(from the back of the book)

Aunt Eloise Drew invites Nancy, Bess, and George to New York to help a friend who has been swindled out of a sizalbe sum of money. There the girls see a performance of the Hoaxters, a magicians' group, who stun their audiences by clever sleight of hand tricks. Because the magicians temporarily remove people's wallets and handbags, Nancy feels the actors aren't above suspicion. Her hunch is borne out and a whirlwind chase ensues.
Nancy, Bess, and George track the Hoaxters to Mexico city, where Nancy is asked to help find a kidnapped child. The young sleuths follow a lead to Los Angeles where danger confront them at every turn. Their enemies resort to theft - even arson - to scare them off the case.