1. The Land of Truthtellers and Liars

• Stephanie: The total number of true statements is even.
• Terence: The number of functions from a set with N elements to itself is N! .
• Parker: At least one of Stephanie and Terence is telling the truth.
• Ellen: There are infinitely many solutions to the equation x^n + y^n = z^n, where x, y, z, and n are positive integers.
• Rachel: K_5, the complete graph on five vertices, can be drawn in the plane without any edges crossing.
• Quincy: Rachel and Iphigenia are both telling the truth.
• Umberto: At least one of Ellen and Laura is lying.
• Laura: The truth of this statement is the same as the truth of Maxim's statement.
• Danielle: Nelly, Sam, and I are all equally honest.
• Imogen: The regular 17-gon can be constructed using a compass and straightedge.
• Franz: Any abelian group is isomorphic to a product of cyclic groups.
• Ichabod: Ari was born with an extra toe on his left foot.
• Maxim: At least one of Oliver and Stanley is telling the truth.
• Irving: Tarquin and Engelbert are both lying.
• Phineas: The number of truthtellers whose names begin with vowels is odd.
• Engelbert: Irving and Abby are both lying.
• Norbert: 1234567 and 7654321 are relatively prime.
• Stanley: Laura and I are both lying.
• Abby: At least one of Umberto and Oliver is telling the truth.
• Hildegard: This statement is true if and only if Ichabod is lying.
• Thaddeus: Exactly one of Norbert and Ichabod is lying.
• Elmer: The surface obtained by gluing together two Mobius strips along their boundaries is a projective plane.
• Iphigenia: 99999999^59 is congruent to 99999999 mod 59.
• Sam: The set of infinite sequences of integers has the same cardinality as the set of polynomials in one variable with rational coefficients.
• Oliver: Noah's father was named 'most likely in his class to end up selling hotdogs at Cleveland stadium'.
• Nelly: Hildegard and Franz both made false statements.
• Tarquin: Every continuous real-valued function on R is differentiable at all but countably many points.