In "The Red Headed League," Sherlock Holmes is presented with a complex case that demands his complete focus. The phrase "It is quite a three pipe problem" signifies the intricacy of the situation at hand, indicating that it will require deep contemplation and extensive smoking of his signature pipe to unravel the mystery. Holmes requests not to be disturbed for fifty minutes, highlighting his need for solitude to process the information and come up with a solution.

This moment emphasizes Holmes's methodical approach to problem-solving, where he immerses himself in thought to connect disparate clues. The story showcases his deductive reasoning and fierce dedication to his work, underscoring the intellectual challenge he willingly embraces. The quote encapsulates the essence of the detective's mind, which thrives on complexity and cultivates a unique atmosphere conducive to significant discoveries.