The following problems require reasoning for their solution. To prove that an answer is correct requires an argument (often containing subsidiary arguments) whose premises are contained in the statement of the problem—and whose final conclusion is the answer to it. If the answer is correct, it is possible to construct a valid argument proving it. In working these problems, readers are urged to concern themselves not merely with discovering the answers but also with formulating arguments to prove that those answers are correct.

Benno Torelli, genial host at Miami’s most exclusive nightclub, was shot and killed by a racketeer gang because he fell behind in his protection payments. After considerable effort on the part of the police, five suspects were brought before the district attorney, who asked them what they had to say for themselves. Each of them made three statements, two true and one false. Their statements were Lefty: I did not kill Torelli. I never owned a revolver in all my life. Spike did it.

Red: I did not kill Torelli. I never owned a revolver. The others are all passing the buck.
Dopey: I am innocent. I never saw Butch before. Spike is guilty.

Spike: I am innocent. Butch is the guilty one. Lefty did not tell the truth when he said I did it.
Butch: I did not kill Torelli. Red is the guilty one. Dopey and I are old pals. Whodunnit?