Perfect crime
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A perfect crime is a crime so well-committed that no evidence is left, and no solution by the police is possible. The concept of the "perfect crime" requires a serious crime that is fully investigated by the police, the courts, investigative journalists and even investigators hired by the wronged party (murder is most commonly named). Petty misdeeds that are not truly investigated (parking violations, shoplifting) do not "count". Crimes that cannot be investigated for legal reasons do not count, either (eg. a crime that cannot be solved because a foreign government refuses to cooperate in an investigation against one of its citizens, or because a suspect has legal immunity, or because an action is dubious, but not truly illegal).
Since evidence must be matched to find the culprit, the best way to commit a perfect crime appears to be outside of the circle of suspects that police can examine. In practice, however, those who commit serious crimes are typically linked to the victim in some way, and the police knows from experience what 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 some minor injuries that can 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 committed the error of spending stolen money too freely, or told the secret to the wrong people.
So, a murder committed by somebody who had never met the victim, has no criminal record, takes nothing and keeps his mouth closed could easily be the perfect crime, but it would be pointless.
The case of Leopold and Loeb is an American case that was almost a perfect crime, but a small detail botched it, and both perpetrators landed in prison.
Would-be perfect crimes are a popular subject in the movies, and many have been made. A few include Double Indemnity, The Postman Always Rings Twice, Witness for the Prosecution, and Dial M for Murder.
Note that many perfect crimes may have been committed, if there were no public or media knowledge of them. It should also be noted that police are fallible, and some never-solved crimes would have been solved, if the police had better resources at their disposal. In the well-known case of Jack the Ripper, evidence was left, but the crimes were never solved.
Some crimes such as the Tylenol scare of 1982 and the Diane Suzuki case of 1985 are referred to as perfect, but a possibility always remains that a culprit will ultimately be identified.