self Maths Puzzle

A boy and a girl are talking.

"I am a boy" - said the child with black hair.

"I am a girl" - said the child with white hair.

At least one of them lied. Who is the boy and who is the girl?

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self Other Question

There are five gears connected in a row, the first one is connected to the second one, the second one is connected to the third one, and so on. If the first gear is rotating clockwise what direction is the fifth gear turning? There are three people (Alex, Brook and Cody), one of whom is a knight, one a knave, and one a spy.

The knight always tells the truth, the knave always lies, and the spy can either lie or tell the truth.

Alex says: "Cody is a knave."
Brook says: "Alex is a knight."
Cody says: "I am the spy."

Who is the knight, who the knave, and who the spy?