Death invites you

Did Harold Vickers, the best-selling author of impossible crimes foresee his own death, or did he possibly even arrange it? When two guests knock on her door with dinner invitations, Mrs. Vickers is dumbfounded, for her husband has been locked in his study for several days. Yet there are sounds and cooking smells emanating from the room, and when the door is broken down, a dead body resembling her husband is slumped over the fully-laden dinner table with its hands and face in a pan in which the oil is still boiling. The room is sealed and nobody could have got out of the room without being seen, yet the food is still cooking. A mysterious half-filled bowl of water sits beneath the shuttered windows.