooms come in precisely two distinct sizes. (For example, rooms 2, 3 and 4 have the same size.)
Who killed Vera?

No Solution Yet Submitted by K Sengupta    
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Solution The butler did it (spoiler) | Comment 1 of 3
Room 1 and 3 border on 2 rooms, Room 4 and 5 border on 3, and Room 2 borders on 4.

So, from clue 1, Vera is not in Room 2. 

So where is Vera?  Not in rooms 1 or 3, since either of these put A and B in the two adjacent rooms, and C and D in the two remaining rooms which are of different sizes, thus violating clue 3.

Also, V is not in room 5, because all of the bordering rooms are large.  Once A and B are accounted for, the C and D rooms are again different sizes, in violation of clue 3. 

So, V must be in room 4, and in order not to violate clue 3, A and B are in the small rooms.  Then D is in room 2 (from clue 4), so C is in Room 3.  Then B is in room 1 (from clue 4) so A is in room 5.

Thus, The only arrangement that works is

Room       Borders on
 1       B      2 rooms 
 2       D      4 rooms
 3       C      2 rooms
 4       V      3 rooms
 5       A      3 rooms

And A is the killer, from clue 1

  Posted by Steve Herman on 2013-03-22 14:53:37
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