Ilyusha is the nine-year-old son of Captain Snegiryov, whom Mitya humiliated; Kolya is the older schoolmate who protected him at school and later abandoned him out of pride. The two occupy Book X and the Epilogue and give the novel its most moving scene.
Ilyusha first appears in Book IV, with stones in hand, throwing them at Alyosha because he is a Karamazov, and biting his finger to the bone. He had seen his father, the captain, dragged by the beard across the square. When Alyosha asks him what he did to him, the boy cries and runs away. He falls ill, and the father tramples the money Katerina Ivanovna sent and shouts that his honor is not for sale; the reason he gives, with his back turned, is his son: what would he tell the boy?
Kolya arrives in Book X at thirteen, with a collection of second-hand ideas, a dog trained in secret, Perezvon, and an enormous fear of looking ridiculous. Alyosha does not refute him: he names the evil, self-love, and treats him as an equal, and Kolya confesses that he is deeply unhappy. Ilyusha dies asking his father to bury him beside the large stone where they used to walk, and at his death he asks the boys to stay with his father.
In the Epilogue, the funeral brings together twelve boys, the broken captain and Alyosha. The request for bread for the sparrows and the boys' promise never to forget their friend are the book's answer to Ivan's question about the price of a child's suffering, not a refutation.