Blackmail or Something Kinder
Test the three theories of the cottage against the three facts every theory had to explain.
The same facts fed three different stories. Score each theory against what it must account for — then see which one the door opened on.
Drawn from The Yellow Face (The Memoirs of Sherlock Holmes, 1893) — read the summary & analysis, or try The Norbury File, this story's game. More at the Game Room and the tool bench.