COPENHAGEN—Denmark, the home of Lego, once pioneered the plastic toy. Now one of the country’s biggest toy retailers wants to ditch plastic and go back to wood and other natural materials. Variety-store chain Flying Tiger Copenhagen has grown rapidly across Europe by offering an eclectic mix of cheap toys, gadgets and household items that are often made of plastic. Typical items include a remote-controlled dinosaur for roughly $19, a set of six stick-on mustaches for $4 or a pair of fluffy unicorn slippers for $13.

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