the room was locked and the door was impossible to break down so phoenix and gumshoe got into the crime scene by climbing down the chimney
the victim was stabbed in the chest and died instantly and the window was closed which can only be done from outside
they found the key in the victims pocket and used it to unlock the door
phoenix looked around and saw two long pieces of string near the door and a wheel near the window
he used these two to figure out how the killer escaped
basically the killer had both strings sticking out under the door he then locked the door and put the key in the victims pocket then opened the window and attacked one string to the hand so he could pull it shut later then another also on the handle but around the wheel as a pully so when he pulled that one the handle would close keep the window fully closed and cant be opened again from outside then the killer went back into the house and pulled on string A to close the window then string B to close the handle
"NOOOOOOOO dammit you got me" said the killer
the end