IN THE LAND OF CONFUSION (This is a LOGIC problem) (Not a collage placement question) (Sorry about that)

All the people in the Land of Confusion are either sages or jesters. Sages are noted for their honesty - they always tell the truth. Jesters, however, are always kidding around and never tell the truth. Unfortunately, there is no way to tell one from the other just by looking at them. Ima Visitor leaves her home in the Enchanted Kingdom and travels to the Land of Confusion. While there, she meets three men: Xavier, Yale and Zachary. Ima asks, “How many of you are sages?”

Xavier says that he is not a jester.

Yale says that Xavier is lying.

Zachary adds, “Yale is lying.”

Can you figure out who is a sage and who is a jester?

Two kids in the Land of Confusion

Ima keeps on walking. Just as she approaches the emperor’s palace, she finds a boy and a girl sitting on the steps, and hears three statements:

“I’m a boy,” says the child with black hair.

“I’m a girl”, says the child with red hair.

“Exactly one of us is a sage,” says the boy.

Are the boy and girl sages and/or jesters, and what color hair does each one have?

A Boast?

Upon entering the emperor’s palace, Ima overheard a man say, “If I am a sage, then so is my son.”

What can you tell about him or his son?

Meeting the King Inside the palace, Ima went looking for the King, and she met some sages. She asked them if the King is a sage or a jester, and they told her that they didn’t know, but that according to their laws, he must be a citizen of the Land of Confusion, either a sage or a jester. Just then, a man entered the hall wearing a crown and a beautiful purple cloak. The sages told Ima that it was the King, and that she could ask him whether he was a sage or a jester. To her question, the King responded, “I am a jester.” Immediately, the sages cried “Imposter! Arrest that man!”

Why?