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Jim Fox was carrying an orange umbrella. The suspect who has no hair was carrying an orange umbrella. Therefore, Jim Fox has no hair. The murderer has red hair, so Jim Fox is not the murderer.
The suspect who has red hair was wearing a red shirt. The suspect who was carrying a purple umbrella was wearing a red shirt. The suspect who was carrying a purple umbrella was wearing black shoes. Therefore, one suspect was wearing a red shirt, has red hair, was carrying a purple umbrella, and was wearing black shoes. But Bill Graig was wearing a blue shirt, Marty Morrison was wearing red shoes, John Brown was carrying a green umbrella, and Jim Fox has no hair. Therefore, the only suspect who could be this suspect is Larry Smith. Since this suspect, Larry Smith, has red hair and the murderer has red hair, he is the murderer.

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