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Step 1
Gather data by researching the crime. This entails both the method of the crime itself and the background of the victim. The crime scene often contains copious amounts of evidence as does the personal history surrounding it. What techniques were used to perpetrate the crime? Was a weapon used? Were other tools involved? How were they used--with precision and care or with extreme sloppiness? Who had access to the crime scene? Who had motivation to conduct the crime? Did the victim have any enemies? Was there someone close to him in a position to perpetrate the crime? As you collect these facts, you'll likely develop some plausible ideas explaining the overall crime.
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Step 2
Develop a hypothesis about how the crime was committed and who, specifically, may have committed it. Police officers often run through the series of events in their head in order to get a picture of what happened. They also work up a list of possible suspects based on plausible motive and access to the crime scene. A theft may have been committed by someone in debt, for example, while murder may have been revenge from an ex-lover. Such hypotheses are based on the basic facts gathered, but may not hold up once the details are more rigorously applied.
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Step 3
Test the hypothesis with the evidence gathered to see if it fits the cold, hard facts. This entails both examining the details on hand and speaking with any suspects or witnesses. For historic crimes, such as the Jack the Ripper murders, such testing may not be possible, which is why it's difficult to definitively solve such crimes unless new evidence comes to light. With more recent cases, it involves grilling suspects to see if their alibis check out, comparing forensic analysis to determine whether a given plan could have worked, searching for suspects if none can currently be found and tracking down any stolen objects if theft was involved. The going hypothesis rarely stands up intact to this process, but as possibilities are eliminated, new hypotheses arise that can be confirmed by continuing to check the facts.
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Step 4
Zero in on the suspect based on repeated experimentation. Sooner or later, the list of possible culprits will be eliminated, either because they had an alibi for the time of the crime, they don't possess the knowledge to conduct it, their motivation is lacking or none of the evidence is linked to them in any way. If Step 3 is successful, it leaves just one or two possible suspects, who can either be arrested if the evidence is strong enough or more thoroughly focused on until more evidence arises linking them to the crime. Again, with historic cases, this may be more difficult because absolute proof doesn't exist. Nevertheless, repeated examination and experimentation with the evidence inevitably leads toward a single conclusion.












