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In the Great Game,Sherlock was able to solve those murders only because Moriarty left him a clue.But it wouldn't have been possible without those right?
I'd like to know how Moriarty concealed all those killings to make them look like accidents.Even when Sherlock solved them,he couldn't prove that it was Moriarty.An now I'm beginning to believe that the guy we saw on TV known as Jim Moriarty isn't actually Moriarty but rather another guy working under the name of Moriarty and the real Moriarty is hiding himself.Or else he wouldn't kill himself on that rooftop.Suicide isn't so simpleHe's basically outsmarting Leopold and Loeb,and even Jack The Ripper...
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Maybe he didn´t exactly conceal them but left too few clues for the police to disclose his crimes?
And with some "willing participants" he had in the police, he could also arrange that some clues or evidence neatly disappeared.