They meet a twelve-sided creature called the Dodecahedron, who leads them to Digitopolis, where they meet the Mathemagician, who is still angry at Azaz, and who will not give his blessing to anything that his brother has approved. Milo maneuvers him into saying he will permit the quest if the boy can show the two have concurred on anything since they banished the princesses. To the number wizard's shock, Milo proves that the two have agreed to disagree, and the Mathemagician gives his reluctant consent.