Seven Keys to Baldpate by Earl Derr Biggers

Baldpate Inn has a mystery and seven keys. The novelist has one. The other six fall into the hands of six apparent lunatics: 1. a hermit who flees from barbers and women has a key, 2. a peroxide blonde who "just loves" men has a key, 3. a college professor who has been laughed out of his job has a key, 4. a political "boss" who eats cigars has a key, 5. a Belle of High Sociétée has a key and, 6. a bold, bad clubman has a key.