The Sunday Morning Mystery

A man was found murdered on Sunday morning. His wife immediately called the police. The police questioned the wife and staff, who provided their alibis:

• The Wife said she was sleeping.
• The Cook was cooking breakfast.
• The Gardener was picking vegetables.
• The Maid was getting the mail.
• The Butler was cleaning the closet.

The police instantly arrested the murderer. Who did it, and how did they know?