It's an accident. She was writing with her pen (6), when she heard a sound in the house. She's american ( so she decided to take her gun (1), crush her cigarette (5), turn off the light to sneak on the burglar (2), take her glasses off because they're useless in the dark (7) and check the house by herself. When she found nothing, she lit a new cigarette to calm down (10) and came back, still in the dark. She was drunk (3) so she tripped on her slipper (9), tried to catch up on her stool but failed (1) and crushed her head agains the wall (4). There is no bullet hole in the wall, and this stain is not a brain-blowing-bullet-stain. The fall from a standing position and the rotation induced by the catch-up tentative explain the weird position of the body. Ther is no murderer and no suicid note. Case closed, Sherlock out.

i managed to fail this.