The Case of Miss Elliott by Baroness Emma Orczy.  
A sequel to the stories published in The Old Man in the Corner, this second book in the series includes twelve new mysterious cases that The Old Man in the Corner unravels over his milk and cheesecake at the ABC Tea Shop, all the while tying and untying knots in a bit of string. His audience is Polly Burton, a young journalist, who has to begrudging admit that the Old Man's solutions are indeed plausible explanations to these cases which have baffled both the police and coroner. Orzy's Old Man is an early 20th century example of the armchair detective.