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In the story The Red Headed League Sherlock Holmes has been told the remarkable story of the League and done some initial research.

Back at Baker Street, he needs time to think hard about the mystery and says to Watson, "It is quite a three pipe problem, and I beg that you won't speak to me for fifty minutes."

In other words, he needs the time it takes to smoke three pipes in order to solve the mystery.

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Q: What does Holmes mean when he says it's a three pipe problem?
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