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In the first episode of BBC's Sherlock, "A Study In Pink" Sherlock insinuates a sexual encounter occurred between Sergeant Donovan and Anderson. He mentions something about Anderson's deodorant, and it vaporizing. Also the clear observations about Donovan's knees.

But how does he know Donovan had not been home when he first saw her? What was the connection he made about the deodorant? I really love Sherlock and the stories woven in it, but sometimes I don't understand many of Sherlock's more subtle deductions.

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Here's my take on this. Sherlock goes to the crime scene, smells the male deodorant Donovan's wearing (throughout the series it has been shown that he has a good nose for identifying perfumes and deodorants) and also observes her knees. She proceeds to annoy him by calling him a freak as well, but he doesn't have enough data yet to say anything to her until he meets Anderson who happens to be wearing the same deodorant. Then he correlates those data together.

As soon as he smells that, he puts the knees connection together with smell and deduces that Anderson's wife is out of town. To be honest, at that point he was more guessing than deducing until Anderson concludes his hypothesis saying "Don't tell me you worked that out? I bet someone told you that."

Once his hypothesis is going in the correct direction then he adds the finishing touch by illustrating how Donovan came over for a chat and managed to scrub the floor sarcastically at him.

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