Six people stayed in a hotel.

1. The six people were three men- Andy, Barry and Clint - and three ladies- Debra, Ellen and Francine.
2. Each stayed in a different one of six rooms arranged like this:

+------+------+------+------+
|      |      |      |      |
|      |  2   |      |   4  | 
|  1   +------+  3   |------+
|      |      |      |      |
|      |      |      |      |
+------+      +------+      | 
|             |             |
|      6      |       5     |
|             |             | 
+-------------+-------------+

3. Andy said: "I stayed in a large room."
4. Barry said: "I stayed in a medium-sized room."
5. Clint said: "I stayed in a small room."
6. Exactly one man lied.
7. Of the three rooms occupied by the men, only the room occupied by the man who lied bordered on exactly two of the rooms occupied by the ladies.

Who lied?

Options are two small rooms and another room, two medium rooms and another room and two large rooms and another room. So options are and liars could be any of the first two let say they are represented by x & y and last is z so the no of ladies adjacent to them are

• 2,4,3 x=2,y=2,z=1
• 2,4,1 x=2,y=2,z=1
• 2,4,5 x=3,y=1,z=2
• 2,4,6 x=2,y=2,z=3
• 1,3,2 x=1,y=3,z=1
• 1,3,4 x=2,y=3,z=1**
• 1,3,5 x=2,y=3,z=2
• 1,3,6 x=1,y=3,y=2
• 5,6,2 x=2,y=2,z=2
• 5,6,4 x=1,y=3,z=1
• 5,6,1 x=2,y=2,z=1
• 5,6,3 x=1,y=2,z=2

Hence its an option where the one who is in a large room is the liar hence Andy.

Posted by Salil on 2014-01-02 02:06:22