The Peacock Feather Murders aka The Ten Teacups by Carter Dickson
Mr Vance Keating a prodigal adventurer is on the lookout for his next kick, and it comes in the form of a secret society called the "Ten Teacups". Keating receives a note inviting him to the meeting of the teacups. Chief Inspector Masters also gets a note telling him about the meeting of the Ten Teacups. This makes Masters very nervous, why? because the last time there was a meeting of the ten teacups someone had been murdered under enigmatic circumstances.
Keating visits an abandoned house for the meeting, the police follow Keating and watch the empty house clandestinely. Very soon shots are fired from inside the house and the police found Mr Keating dead, lying next to a table which has ten teacups arranged in a circular manner. Keating has been shot through the back of his head and spine. The Police search the whole house and not a living soul is found. No one came inside the house, no one went out. How did Mr Keating managed to get shot?