The owner of the mansion has been murdered. The visitors to the mansion were Allen, Bixby, and Crain.

- The murderer, who was one of the three visitors, arrived at the mansion later than at least one of the other two visitors.
- A detective, who was one of the three visitors, arrived at the mansion earlier than at least one of the other two visitors.
- The detective arrived at the mansion at midnight.
- Neither Allen nor Bixby arrived at the mansion after midnight.
- The earlier arriver of Bixby and Crain was not the detective.
- The later arriver of Allen and Crain was not the murderer.

Who was the murderer?

Well first, could two of the guests have arrived together?

Assume that last two arrive together. From (2), the detective arrived first. From (3), he arrived at midnight. But this contradicts (4), so the last two did not arrive together.

Assume that the first two arrived together. From (2) and (3), one of them was the detective and they arrived at midnight. From (4), Crain was the later visitor. From (1), the last guest was the murderer. But this contradicts (6), so the first two did not arrive together.

So, the three visitors arrived separately. When did the detective arrive? From (2), he did not arrive last. From (3) + (4), he did not arrive first. Therefore, the detective was the 2nd visitor, at midnight. From (4), Crain was the last visitor. From (5), Bixby arrived first, so Allen arrived 2nd.

And who was the murderer? From (6), it was not Crain.

From (1), it was not Bixby. So it must be Allen!

(Cool! I was really hoping the detective did it).

Final answer:

Allen, the detective and murderer, arrived at midnight.

Bixby arrived before midnight and Crain arrived after.

*Edited on ***January 24, 2013, 2:00 pm**