A Dead Man And A Pencil Riddle

there was a double appartment building with 100 flors. a woman living on the 100th floor was good friends with a man also living on the 100th floor Mr.Barker. the woman noticed that Mr.Barker hadnt come out of his room for about a week so the woman called the police to see why. when the police came to Mr.Barkers room he wouldnt awnser the door so the police had no choice but to knock the door down. when they did in the room was nothing but a broken pencil on the floor a dead man sitting in a chair with a bullet in his forehead and a locked door. the man in the chair was Mr.Barker.How did Mr Baker get shot if the Door was locked from the inside and noone was in the room. *HINT*think about the pencil.

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