First thing to know about larceny by trick is that it is a subset of larceny. If you see a larceny by trick, and the question asks whether there is a larceny, the answer is yes.
Larceny by trick occurs when possession of another's personal property is gained by means of a promise or statement the defendant knows to be false at the time it is made.
If you ask to borrow something, but intend to keep it, that's a larceny by trick. Same goes for taking out a loan you do not intend to repay.
If you borrow something with the intent of returning it, but later change your mind and decide to keep it, there's still a larceny, but not larceny by trick.
If you enter into a riddle contest to determine ownership of a disputed item, and ask an unfair riddle (ie: a riddle that cannot be answered), thereby gaining possession of the item, you have committed a larceny by trick. However, if you ask something that is simply not a riddle at all, and the other party answers it incorrectly, by answering it at all, the other party has given up any right to object to the question, and no larceny has been committed. The other party could object to the question and force a disqualification, but not after attempting to answer.