Dr. Jake Wexler is a forty-five-year-old podiatrist who is seemingly happy and content with life. Underneath his mask of happiness, humor, and wit, however, he's just a man in need of some attention and excitement in life; he wants to do something more than just be a foot doctor, and his obnoxious wife only fuels this desire, as she often ridicules his profession. Thus, he decides to try gambling and becomes a bookie, or a bookmaker.

Madame Sun Lin Hoo is a twenty-eight-year-old Chinese woman who is married to the fifty-year-old restaurant owner James Shin Hoo and wishes to move back to China. Madame Hoo struggles with the English language and doesn't have anyone to help her learn it—she doesn't have any close friends, and her acquaintances tend to ignore her. Thus, she becomes a burglar and steals valuable objects from people in order to feel some connection to them.

The twenty-year-old Angela Wexler is Dr. Jake Wexler's eldest daughter. From the very start, it becomes clear that her pretentious mother, Grace, favors her over her sister, Turtle, as she's the classic "perfect child"—she's beautiful, privileged, and engaged to a surgeon. However, Angela doesn't want to be perfect and she doesn't want to get married so young; she wishes to become a doctor herself and wants people to acknowledge her character, skills, and intelligence, not just her beauty. Angry and desperate, she decides to set off bombs in order to change the way everyone perceives her and to take back control of her life. Angela Wexler is the bomber.

Finally, Sydelle Pulaski is the mistake, as she was accidentally invited to participate in the Westing Game and to be a tenant of Sunset Towers and a potential heir of Sam Westing instead of Sybil Pulaski.

Ellen Raskin's rather humorous mystery novel centers on sixteen "heirs" to a fortune who must discover the murderer of Sam Westing, an industry magnate. In order to do so, they must play the mysterious Westing game and determine the culprit in order to win a huge inheritance.

Before the so-called heirs are convened, these tenants of the Sunset Towers--which ironically face East--have been sold apartments by Barney Northrup. The narrator describes the "specially selected tenants" as 

A dressmaker, a secretary, an inventor, a doctor, a judge. And, oh yes, one was a bookie, one was a burglar, one was a bomber, and one was a mistake. Barney Northrup had rented one of the apartments to the wrong person.

• The bookie is Dr. Wexler, the podiatrist, who becomes fixated on gambling.
• The burglar is Mrs. Hoo, the second wife of the restaranteur who pilfers in order to save enough to return to China.
• The bomber is Angela Wexler who sets a bomb on herself, perhaps, to mar her beauty so that others will perceive her in more than a superficial way.
• The mistake is Sydelle Pulaski. She is a mistake because it was Sybil Pulaski that the private investigator Otis Amber was to have selected;...