Vengeance in Death question

There used to be paperback books which were fully-fledged contemporary murder-mystery stories (corpses, clues, etc) and the gimmick was that the solution was not provided at the end of the book! You read to the end, and then scratched your head and put together the solution yourself, typed it up, then mailed it in to the publisher. There were prizes of (as much as) $5,000.

Does anyone remember the names of these kind of books? Publishing companies?

I recall one I read which was based on a Halloween-party murder; it was a girl as the lead character, told in first-person singular; and the book follows her along as she gradually realizes which one of her friends is a murderer.

Thanks in advance.