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 Hotel Room Rumination (Posted on 2013-12-26)
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?

 No Solution Yet Submitted by K Sengupta Rating: 3.5000 (2 votes)

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 Tedious analytical solution | Comment 2 of 5 |
Well, there are 3 possible cases:

a) The men stayed in 2 mediums and one other room
c) The men stayed in 2 larges and one other room
e) The men stayed in 2 smalls and one other room

For each of these there are four sub cases

a1) The men stay in 1,3,2.  Fails.  Nobody are near two ladies.
a2) The men stay in 1,3,4.  This works. Only 1 is near two ladies.
a3) The men stay in 1,3,5.  Fails.  Both 1 and 5 are near two ladies.
a4) The men stay in 1,3,6.  Fails.  Both 3 and 6 are near two ladies.
b1) The men stay in 5,6,1.  Fails.  Both 5 and 6 are near two ladies.
b2) The men stay in 5,6,2.  Fails.  Both 2 and 6 are near two ladies.
b3) The men stay in 5,6,3.  Fails.  Both 3 and 6 are near two ladies.
b4) The men stay in 5,6,4.  Fails.  Nobody are near two ladies.
c1) The men stay in 2,4,1.  Fails.  Both 2 and 4 are near two ladies.
c2) The men stay in 2,4,3.  Fails.  Both 2 and 3 are near two ladies.
c3) The men stay in 2,4,5.  Fails.  Neither of the small rooms are near two ladies.
c4) The men stay in 2,4,6.  Fails.  Both 2 and 4 are near two ladies.

The only solution is that the mean are in 1,3, and 4.  Since none of these are large rooms, Andy is the liar.

Well, that was tedious.  Maybe I should have used a computer.

 Posted by Steve Herman on 2013-12-27 01:12:56

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