In the novel Paper Towns, the conflict is twofold. Firstly, the external conflict—which begins, unconventionally, in the second act of the story—is Quentin's search for his friend Margo, who has gone missing. Quentin and his friends go on a quest to find her using clues that she had left behind. They succeed, but, rather than being ecstatic to see them again, Margo is surprised and insists on staying behind instead of returning home with them. This conflict can thus be considered ultimately unresolved.
The internal conflict revolves around Quentin and his love for an idealized version of Margo that exists only in his mind. Throughout the novel, which is narrated from Quentin's point of view, Margo is consistently described in romanticized terms. However, upon her disappearance, Quentin is forced to confront the fact that the real Margo may not live up to the perfect image of her that he has conjured for himself. This is further confirmed when Quentin gets angry at Margo for not wanting to return home with him and his friends, and Margo immediately retorts that he did not chase after her in order to help her, but rather in order to be the knight in shining armor who saves the troubled damsel and wins her heart in the end. Margo's running away forces Quentin to reconcile the Margo from the night during which they executed her revenge plan and the Margo who simply wanted to disappear into a town that existed only on paper. This conflict is resolved when Quentin comes to terms with the fact that he had idealized Margo, and the two of them part on civil terms at last.
There are multiple conflicts and resolutions in this psychologically oriented action story. Nonetheless, the main conflict and resolution are Quentin's quest, with friends, for Margo after her night of revenge and their journey through the clues left in Whitman's Leaves of Grass.
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