The Invisible Host — Gwen Bristow

Eight people received the invitation. A beautiful society queen. A famous professor. A powerful business tycoon. A brilliant playwright. A renowned woman lawyer. An eminent politician. An ardent youthful radical. A glamorous stage and screen star. All arrived at the fabulous penthouse suite prepared for a memorable evening.

The evening was memorable indeed. Soon they discovered that they were prisoners in this place, and that their mysterious host would kill them one by one unless they could solve his riddles. All eight guests suddenly realized that they had a companion. The ninth guest was death...

The book was first published as THE INVISIBLE HOST by Bristow and her husband, Bruce Manning in 1930. It was made into the 1934 movie, THE NINTH GUEST, with the script by Bristow, Manning, Owen Davis and Garnett Weston.

I've found THE NINTH GUEST (1932) published under the name of one of the other screenwriters, Owen Davis. I'm not sure how this fits into the scheme of things. The only dated Bristow/Manning copies with this title I've seen online are from 1957.