Perfect crime
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A perfect crime is a crime committed so carefully that no evidence is apparent, and the culprit cannot be traced.
Since evidence must be matched to find the culprit, the best way to commit a perfect crime appears to be one outside the circle of suspects that police can question. In practice, however, those who commit serious crimes are usually linked to the victim in some way, and the police know from experience which people to question. A crime based on a chance meeting, such as a rape followed by murder or a mugging, can go undetected if no connection remains. A rapist will, however, most likely leave his DNA in the form of semen and sustain minor injuries that might betray him. A mugger will take the belongings of his victim which can give him away. Moreover, the police will have the fingerprints and DNA of convicted felons on file. Many successful criminals spend stolen money too freely, or brag about their crime.
Thus a murder committed by somebody who had never before met the victim, has no criminal record, steals nothing and doesn't tell anyone might easily be a perfect crime, but it might be apparently motiveless.
The case of Leopold and Loeb is an American case that was almost a perfect crime, but they overlooked one small detail, and both perpetrators landed in prison.
Would-be perfect crimes are a popular subject in crime fiction and movies. They include Double Indemnity, Strangers on a Train, The Postman Always Rings Twice, Witness for the Prosecution, and Dial M for Murder.
No doubt many perfect crimes may have been committed and remain undiscovered. It should also be noted that police are fallible, and some crimes might have been solved if the police had better resources at their disposal or had not overlooked vital evidence. In the well-known case of Jack the Ripper, plenty of evidence was left at the crime scenes, but the crimes were never solved.
Some crimes such as the Zodiac murders of the late 1960s, the Tylenol scare of 1982, and the Diane Suzuki case of 1985 are referred to as perfect, but the possibility always remains that a culprit will ultimately be identified.