In Hamlet, what trick is Reynaldo supposed to use to get information about Laertes?
In Act Two, Scene 1, Polonius employs Reynaldo to travel to France and begin asking around for his son, Laertes. Polonius instructs Reynaldo to pretend to be Laertes' friend and begin to make up unflattering stories about Laertes by mentioning that he is a party animal, gambler, and alcoholic. Polonius wants Reynaldo to mention Laertes' faults lightly in hopes that a French citizen will recognize Laertes and reveal his true behavior. This "plan" is a bit ridiculous but is in alignment with Polonius' character throughout the play. Polonius is simply curious if Laertes is behaving himself and wants to find out in a rather roundabout way. Reynaldo agrees to travel to France and learn about Laertes' behavior through indirect, dishonest means. He is prepared to lie about Laertes in hopes that a French citizen will agree and confirm Laertes' bad behavior.
It isn't so much of a trick as just passive-aggressive information gathering. At Polonious' behest, Reynaldo (who has just thirteen lines in the entire play, by the way) is sent off to Paris to find out if Laeretes is behaving properly, or at least in the way his father has deemed acceptable. Polonius instructs Reynaldo to inquire about his activites from other Danes ("Danskers") in the city who can provide this information.
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Polonius tells him (lines 20-35 in my Arden) to slander Laertes to people who know him so that the truth will come out. He says that if Laertes is actually good, people who know him will protest and say that Reynaldo is not speaking the truth, but if the lies Reynaldo spreads have some truth in them, then the people he is talking to will open up more and tell more juicy tidbits. So by slander he will get more information than just by asking around.